# Interpreting SIGNs.

The rich variety of securities innovations in recent years continues
to intrigue academicians and practitioners alike.(1) The array of
innovative securities includes a variety of equity-linked debt
securities, some of which base the equity component of the security on
the share price of a single corporation and others of which base it on
the value of a particular stock index, such as the Standard &
Poor's 500 Index (the "S&P 500"). McConnell and
Schwartz |13~ analyze an example of corporate-equity-linked debt, called
LYONs (liquid yield option notes), which takes the form of a corporate
zero coupon convertible bond that incorporates both call option and put
option features. Chance and Broughton |3~ and Chen and Kensinger |4~
analyze equity-linked certificates of deposit. Chen and Sears |5~
analyze an example of stock-index-linked debt, called SPINs (Standard
& Poor's 500 Index subordinated notes), which takes the form of
a coupon-bearing note with the principal repayment linked to the S&P
500. They decompose SPINs into debt and equity components, develop a
valuation methodology, and demonstrate that the prices produced by their
model closely track the observed market prices of the SPINs. This paper
deals with a recently introduced security that closely resembles the
SPINs: a zero coupon note with the single payment linked to the S&P
500. I employ a valuation methodology similar to Chen and Sears's
to try to answer the question: To what extent are S&P 500-linked
notes truly innovative?

On January 28, 1991, the Republic of Austria publicly offered $100 million principal amount of stock index growth notes ("SIGNs") in the United States |16~. The issuance of SIGNs raises a number of interesting issues, such as: (i) why would the Republic of Austria issue equity-linked notes whose contingent return is tied to the appreciation in the value of an American share price index, and (ii) is the security innovative in the sense that it represents an investment vehicle whose after-tax and after-transaction-cost returns investors could not duplicate more cheaply with financial instruments already in existence, and if so, what factors are responsible for the net benefit?

I. Description of SIGNs

The SIGNs mature in approximately 5.5 years and make no payments of interest prior to maturity. The prospectus for the SIGNs |16~ describes them as contingent interest notes. The single interest payment, payable at maturity, is equal to the greater of zero and

10 ||P.sub.m~ - 336.69/336.69~

where |P.sub.m~ denotes the average closing value of the S&P 500 for the 30 business days immediately preceding the second business day prior to the maturity date. The initial offering price was $10 per SIGN. If the value of the S&P 500 is below 336.69 on the maturity date, the holder receives $10. If the value exceeds 336.69, the holder gets $10 plus $10 multiplied by the percentage appreciation in the S&P 500 above 336.69. Also, the SIGNs are not redeemable by either the issuer or the holders prior to their scheduled maturity date. The SIGNs were marketed principally to retail investors, and they are listed on the New York Stock Exchange.(2) The financial press reports the daily prices of the SIGNs among the prices of common stocks traded on the New York Stock Exchange.

A. Characterization of SIGNs

SIGNS may be characterized as a package consisting of (i) a 5.5-year zero coupon note, plus (ii) a 5.5-year European call option, or warrant, on the S&P 500 with a strike price of 336.69. Exhibit 1 illustrates this interpretation. The SIGNs were offered for sale on Monday, January 28, 1991. The closing value of the S&P 500 the preceding business day, Friday, January 25, 1991, was 336.07. The call option was approximately at-the-money on the issue date because the strike price is 336.69. The outstanding debt of the Republic of Austria is rated Aaa by Moody's Investors Service and AAA by Standard & Poor's Corporation. Thus, a close substitute for SIGNs that is available to investors is a unit consisting of zero coupon Treasury securities (called Treasury strips), which are readily available in the capital market, and call options on the S&P 500, which are traded on the Chicago Board of Options Exchange. The Treasury strips involve zero default risk; however, the degree of default risk associated with Republic of Austria securities is slight due to the triple-A rating. The call option imbedded in the SIGNs is European-type just like the exchange-traded call options on the S&P 500.

B. Taxation of SIGNs(3)

The prospectus for the SIGNs suggests that they will be taxed as so-called contingent interest notes |16, p. S-13~. The prospectus notes that the Internal Revenue Service had not yet published final regulations governing the tax treatment of contingent interest notes. The proposed contingent interest regulations then outstanding were based on the premise that when the amount of interest that will ultimately be payable is contingent on the future value of an index or some other future event, the tax liability can not be determined until the amount of interest can be established with a reasonable degree of certainty. Because of the risk that the S&P 500 could decline below the strike price of the call option embedded in the SIGNs right up to the SIGNs' maturity date, the amount of interest payable cannot be conclusively determined until the maturity date. Consequently, interest on the SIGNs would not be taxable until the maturity date.

If the SIGNs were instead taxed as a unit consisting of a zero coupon note plus a long-dated call option, each component would be taxed separately. Under the original issue discount rules, the interest implicit in the amortization of the discount on the zero coupon bond component of the SIGNs would be taxed annually over the life of the instrument. Since the embedded call option is not exchange-traded, the call option component of the SIGNs would not be taxed on an annual basis under the mark-to-market rules that apply to exchange-traded options. Thus the tax treatment of the returns is potentially more favorable to investors under the contingent-interest-note interpretation of SIGNs than under the zero-coupon-note-with-call-option financial interpretation and may be much more favorable than the alternative of buying a Treasury strip and exchange-traded S&P 500 call options. On February 28, 1991, the Internal Revenue Service published proposed regulations |15~ under which any SIGNs issued on or after February 20, 1991, would be taxed in accordance with the zero-coupon-note-with-call-option interpretation of SIGNs. The proposed regulations do not affect the Republic of Austria SIGNs because they were issued prior to the February 20th effective date.(4)

The tax discussion in the SIGNs prospectus suggests a possible motivation behind the creation of SIGNs: tax arbitrage. To the extent contingent-interest tax treatment would defer income taxes that would be payable by taxable investors if the issuer sold a package consisting of a zero coupon note together with a call option on the S&P 500, a tax arbitrage could result if the issuer pays income taxes at a lower rate than investors. The Republic of Austria is not taxable (in the United States or anywhere else) and so the timing of any potential interest tax deductions is of no consequence to it. But the deferral of income taxes would be valuable to taxable investors who purchase the Republic of Austria SIGNs. Even though the recently proposed Internal Revenue Service regulations would reduce the magnitude of the gain from tax arbitrage in the future, SIGNs still enjoy a tax advantage vis-a-vis the alternative of purchasing a Treasury strip and exchange-traded S&P 500 options. In any case, investigating the magnitude of the tax arbitrage associated with the Republic of Austria SIGNs could yield some insight as to why the Republic of Austria SIGNs were issued.

C. SIGNs versus SPINs

The SIGNs closely resemble SPINs, a product Salomon Brothers Inc, developed more than six years ago. The SPINs paid a two percent rate of interest and a return at maturity that was contingent on the appreciation in the S&P 500 between the date of issue and the maturity date |18~. That issue was designed for institutional investors but press reports suggested that it met with investor resistance.(5) There were no subsequent issues of SPINs. Chen and Sears |5~ analyze SPINs and show that when the bond and call option components are valued separately and the values added, the resulting valuations closely track the market values of the SPINs, at least after an initial seasoning period and before the stock market crash in October 1987.

Since the SPINs were issued, there have been several other issues of equity-indexed notes sold in the European capital markets. Such notes have been issued with equity-contingent returns based on the FT-SE 100 (London) stock market index, CAC 40 (Paris) index, DAX (Frankfurt) index, and Nikkei 225 (Tokyo) index, and possibly on other stock market indexes as well. The method of analysis developed in this paper could be applied to these other equity-linked debt instruments.

II. Valuation of SIGNs

SIGNs can be valued relative to a comparable package consisting of a triple-A-rated 5.5-year zero coupon note plus an (approximately) at-the-money 5.5-year European call option on the S&P 500. The true value of each SIGN, denoted V, can be expressed as

V = B + C + T + E + R (1)

where

B = Value of the zero coupon bond component;

C = Value of the call option component;

T = Value resulting from tax arbitrage, if any;

E = Reduction, if any, in transaction costs vis-a-vis acquiring a comparable zero coupon bond and purchasing call options on the S&P 500 separately (or dynamically replicating the call option component); and

R = Value, if any, attributable to creating an investment alternative that is not otherwise available to the investors who purchased the SIGNs.

If a new security gives rise to risk-return combinations that investors could not have achieved previously, either due to market incompleteness or due to market imperfections that precluded certain investors from achieving the risk-return combinations the new security provides, for example, due to the indivisibility of exchange-traded options, then R |is greater than~ 0. If the new security reduces taxes or transaction costs, as compared to previously existing investment vehicles that provide similar risk-return combinations before taxes and transaction costs, then T |is greater than~ 0 or E |is greater than~ 0, respectively.

Call options on the S&P 500 with a time to expiration of 5.5 years are not available on any of the options exchanges. In 1991, the Chicago Board of Options Exchange introduced a form of option it calls LEAPS (long-term equity anticipation securities), which have a longer time to expiration than exchange-traded options have traditionally had. LEAPS on the S&P 500 Index were introduced in January 1991 with two expiration months, December 1992 and December 1993 (roughly two years and three years from issue, respectively) |20~. The LEAPS on the S&P 500 are European-style. To date, trading has been thin.(6)

An investor who wished to duplicate the return stream of the SIGNs would have two basic choices for the call option component: (i) try to purchase a customized option in the over-the-counter market, which is generally limited to institutional investors entering into contracts with broker-dealers having face value of $1 million or more, or (ii) employ dynamic replication, which involves adjusting a portfolio consisting of risk-free securities and either the underlying stock (or in the case of stock index options, either the underlying stocks or stock index futures) or shorter-term options on the same underlying stock. The seminal paper by Black and Scholes |2~ develops their well-known option valuation model based on the premise that an investor can replicate exactly the returns to any stock option by forming correctly, and continuously adjusting, a portfolio consisting of the underlying stock and the risk-free asset. However, Leland |11~ points out that continuous rebalancing is impractical in the presence of nontrivial transaction costs and develops a technique for replicating option returns in the presence of transaction costs. An alternative replication strategy presented by Choie and Novomestky |6~ builds on the earlier work of Jones |10~ and involves replicating the distribution of possible prices for a long-term option at some future date by forming a portfolio consisting of risk-free securities and shorter-term options on the same underlying stock and then rolling over this portfolio at discrete intervals.

The SIGNs were sold in small denominations ($10 per SIGN) primarily to retail investors, who would not have had access to the over-the-counter market on account of the small transaction size. The second alternative, dynamic replication, would entail transaction costs as the replicating portfolio was rebalanced. Figlewski |7~ shows that a retail investor engaging in small transactions would find it prohibitively expensive to rebalance the replicating portfolio frequently. In each case he considered, the transaction costs involved in the dynamic replication strategy, with daily rebalancing, exceeded the initial price of the option--in some cases by as much as a factor of five. For at least some retail investors, then, dynamic replication would not be a viable alternative to investing in SIGNs.

A. Value of the Zero Coupon Bond Component

The Republic of Austria has a large number of outstanding issues of U.S.-dollar-denominated bonds, including one issue of zero coupon bonds maturing July 17, 1995, that trades in the Eurodollar bond market. On January 28, 1991, the 1995 zero coupon issue had a price of 70 3/8% per bond, which implies a yield to maturity of 8.05% per annum semiannually compounded.(7) Based on an 8.05% yield to maturity, on January 28, 1991. the zero coupon bond component of each SIGN was worth approximately B = 10/|(1 +0.0805/2).sup.11~ = $6.48.

B. Value of the Call Option Component

The call option component can be valued using the Black-Scholes model modified to account for dividend-paying stocks. This model rests on several important assumptions (see Black and Scholes |2~), such as perfect markets, constant short-term interest rate, and constant volatility of the stock price. To the extent these assumptions are not satisfied, the true value of the call option component could deviate from the calculated value.(8) However, Chen and Sears |5~ report that the Black-Scholes option pricing model produced satisfactory results when used to value the call option component of SPINs, whose initial time to expiration is close to the SIGNs' initial time to expiration.

The common stocks that comprise the S&P 500 were paying cash dividends at the rate of $11.10 per year as of January 28, 1991, implying a dividend yield at the annual rate of q = 11.10/336.07 = 3.30%. I assumed that dividends on the S&P 500 occur at a continuous rate, which seems reasonable in view of the large number of stocks that comprise the index. I used the following modified Black-Scholes model, initially developed by Merton |14~ and later applied to stock index options by Hull |9~, to value the call option component of the SIGNs:

C = S|e.sup.-qt~N(|d.sub.1~) - X|e.sup.-rt~N(|d.sub.2~) (2)

where

|d.sub.1~ = |ln(S/X) + (r - q + (||Sigma~.sup.2~/2))t~/||Sigma~|square root of t~;

|d.sub.2~ = |d.sub.1~ - |Sigma~|square root of t~;

S = Current value of the S&P 500;

X = Strike price;

t = Time to expiration;

r = Continuously compounded riskless rate;

q = Continuous annual dividend yield on the S&P 500 portfolio; and

|Sigma~ = Standard deviation of the rate of return on the S&P 500.

Following Chen and Sears, the riskless rate is proxied by the continuously compounded equivalent yield of the Treasury note that matures closest to the maturity date of the SIGNs. The closest maturing Treasury note is the 7 7/8% Treasury note due July 1996, which had a continuously compounded equivalent yield of 7.60% on January 28, 1991. An estimate for the volatility |Sigma~ was obtained by calculating the value of |Sigma~ implicit in the closing price on January 25, 1991, of the S&P 500 LEAPS call option expiring in December 1993 -- the only LEAPS call option quoted that day in the Wall Street Journal. This procedure yielded the estimate |Sigma~ = 17.98%.(9) Because calculating just a single implied volatility is potentially error-prone, I also estimated implied volatilities for S&P 500 options with a strike price of approximately 336.07 and obtained estimates for |Sigma~ between 16.95% and 19.02%, which seem consistent with the 17.98% estimate obtained from the December 1993 S&P 500 LEAPS contract.(10) I report the sensitivity of the value of the call option component to variation in |Sigma~ within this range later in the paper.

For the SIGNs, the strike price is X = $10, so it is necessary to rescale the S&P 500: S = 10(336.07/336.69) = $9.98. The riskless rate is r = 7.60%, q = 3.3%, |Sigma~ = 17.98%, and t = 5.5 years. The estimated value of the call option component of the SIGNs was obtained by substituting these parameter values into Equation (2) and solving for C = $2.30.

C. Value of the Tax Arbitrage

The value of the tax arbitrage created through the introduction of SIGNs equals the sum of (i) the tax benefit resulting from the investor's ability to defer income taxes on the amortization of the zero coupon bond component, plus (ii) the tax benefit resulting from the investor's ability to defer income taxes that would otherwise be incurred under the mark-to-market rules. Exhibit 2 shows the calculation of the period-by-period tax liabilities that an individual investor in the 31% tax bracket would incur on a freely traded zero coupon bond that matched the zero coupon bond component of the SIGNs. The present-value tax savings that result from the tax deferral on the zero coupon bond component, denoted |T.sub.1~, are equal to the difference between the present value of the tax liabilities given in Exhibit 2 and the present value of the deferred tax liability on the zero coupon bond component of the SIGN:

|Mathematical Expression Omitted~

In Equation (3), |L.sub.1~(t) denotes the tax liability calculated for period t in Exhibit 2. This stream of tax liabilities is discounted at the average after-tax yield at which coupon-bearing Republic of Austria debt maturing in approximately 5.5 years was trading on January 28, 1991.(11) The single tax liability that would be owing at maturity under the contingent-interest tax treatment is discounted at the after-tax yield on the outstanding Republic of Austria zero coupon debt issue.

Note that if the S&P 500 is less than 336.69 when the SIGNs mature, the SIGNs holders get a tax deduction for the portion of the $10 public offering price that must be TABULAR DATA OMITTED allocated to the embedded call option (i.e., the premium they implicitly paid for the embedded call option, which equals the $10 public offering price minus the $6.48 value allocated to the zero coupon bond component). So |T.sub.1~ approximates the minimum present-value tax liability that a taxable investor would incur under the new proposed Internal Revenue Service regulations issued February 28, 1991, as a result of investing in SIGNs and holding each SIGN until it matures. The approximation is due to the fact that under current tax law (as discussed below), the tax rate on option gains or losses is 29.2% for individual investors in the peak (i.e., 31%) tax bracket.

The value of the tax deferral on the call option component equals the difference between the present value of the tax liabilities the investor would owe under the mark-to-market tax treatment that applies to exchange-traded options and the present value of the deferred tax liability on the call option component. Both present values will depend on the behavior of the S&P 500 over the life of the SIGNs, which is unpredictable due to the random nature of share price movements.

Exhibit 3 provides a very crude estimate of the expected value of the tax deferral on the call option component under the following assumptions. Ibbotson Associates |21~ has calculated an arithmetic mean total rate of return for the S&P 500 of 12.4% per annum for the period 1926-1989. The calculation of the value of the call option component assumed a 3.3% annual dividend yield. I continue to make this assumption for the sake of consistency. The difference between the 12.4% total return and the 3.3% dividend yield implies an expected rate of capital appreciation for the S&P 500 of 9.1% per annum, which I use for the purpose of the approximate tax calculation. I report the sensitivity of the value of the tax arbitrage to variation in the average annual rate of appreciation in the S&P 500 later in the paper. In Exhibit 3, I assume a 9.1% rate of appreciation in the S&P 500 for each year until the Republic of Austria SIGNs mature. I also assume in Exhibit 3 that the tax liability is calculated and promptly paid each December 31st. The estimated values for the embedded call option were obtained by applying Equation (2) with the parameter values given in Exhibit 3. Assuming a 9.1% annual rate of appreciation, the present-value tax savings that result from the tax deferral on the call option component, denoted |T.sub.2~, is(12)

|Mathematical Expression Omitted~

The stream of tax liabilities |L.sub.2~(t) in Equation (4) that would arise under the mark-to-market tax rules is taken from Exhibit 3. The second term on the right-hand side of Equation (4) represents the present value of the deferred tax liability on the gain on the call option embedded in the SIGN when the S&P 500 appreciates at a 9.1% annual rate. The tax rate is 29.2% because, under current tax law, 60% of the gain or loss on an investment in options is taxed as long-term gain or loss (currently taxed at a 28% peak individual rate) and the remaining 40% is taxed as short-term gain or loss (currently taxed at a 31% peak individual rate), for a blended rate of 29.2% (= 0.6|28~ + 0.4|31~).

The total value of the tax arbitrage created by the SIGNs, based on a 9.1% annual rate of appreciation, is T = |T.sub.1~ + |T.sub.2~ = $0.11 + 0.09 = $0.20 per SIGN, or roughly two percent of the public offering price per SIGN.

Under the new proposed tax regulations, future issues of SIGNs would benefit only from the tax arbitrage on the call option component. The new proposed regulations, which would require investors to pay tax on the zero coupon bond component each year as the discount amortizes, would cut the tax arbitrage benefit roughly in half (from 2.0% to 0.9% of the value of each SIGN).

D. Value of the Reduction in Transaction Costs

The underwriting discount for the SIGNs amounted to $0.50 per SIGN, which the issuer, the Republic of Austria, paid out of its gross proceeds. For purposes of analyzing the impact of the creation of SIGNs on the transaction costs an investor would incur, I compare the relative transaction costs associated with (i) purchasing 1,000 SIGNs, which would have cost $10,000, and (ii) purchasing a Treasury strip with $10,000 principal amount and a portfolio that replicates the call option component of each SIGN. The expected transaction costs associated with a dynamic replication strategy are difficult to estimate. They depend importantly on such factors as the frequency with which the replicating portfolio is rebalanced, the average size of the rebalancing transactions (due to the economies of scale in securities transactions), and the class of investor involved (see Figlewski |7~). Building on the work of Leland |11~, Swidler and Diltz |22~ estimate that the after-tax transaction costs involved in dynamically replicating long-dated call options, called Scores, varied between 1.3% and 4.2% of the Score's price. For comparative purposes, I also estimated the transaction costs associated with rolling over a series of shorter-dated S&P 500 call option contracts.

The estimated value of the call option component is $2.30. If the dynamic replication transaction costs are between 1.3% and 4.2% of this estimated value, they amount to between $0.03 and $0.10 per SIGN. These estimates will tend to understate the transaction costs associated with dynamically replicating a 5.5-year call option on the S&P 500 if the Scores in Swidler and Diltz's sample had times to expiration less than 5.5 years (which they may have) because longer-dated options are more costly to replicate dynamically (see Leland |11~ and Swidler and Diltz |22~).

Next, I consider the rollover alternative. Simply rolling over shorter-dated options will not replicate a longer-dated option's return stream; such a strategy is riskier than purchasing the longer-dated option. I consider the rollover alternative in order to gauge the reasonableness of the $0.03 to $0.10 estimated transaction costs for dynamic replication. Each S&P 500 LEAPS contract represents 100 options. The strike price equals the value of the S&P 500 divided by 10. In contrast, the standard S&P 500 index options contracts, which also represent 100 options, have a strike price equal to the value of the S&P 500. Thus, the S&P 500 contract with strike price 335 and expiring February 1991 has an aggregate strike price of $33,500. The S&P 500 LEAPS contract with strike price 35 and expiring December 1993 has an aggregate strike price of $3,500. Consequently, an investor with $10,000 to invest could purchase either 1,000 SIGNs or one Treasury strip plus three S&P 500 LEAPS contracts but could not use standard S&P 500 option contracts for this purpose because they are not divisible.

The commission on three S&P 500 LEAPs contracts amounts to approximately 3.76% of the market value of the contract.(13) The following calculation leads to a rough estimate of the transaction cost savings that would result, net of investor taxes at a 31% rate, from the introduction of SIGNs. The call option component of the SIGNs was valued at $2.30. Applying the 3.76% commission rate to the $2.30 market value of the embedded call option gives $0.086 per SIGN. The transaction cost is added to the investor's tax basis in the option contract, and the associated tax shield is realized at the time the option is sold or expires (through the decrease in gain or increase in loss for tax purposes, which is equal to the amount of the transaction cost added to the investor's tax basis). If it is assumed that the alternative to buying 1,000 SIGNs is to purchase a unit consisting of one Treasury strip and LEAPS contracts with an equivalent value of $2.30 (per SIGN) that would be rolled over at the end of three years, then the investor's present-value after-tax transaction costs associated with purchasing the LEAPS contracts, denoted |E.sub.1~, would amount to roughly

|Mathematical Expression Omitted~

assuming a 31% investor tax rate and a discount rate equal to the average after-tax yield to an individual investor at which Republic of Austria bonds maturing in approximately 5.5 years were trading. This value exceeds the $0.03 to $0.10 transaction cost range estimated earlier, which I noted might understate the cost of replicating a 5.5-year option. Accordingly, to be conservative, I use the $0.12 cost estimate in the balance of the paper.

The approximate transaction cost associated with purchasing a Treasury strip is $50 per $10,000 principal amount, or 0.5% of the principal amount. Each SIGN has principal amount of $10, implying a proportionate commission of $0.05, assuming the investor purchased 1,000 SIGNs. This cost would be amortized for tax purposes over the 5.5-year life of the SIGNs so that the present-value after-tax cost, denoted |E.sub.2~, is

|Mathematical Expression Omitted~

Purchasers of SIGNs in the secondary market would pay a transaction cost of $32 per round lot (100 SIGNs), or $0.32 per SIGN.(14) A purchaser of 1,000 SIGNs at $10 per SIGN would pay a transaction cost of $95, or $0.095 per SIGN. This cost is added to their tax basis, which generates a tax shield at the time the SIGNs are sold. There is an opportunity cost to the extent of the time value of money foregone. Assuming the purchase of 1,000 SIGNs, the present-value after-tax transaction cost, denoted |E.sub.s~, is |E.sub.s~ = $0,095|1-1/||1 + (1 - 0.31)0.0805/2~.sup.11~~ = $0.02 per SIGN, where I have discounted at the after-tax Republic of Austria zero coupon yield because the tax payment is assumed to be made at maturity.

The present-value after-tax transaction cost savings equals the difference between the present-value after-tax transaction costs associated with the Treasury-strip-with-LEAPS unit (|E.sub.1~ + |E.sub.2~) and the present-value after-tax transaction costs associated with the SIGNs (|E.sub.s~). The savings amount to E = |E.sub.1~ + |E.sub.2~ - |E.sub.s~ = $0.12 + 0.04 - 0.02 = $0.14 per SIGN, assuming a total investment of approximately $10,000 (i.e., 1,000 SIGNs). These savings are due to the relatively low cost of purchasing the call option when it is embedded in the SIGN.(15) Thus, the introduction of SIGNs permits investors to purchase options more cheaply than they could purchase exchange-traded options.

E. Value Potentially Attributable to Creation of a Longer-Dated Option

The creation of a new security can benefit investors if it reduces the impact of market imperfections or makes the capital markets more complete (see Van Horne |24~). As already noted, the returns generated by the 5.5-year call option component of the SIGNs can not be duplicated by rolling over a shorter-term position in either the standard S&P 500 option contract or the new S&P 500 LEAPS contract. Moreover, dynamic replication would be prohibitively expensive for at least some retail investors because of transaction costs. One of the potential sources of value attributable to the creation of the call option embedded in the SIGNs is the value to investors (principally retail investors) who desire a long-dated call option on the S&P 500 but cannot buy one in the over-the-counter market due to market imperfections, such as restricted market access, limitation on contract size, etc. SIGNs would potentially be even more valuable to those retail investors who would find it prohibitively expensive to dynamically replicate the long-dated call option because of transaction costs.

With the strike price of the S&P 500 option contract at 336.69, the standard contract size would be 100 times the index value, or $33,669, which corresponds to approximately 3,367 SIGNs based on the $10 public offering price. The minimum denomination for a Treasury strip is $10,000 principal amount, which corresponds to 1,000 SIGNs. An individual investor who wished to invest only a few thousand dollars would, of course, derive a benefit from SIGNs due to the indivisibility of both Treasury strips and standard S&P 500 option contracts. Only in this limited sense has the creation of SIGNs given rise to investment opportunities that did not previously exist. The benefit is due to market imperfections in the form of limited (small) investor access to the over-the-counter options markets, the indivisibility of exchange-traded options contracts, and the transaction costs retail investors would incur in implementing a dynamic replication strategy.

The new S&P 500 LEAPs contract has mitigated the impact of these imperfections in two ways: (i) the time to expiration of exchange-traded options has been extended, and (ii) the contract size is just one-tenth of the contract size for the standard S&P 500 options contracts. Nevertheless, the minimum size of a Treasury-strip-with-call-option transaction would involve buying $10,000 principal amount of Treasury strips, and SIGNs would permit even smaller (embedded) zero coupon bond purchases.

Returning to Equation (1), the SIGNs were sold to investors at a price of V = $10.00. I have estimated values for B, C, T, and E. Based on those values, Equation (1) implies a value for R, the value, if any, attributable to creating an investment alternative that is not otherwise available to the investors who purchased the SIGNs. From Equation (1), the implied value of R is

R = V - (B + C + T + E) = $10.00

- (6.48 + 2.30 + 0.20 + 0.14) = $0.88

for investors who could afford to purchase 1,000 SIGNs. For these investors, as well as for larger investors, SIGNs are inferior to the alternative of buying Treasury strips and S&P 500 call options, unless the value they attribute to being able to purchase a 5.5-year call option on the S&P 500 instead of having to replicate one dynamically is at least $0.88.

For investors who could not afford to purchase even 1,000 SIGNs, the tax savings T would still have value but because there is no close substitute for SIGNs, it is not meaningful to attribute any transaction cost savings to SIGNs in this case. For these investors, the implied value of R is

R = V - B - C - T = $10.00 - 6.48 - 2.30 - 0.20 = $1.02.

The value that might be attributable to reducing the impact of market imperfections, in particular, permitting smaller transactions to take place in S&P 500 call options, amounts to approximately $1.02 per SIGN, or 10.2% of the market value of each SIGN.

The estimated value for R was calculated as a residual based on the observed initial offering price V = $10.00 and the values estimated for B, C, T, and E. The estimated value of R will therefore include the effect of any mispricing that might have occurred. Chen and Sears |5~ found mispricing in the case of a similar financial instrument, SPINs, during the four-month period immediately following their issuance. I investigate the possibility of mispricing in Section IV.

III. Sensitivity Analysis

The upper panel of Exhibit 4 shows the sensitivity of the value of the call option component to the stock price volatility |Sigma~ and the dividend yield q. The volatilities implied in the S&P 500 call option prices on January 28, 1991, were between 16.95% and 19.02%. I used a somewhat wider range in Exhibit 4. The 3.3% dividend yield is toward the low end of the historical range. The dividend yield for the S&P 500 has typically been in the range from 3% to 6% |19~. Within the indicated ranges for |Sigma~ and q, the value of the embedded call option varies between $1.35 and $2.52. Adding the $6.48 value of the zero coupon bond component, the combined value of the debt and equity components of the SIGNs is between $7.83 and $9.00, significantly lower than the $10.00 price at which the Republic of Austria SIGNs were offered to investors.

The lower panel of Exhibit 4 indicates the sensitivity of the value of the tax arbitrage to different rates of S&P 500 appreciation based on the range of call option values calculated in the upper panel. The value of the tax arbitrage is sensitive to the appreciation rate but is not particularly sensitive to variation in |Sigma~ or q. The value of the tax arbitrage is between $0.14 and $0.40 per SIGN for annual appreciation rates between 6% and 18%. Adding the value of the tax arbitrage to the combined value of the debt and equity components of the SIGNs gives a range of $7.97 (= 7.83 + 0.14) to $9.40 (= 9.00 + 0.40), still significantly below the initial public offering price.

Based on the $10.00 initial public offering price, investors would have found it cheaper to buy a Treasury strip and dynamically replicate the 5.5-year call option, provided the present value of the after-tax transaction costs was less than $0.60 (= 10.00 - 9.40), which is more than four times the transaction cost savings I estimated. Nevertheless, Figlewski's |7~ results imply that at least for some retail investors, dynamic replication would not have been a cost effective alternative to the SIGNs. As noted at the beginning of the paper, the SIGNs were marketed principally to retail investors.

IV. Price Behavior of SIGNs in the Secondary Market

This section investigates the price behavior of SIGNs between their issuance and December 31, 1992. Chen and Sears |5~ found that SPINs went through a seasoning process. During the four months immediately following their issuance, the market price of the SPINs exceeded the price predicted by their model by between 4.93% and 5.86% (depending on which version of their model is used). Thereafter, the market price and the predicted price were within one percent of one another over a period of several months (until the October 1987 crash).

I used the model developed in this paper to estimate values for B, C, T, and E in Equation (1) for the last trading day of each month between February 1991 and December 1992. The 23 month-end values of B + C + T + E, together with the value $9.12 estimated as of the January 28, 1991 initial offering date, are plotted in Exhibit 5 along with the closing SIGNs price for each of those trading days. Data concerning Republic of Austria bond yields, Treasury yields, the value of the S&P 500, the annual dividend yield on the S&P 500 portfolio, the volatility of the rate of return on the S&P 500, and the price of the SIGNs were obtained from Bloomberg, L.P.

The predicted value of the SIGNs was 8.80% below the market price on January 28, 1991. At the end of February 1991, the predicted value was $9.84, which differed from the $10.00 market price by only 1.60%. At the end of March 1991, the predicted value was $10.03, which slightly exceeded the $10.00 market price. Thereafter, the predicted value and the market price approximate one another and fluctuate similarly. Over the February 1991-December 1992 period, the end-of-month predicted value exceeded the end-of-month market price by 2.03% on average.(16)

The price behavior of the SIGNs in relation to the predicted prices suggests that investors may have initially overvalued the SIGNs but that the mispricing was eliminated within roughly one to two months. However, an alternative explanation is also possible: Only a comparatively small number of investors placed a positive value on having investment opportunities previously unavailable to them because of option contract indivisibilities, and the demand for SIGNs from this source was fully satisfied in the initial offering and in the secondary market during the first two months of trading. In any case, the subsequent trading behavior of the SIGNs suggests that after the first two months of trading, R = 0, and hence that the value of the innovation should be attributed primarily to the value of the tax arbitrage it created (measured by T) and to the reduction in after-tax transaction costs it made possible (measured by E).

V. Measuring the Arbitrage Gain Realized by the Republic of Austria

The $0.50 underwriting discount per SIGN was paid by the Republic of Austria. The prospectus for the SIGNs disclosed that the Republic of Austria would use approximately 30% of the net proceeds of the SIGNs issue to hedge its contingent S&P 500 liability |16, p. S-5~. The net proceeds per SIGN amounted to $9.50. The cost of the hedge amounted to approximately $2.85 (= 0.3 x 9.50), leaving proceeds net of hedging costs amounting to $6.65. I calculated earlier that the bond component of each SIGN was worth $6.48. Hence, if the Republic of Austria could purchase a matching 5.5-year call option on the S&P 500 for $2.85, it would perfectly hedge its contingent liability and realize a riskless arbitrage profit of $0.17 (= 6.65 - 6.48) per SIGN. Put somewhat differently, the profit of $0.17 per SIGN would effectively reduce the Republic of Austria's cost of issuing 5.5-year zero coupon debt to r that solves

6.65 = 10/|(1 + (r/2)).sup.11~ r = 7.56% per annum

for a saving of 49 basis points per annum relative to the 8.05% per annum cost of a conventional zero coupon issue.

VI. Conclusions

The quick response by the Internal Revenue Service to the introduction of SIGNs reflects its concern about the potential for tax arbitrage. The Internal Revenue Service has become increasingly vigilant in recent years in trying to spot securities innovations whose principal rationale is tax arbitrage. In the case of SIGNs, the tax arbitrage represents approximately $0.20 per SIGN, or 2.0% of the value of each SIGN, and a total of $2.0 million for the entire Republic of Austria issue. The change in tax treatment, had it applied to the Republic of Austria issue, would have reduced the value of the tax arbitrage by approximately $1.1 million.

Returning to the two questions posed at the beginning of the paper: (i) the Republic of Austria issued SIGNs in order to take advantage of an opportunity to earn an arbitrage profit, and (ii) SIGNs were innovative in the sense that they gave rise to a tax arbitrage, enabled an investor to avoid the transaction costs associated with dynamically replicating a 5.5-year call option on the S&P 500, and created an opportunity for small investors to purchase long-term S&P 500 call options that is not otherwise available to them due to market imperfections. SIGNs also represent a good example of how a new security can yield attractive returns to an innovator who takes advantage of an opportunity to create a tax arbitrage or reduce the impact of market imperfections.

1 Finnerty |8~ and Tufano |23~ describe a range of securities innovations that typify the process of securities innovation.

2 Debt instruments sold in the United States typically have a principal amount of $1,000. The $10 denomination is designed to appeal to retail investors. While the issue was lead managed by Goldman Sachs & Co., the three co-managers, Dean Witter Reynolds Inc., Oppenheimer & Co., Inc., and A.G. Edwards & Sons. Inc., are all nationally recognized securities firms with a strong retail business (i.e., individual investors as opposed to financial institutions). Also, the underwriting spread was $0.50 per SIGN, or 5% of the public offering price, which is the size of spread typically observed in the equity market rather than in an institutional debt offering.

3 This section is based on discussions with tax consultants at Deloitte & Touche, New York, NY, and tax counsel at Howard, Darby & Levin, New York, NY.

4 As of April 16, 1993, the IRS still had not issued final regulations.

5 The preliminary prospectus specified a zero coupon issue. Press reports indicated that investors objected to the zero coupon structure. Salomon set a two percent coupon but raised the strike price of the embedded call option to compensate for the two percent coupon |18~.

6 As of December 31, 1992, total open interest in the S&P 500 LEAPS amounted to 20,692 call option contracts (versus 318,484 contracts for the standard S&P 500 call option) and 112,479 put option contracts (versus 396,804 contracts for the standard S&P 500 put option). The difference in dollar value of open interest is even greater because each LEAPS contract is based on one-tenth of the value of the S&P 500 whereas each standard S&P 500 contract is based on the full index value.

7 The bond price was obtained from Bloomberg, L.P., which obtains its pricing data from Merrill Lynch Capital Markets.

8 Prior studies have come to conflicting conclusions regarding the accuracy of Black-Scholes options pricing (see Black |1~, MacBeth and Merville |12~, and Rubinstein |17~).

9 The parameter values used in this estimation were S = 33.607, X = 35.00, t = 2.8904 years (to December 18, 1993), q = 0.033, r = 0.0722, and observed price = $4.75. Note that the S&P 500 LEAPS contracts are based on one-tenth of the value of the S&P 500.

10 The estimated implied volatilities by contract were 17.67% (February 1991 at 335), 19.02% (March 1991 at 335), 16.95% (February 1991 at 340), 18.57% (March 1991 at 340), and 18.84% (June 1991 at 340). I used the 17.98% estimate because the S&P 500 LEAPS contract expires much later than these other contracts and therefore seems more appropriate. Alternatively, I could have employed the implicit weighting scheme outlined by Whaley |25~ to weight the various implied volatilities, but using the simple estimate seemed more appropriate for the reason just given.

11 The Republic of Austria had three publicly traded coupon-bearing issues that were scheduled to mature around the time the SIGNs are scheduled to mature. These three issues and their yields to maturity on January 28, 1991, were: (i) 7 3/4% due May 8, 1996 yielding 8.54% per annum semiannually compounded, (ii) 7 3/4% due February 18, 1997 yielding 8.34%, and (iii) 9 1/4% due June 28, 1996 yielding 8.21%. All prices and yields were obtained from Bloomberg, L.P. The average of these three yields, 8.36%, was used to discount the stream of tax liabilities, |L.sub.1~(t), in Equation (3).

12 |T.sub.2~ is a random variable whose expected value depends upon the path-dependent values of the call option component of the SIGN. The expected value of |T.sub.2~ might be roughly estimated, for given expected return and volatility, in the following manner. The Black-Scholes option pricing model implicitly assumes a lognormal diffusion process. Given expected rate of return |Mu~ = 12.4%, volatility |Sigma~ = 17.98%, and continuous dividend yield q = 3.3%, the rate of share price appreciation for any time interval of length t will be distributed approximately normal with mean (|Mu~ - q)t and variance ||Sigma~.sup.2~t. The share prices and call option prices corresponding to the five rates of appreciation (|Mu~- q)t, (|Mu~- q)t|+ or -~|Sigma~|square root of t~ and (|Mu~ - q)t|+ or -~2|Sigma~|square root of t~ can be determined for each time t = 1, 2, 3, 4, 5 and 6 from this distribution. By approximating the normal distribution discretely and estimating |T.sub.2~ for each of the five rates of appreciation, I estimated the expected value of |T.sub.2~ to be approximately $0.09, the same value estimated by considering only the expected rate of share price appreciation (9.1% per annum). Details of the calculation are available from the author.

13 The estimated commission rates quoted in this paper were obtained from Pershing Securities, a subsidiary of Donaldson Lufkin & Jenrette. The commission on the three contracts is calculated as $35 plus 0.013 multiplied by the market value of the contracts, if the market value is under $3,000. The fractional component decreases for transaction sizes greater than $3,000. On January 28, 1991, the December 1993 LEAPS 35 contract was quoted at $4.75 per underlying option, implying a total market value of $475 per contract. The commission is $35 + 0.013(3)(475) = $53.53 for the three contracts, or 3.76% (= 53.53/1425) of the market value of the three contracts.

14 Calculated as $25 plus 7/10 of 1% of the value of the transaction.

15 If instead it is assumed that the investor would roll over a position in the standard six-month S&P 500 contract, the commission would amount to

approximately 2.75% of the value of the transaction for one contract. But each standard S&P 500 option contract has an aggregate strike price equal to 100 times the S&P 500. If it is assumed that the investor would be able to purchase sufficient SIGNs to obtain an aggregate call option component equivalent to one standard S&P 500 contract, then the 2.75% commission rate would be achievable. If the strike price of the S&P 500 contract is 335, for example, the investor would have to be able to purchase 3,350 SIGNs, at an aggregate cost of $33,500. Applying the 2.75% commission rate to the $2.30 market value of the embedded call option gives $0.063 per SIGN. The stream of after-tax transaction costs associated with rolling over the six-month options every six months has a present value of

|Mathematical Expression Omitted~

The transaction cost savings amount to E = $0.42 + 0.04 - 0.02 = $0.44 per SIGN, which represents 88% of the gross underwriting commission. In establishing the price at which to sell the SIGNs, the underwriters would presumably try to price the SIGNs so as to recover the underwriting spread from investors. If so, this analysis suggests that the underwriters of the Republic of Austria SIGNs issue viewed the rollover of standard S&P 500 option contracts, rather than S&P 500 LEAPS, as the most appropriate benchmark, perhaps because of the very thin trading to date in the S&P 500 LEAPS contracts.

16 The predicted value begins to exceed the market price persistently beginning in March 1992. For the 23-month period, February 1991 to December 1992, the 2.03% average differential is significant at the 0.05 level (t = 2.23).

References

1. F. Black. "Fact and Fantasy in the Use of Options," Financial Analysts Journal (July-August 1975), pp. 36-41, 61-72.

2. F. Black and M. Scholes, "The Pricing of Options and Corporate Liabilities," Journal of Political Economy (May-June 1973), pp. 637-654.

3. D.M. Chance and J.B. Broughton, "Market Index Depository Liabilities: Analysis, Interpretation, and Performance," Journal of Financial Services Research (December 1988), pp. 335-352.

4. A.H. Chen and J.W. Kensinger, "An Analysis of Market-Index Certificates of Deposit," Journal of Financial Services Research (July 1990), pp. 93-110.

5. K.C. Chen and R.S. Sears, "Pricing the SPIN," Financial Management (Summer 1990), pp. 36-47.

6. K.S. Choie and F. Novomestky, "Replication of Long-Term with Short-Term Options," Journal of Portfolio Management (Winter 1989), pp. 17-19.

7. S. Figlewski, "Options Arbitrage in Imperfect Markets," Journal of Finance (December 1989), pp. 1289-1311.

8. J.D. Finnerty, "Financial Engineering in Corporate Finance: An Overview," Financial Management (Winter 1988), pp. 14-33.

9. J. Hull, Options, Futures, and Other Derivative Securities, Englewood Cliffs, NJ, Prentice-Hall, 1989, Ch. 6.

10. E.P. Jones. "Option Arbitrage and Strategy with Large Price Changes," Journal of Financial Economics (March 1984), pp. 91-114.

11. H.E. Leland, "Option Pricing and Replication with Transactions Costs," Journal of Finance (December 1985), pp. 1283-1301.

12. J.D. MacBeth and L.J. Merville, "An Empirical Examination of the Black-Scholes Call Option Pricing Model," Journal of Finance (December 1979), pp. 1173-1186.

13. J.J. McConnell and E.S. Schwartz, "LYON Taming," Journal of Finance (July 1986), pp. 561-576.

14. R.C. Merton, "Theory of Rational Option Pricing," Bell Journal of Economics and Management Science (Spring 1973), pp. 141-183.

15. "Proposed Regulation 1.1275-4(g)," Standard Federal Tax Reports, Commerce Clearing House, February 28, 1991, p. 57,679-2.

16. Republic of Austria, Stock Index Growth Notes ("SIGNs") due August 15, 1996, prospectus, January 28, 1991.

17. M. Rubinstein, "Nonparametric Tests of Alternative Option Pricing Models Using All Reported Trades and Quotes on the 30 Most Active CBOE Option Classes from August 23, 1976 through August 31, 1978," Journal of Finance (June 1985), pp. 455-480.

18. Salomon Inc, 2% Standard & Poor's 500 Index Subordinated Notes, prospectus, August 21, 1986.

19. Security Price Index Record, New York, Standard & Poor's Corporation, 1990, p. 119.

20. "SPX LEAPS - Contract Specifications," Chicago, Chicago Board Options Exchange, 1990.

21. Stocks, Bonds, Bills, and Inflation: 1990 Yearbook, Chicago, Ibbotson Associates, 1990.

22. S. Swidler and J.D. Diltz, "Implied Volatilities and Transaction Costs." Journal of Financial and Quantitative Analysis (September 1992), pp. 437-447.

23. P. Tufano, "Financial Innovation and First-Mover Advantages," Journal of Financial Economics (December 1989), pp. 213-240.

24. J.C. Van Horne, "Of Financial Innovations and Excesses," Journal of Finance (July 1985), pp. 621-631.

25. R. Whaley, "Valuation of American Call Options on Dividend-Paying Stocks: Empirical Tests," Journal of Financial Economics (March 1982), pp. 29-58.

John D. Finnerty is a Professor of Finance at Fordham University and a General Partner with McFarland Dewey & Co., New York, New York.

On January 28, 1991, the Republic of Austria publicly offered $100 million principal amount of stock index growth notes ("SIGNs") in the United States |16~. The issuance of SIGNs raises a number of interesting issues, such as: (i) why would the Republic of Austria issue equity-linked notes whose contingent return is tied to the appreciation in the value of an American share price index, and (ii) is the security innovative in the sense that it represents an investment vehicle whose after-tax and after-transaction-cost returns investors could not duplicate more cheaply with financial instruments already in existence, and if so, what factors are responsible for the net benefit?

I. Description of SIGNs

The SIGNs mature in approximately 5.5 years and make no payments of interest prior to maturity. The prospectus for the SIGNs |16~ describes them as contingent interest notes. The single interest payment, payable at maturity, is equal to the greater of zero and

10 ||P.sub.m~ - 336.69/336.69~

where |P.sub.m~ denotes the average closing value of the S&P 500 for the 30 business days immediately preceding the second business day prior to the maturity date. The initial offering price was $10 per SIGN. If the value of the S&P 500 is below 336.69 on the maturity date, the holder receives $10. If the value exceeds 336.69, the holder gets $10 plus $10 multiplied by the percentage appreciation in the S&P 500 above 336.69. Also, the SIGNs are not redeemable by either the issuer or the holders prior to their scheduled maturity date. The SIGNs were marketed principally to retail investors, and they are listed on the New York Stock Exchange.(2) The financial press reports the daily prices of the SIGNs among the prices of common stocks traded on the New York Stock Exchange.

A. Characterization of SIGNs

SIGNS may be characterized as a package consisting of (i) a 5.5-year zero coupon note, plus (ii) a 5.5-year European call option, or warrant, on the S&P 500 with a strike price of 336.69. Exhibit 1 illustrates this interpretation. The SIGNs were offered for sale on Monday, January 28, 1991. The closing value of the S&P 500 the preceding business day, Friday, January 25, 1991, was 336.07. The call option was approximately at-the-money on the issue date because the strike price is 336.69. The outstanding debt of the Republic of Austria is rated Aaa by Moody's Investors Service and AAA by Standard & Poor's Corporation. Thus, a close substitute for SIGNs that is available to investors is a unit consisting of zero coupon Treasury securities (called Treasury strips), which are readily available in the capital market, and call options on the S&P 500, which are traded on the Chicago Board of Options Exchange. The Treasury strips involve zero default risk; however, the degree of default risk associated with Republic of Austria securities is slight due to the triple-A rating. The call option imbedded in the SIGNs is European-type just like the exchange-traded call options on the S&P 500.

B. Taxation of SIGNs(3)

The prospectus for the SIGNs suggests that they will be taxed as so-called contingent interest notes |16, p. S-13~. The prospectus notes that the Internal Revenue Service had not yet published final regulations governing the tax treatment of contingent interest notes. The proposed contingent interest regulations then outstanding were based on the premise that when the amount of interest that will ultimately be payable is contingent on the future value of an index or some other future event, the tax liability can not be determined until the amount of interest can be established with a reasonable degree of certainty. Because of the risk that the S&P 500 could decline below the strike price of the call option embedded in the SIGNs right up to the SIGNs' maturity date, the amount of interest payable cannot be conclusively determined until the maturity date. Consequently, interest on the SIGNs would not be taxable until the maturity date.

If the SIGNs were instead taxed as a unit consisting of a zero coupon note plus a long-dated call option, each component would be taxed separately. Under the original issue discount rules, the interest implicit in the amortization of the discount on the zero coupon bond component of the SIGNs would be taxed annually over the life of the instrument. Since the embedded call option is not exchange-traded, the call option component of the SIGNs would not be taxed on an annual basis under the mark-to-market rules that apply to exchange-traded options. Thus the tax treatment of the returns is potentially more favorable to investors under the contingent-interest-note interpretation of SIGNs than under the zero-coupon-note-with-call-option financial interpretation and may be much more favorable than the alternative of buying a Treasury strip and exchange-traded S&P 500 call options. On February 28, 1991, the Internal Revenue Service published proposed regulations |15~ under which any SIGNs issued on or after February 20, 1991, would be taxed in accordance with the zero-coupon-note-with-call-option interpretation of SIGNs. The proposed regulations do not affect the Republic of Austria SIGNs because they were issued prior to the February 20th effective date.(4)

The tax discussion in the SIGNs prospectus suggests a possible motivation behind the creation of SIGNs: tax arbitrage. To the extent contingent-interest tax treatment would defer income taxes that would be payable by taxable investors if the issuer sold a package consisting of a zero coupon note together with a call option on the S&P 500, a tax arbitrage could result if the issuer pays income taxes at a lower rate than investors. The Republic of Austria is not taxable (in the United States or anywhere else) and so the timing of any potential interest tax deductions is of no consequence to it. But the deferral of income taxes would be valuable to taxable investors who purchase the Republic of Austria SIGNs. Even though the recently proposed Internal Revenue Service regulations would reduce the magnitude of the gain from tax arbitrage in the future, SIGNs still enjoy a tax advantage vis-a-vis the alternative of purchasing a Treasury strip and exchange-traded S&P 500 options. In any case, investigating the magnitude of the tax arbitrage associated with the Republic of Austria SIGNs could yield some insight as to why the Republic of Austria SIGNs were issued.

C. SIGNs versus SPINs

The SIGNs closely resemble SPINs, a product Salomon Brothers Inc, developed more than six years ago. The SPINs paid a two percent rate of interest and a return at maturity that was contingent on the appreciation in the S&P 500 between the date of issue and the maturity date |18~. That issue was designed for institutional investors but press reports suggested that it met with investor resistance.(5) There were no subsequent issues of SPINs. Chen and Sears |5~ analyze SPINs and show that when the bond and call option components are valued separately and the values added, the resulting valuations closely track the market values of the SPINs, at least after an initial seasoning period and before the stock market crash in October 1987.

Since the SPINs were issued, there have been several other issues of equity-indexed notes sold in the European capital markets. Such notes have been issued with equity-contingent returns based on the FT-SE 100 (London) stock market index, CAC 40 (Paris) index, DAX (Frankfurt) index, and Nikkei 225 (Tokyo) index, and possibly on other stock market indexes as well. The method of analysis developed in this paper could be applied to these other equity-linked debt instruments.

II. Valuation of SIGNs

SIGNs can be valued relative to a comparable package consisting of a triple-A-rated 5.5-year zero coupon note plus an (approximately) at-the-money 5.5-year European call option on the S&P 500. The true value of each SIGN, denoted V, can be expressed as

V = B + C + T + E + R (1)

where

B = Value of the zero coupon bond component;

C = Value of the call option component;

T = Value resulting from tax arbitrage, if any;

E = Reduction, if any, in transaction costs vis-a-vis acquiring a comparable zero coupon bond and purchasing call options on the S&P 500 separately (or dynamically replicating the call option component); and

R = Value, if any, attributable to creating an investment alternative that is not otherwise available to the investors who purchased the SIGNs.

If a new security gives rise to risk-return combinations that investors could not have achieved previously, either due to market incompleteness or due to market imperfections that precluded certain investors from achieving the risk-return combinations the new security provides, for example, due to the indivisibility of exchange-traded options, then R |is greater than~ 0. If the new security reduces taxes or transaction costs, as compared to previously existing investment vehicles that provide similar risk-return combinations before taxes and transaction costs, then T |is greater than~ 0 or E |is greater than~ 0, respectively.

Call options on the S&P 500 with a time to expiration of 5.5 years are not available on any of the options exchanges. In 1991, the Chicago Board of Options Exchange introduced a form of option it calls LEAPS (long-term equity anticipation securities), which have a longer time to expiration than exchange-traded options have traditionally had. LEAPS on the S&P 500 Index were introduced in January 1991 with two expiration months, December 1992 and December 1993 (roughly two years and three years from issue, respectively) |20~. The LEAPS on the S&P 500 are European-style. To date, trading has been thin.(6)

An investor who wished to duplicate the return stream of the SIGNs would have two basic choices for the call option component: (i) try to purchase a customized option in the over-the-counter market, which is generally limited to institutional investors entering into contracts with broker-dealers having face value of $1 million or more, or (ii) employ dynamic replication, which involves adjusting a portfolio consisting of risk-free securities and either the underlying stock (or in the case of stock index options, either the underlying stocks or stock index futures) or shorter-term options on the same underlying stock. The seminal paper by Black and Scholes |2~ develops their well-known option valuation model based on the premise that an investor can replicate exactly the returns to any stock option by forming correctly, and continuously adjusting, a portfolio consisting of the underlying stock and the risk-free asset. However, Leland |11~ points out that continuous rebalancing is impractical in the presence of nontrivial transaction costs and develops a technique for replicating option returns in the presence of transaction costs. An alternative replication strategy presented by Choie and Novomestky |6~ builds on the earlier work of Jones |10~ and involves replicating the distribution of possible prices for a long-term option at some future date by forming a portfolio consisting of risk-free securities and shorter-term options on the same underlying stock and then rolling over this portfolio at discrete intervals.

The SIGNs were sold in small denominations ($10 per SIGN) primarily to retail investors, who would not have had access to the over-the-counter market on account of the small transaction size. The second alternative, dynamic replication, would entail transaction costs as the replicating portfolio was rebalanced. Figlewski |7~ shows that a retail investor engaging in small transactions would find it prohibitively expensive to rebalance the replicating portfolio frequently. In each case he considered, the transaction costs involved in the dynamic replication strategy, with daily rebalancing, exceeded the initial price of the option--in some cases by as much as a factor of five. For at least some retail investors, then, dynamic replication would not be a viable alternative to investing in SIGNs.

A. Value of the Zero Coupon Bond Component

The Republic of Austria has a large number of outstanding issues of U.S.-dollar-denominated bonds, including one issue of zero coupon bonds maturing July 17, 1995, that trades in the Eurodollar bond market. On January 28, 1991, the 1995 zero coupon issue had a price of 70 3/8% per bond, which implies a yield to maturity of 8.05% per annum semiannually compounded.(7) Based on an 8.05% yield to maturity, on January 28, 1991. the zero coupon bond component of each SIGN was worth approximately B = 10/|(1 +0.0805/2).sup.11~ = $6.48.

B. Value of the Call Option Component

The call option component can be valued using the Black-Scholes model modified to account for dividend-paying stocks. This model rests on several important assumptions (see Black and Scholes |2~), such as perfect markets, constant short-term interest rate, and constant volatility of the stock price. To the extent these assumptions are not satisfied, the true value of the call option component could deviate from the calculated value.(8) However, Chen and Sears |5~ report that the Black-Scholes option pricing model produced satisfactory results when used to value the call option component of SPINs, whose initial time to expiration is close to the SIGNs' initial time to expiration.

The common stocks that comprise the S&P 500 were paying cash dividends at the rate of $11.10 per year as of January 28, 1991, implying a dividend yield at the annual rate of q = 11.10/336.07 = 3.30%. I assumed that dividends on the S&P 500 occur at a continuous rate, which seems reasonable in view of the large number of stocks that comprise the index. I used the following modified Black-Scholes model, initially developed by Merton |14~ and later applied to stock index options by Hull |9~, to value the call option component of the SIGNs:

C = S|e.sup.-qt~N(|d.sub.1~) - X|e.sup.-rt~N(|d.sub.2~) (2)

where

|d.sub.1~ = |ln(S/X) + (r - q + (||Sigma~.sup.2~/2))t~/||Sigma~|square root of t~;

|d.sub.2~ = |d.sub.1~ - |Sigma~|square root of t~;

S = Current value of the S&P 500;

X = Strike price;

t = Time to expiration;

r = Continuously compounded riskless rate;

q = Continuous annual dividend yield on the S&P 500 portfolio; and

|Sigma~ = Standard deviation of the rate of return on the S&P 500.

Following Chen and Sears, the riskless rate is proxied by the continuously compounded equivalent yield of the Treasury note that matures closest to the maturity date of the SIGNs. The closest maturing Treasury note is the 7 7/8% Treasury note due July 1996, which had a continuously compounded equivalent yield of 7.60% on January 28, 1991. An estimate for the volatility |Sigma~ was obtained by calculating the value of |Sigma~ implicit in the closing price on January 25, 1991, of the S&P 500 LEAPS call option expiring in December 1993 -- the only LEAPS call option quoted that day in the Wall Street Journal. This procedure yielded the estimate |Sigma~ = 17.98%.(9) Because calculating just a single implied volatility is potentially error-prone, I also estimated implied volatilities for S&P 500 options with a strike price of approximately 336.07 and obtained estimates for |Sigma~ between 16.95% and 19.02%, which seem consistent with the 17.98% estimate obtained from the December 1993 S&P 500 LEAPS contract.(10) I report the sensitivity of the value of the call option component to variation in |Sigma~ within this range later in the paper.

For the SIGNs, the strike price is X = $10, so it is necessary to rescale the S&P 500: S = 10(336.07/336.69) = $9.98. The riskless rate is r = 7.60%, q = 3.3%, |Sigma~ = 17.98%, and t = 5.5 years. The estimated value of the call option component of the SIGNs was obtained by substituting these parameter values into Equation (2) and solving for C = $2.30.

C. Value of the Tax Arbitrage

The value of the tax arbitrage created through the introduction of SIGNs equals the sum of (i) the tax benefit resulting from the investor's ability to defer income taxes on the amortization of the zero coupon bond component, plus (ii) the tax benefit resulting from the investor's ability to defer income taxes that would otherwise be incurred under the mark-to-market rules. Exhibit 2 shows the calculation of the period-by-period tax liabilities that an individual investor in the 31% tax bracket would incur on a freely traded zero coupon bond that matched the zero coupon bond component of the SIGNs. The present-value tax savings that result from the tax deferral on the zero coupon bond component, denoted |T.sub.1~, are equal to the difference between the present value of the tax liabilities given in Exhibit 2 and the present value of the deferred tax liability on the zero coupon bond component of the SIGN:

|Mathematical Expression Omitted~

Exhibit 2. Calculation of the Periodic Tax Liabilities Associated with the Zero Coupon Bond Component of the Republic of Austria SIGNs Beginning Ending Tax Period Basis Accrual(a) Basis Liability(b) 1 $6.48 $0.26 $6.74 $0.081 2 6.74 0.27 7.01 0.084 3 7.01 0.28 7.29 0.087 4 7.29 0.29 7.58 0.090 5 7.58 0.31 7.89 0.096 6 7.89 0.32 8.21 0.099 7 8.21 0.33 8.54 0.102 8 8.54 0.34 8.88 0.105 9 8.88 0.36 9.24 0.112 10 9.24 0.37 9.61 0.115 11 9.61 0.39 10.00 0.121 Notes : a Calculated at an 8.05% per annum semiannually compounded yield to maturity. b Calculated at a 31% marginal income tax rate.

In Equation (3), |L.sub.1~(t) denotes the tax liability calculated for period t in Exhibit 2. This stream of tax liabilities is discounted at the average after-tax yield at which coupon-bearing Republic of Austria debt maturing in approximately 5.5 years was trading on January 28, 1991.(11) The single tax liability that would be owing at maturity under the contingent-interest tax treatment is discounted at the after-tax yield on the outstanding Republic of Austria zero coupon debt issue.

Note that if the S&P 500 is less than 336.69 when the SIGNs mature, the SIGNs holders get a tax deduction for the portion of the $10 public offering price that must be TABULAR DATA OMITTED allocated to the embedded call option (i.e., the premium they implicitly paid for the embedded call option, which equals the $10 public offering price minus the $6.48 value allocated to the zero coupon bond component). So |T.sub.1~ approximates the minimum present-value tax liability that a taxable investor would incur under the new proposed Internal Revenue Service regulations issued February 28, 1991, as a result of investing in SIGNs and holding each SIGN until it matures. The approximation is due to the fact that under current tax law (as discussed below), the tax rate on option gains or losses is 29.2% for individual investors in the peak (i.e., 31%) tax bracket.

The value of the tax deferral on the call option component equals the difference between the present value of the tax liabilities the investor would owe under the mark-to-market tax treatment that applies to exchange-traded options and the present value of the deferred tax liability on the call option component. Both present values will depend on the behavior of the S&P 500 over the life of the SIGNs, which is unpredictable due to the random nature of share price movements.

Exhibit 3 provides a very crude estimate of the expected value of the tax deferral on the call option component under the following assumptions. Ibbotson Associates |21~ has calculated an arithmetic mean total rate of return for the S&P 500 of 12.4% per annum for the period 1926-1989. The calculation of the value of the call option component assumed a 3.3% annual dividend yield. I continue to make this assumption for the sake of consistency. The difference between the 12.4% total return and the 3.3% dividend yield implies an expected rate of capital appreciation for the S&P 500 of 9.1% per annum, which I use for the purpose of the approximate tax calculation. I report the sensitivity of the value of the tax arbitrage to variation in the average annual rate of appreciation in the S&P 500 later in the paper. In Exhibit 3, I assume a 9.1% rate of appreciation in the S&P 500 for each year until the Republic of Austria SIGNs mature. I also assume in Exhibit 3 that the tax liability is calculated and promptly paid each December 31st. The estimated values for the embedded call option were obtained by applying Equation (2) with the parameter values given in Exhibit 3. Assuming a 9.1% annual rate of appreciation, the present-value tax savings that result from the tax deferral on the call option component, denoted |T.sub.2~, is(12)

|Mathematical Expression Omitted~

The stream of tax liabilities |L.sub.2~(t) in Equation (4) that would arise under the mark-to-market tax rules is taken from Exhibit 3. The second term on the right-hand side of Equation (4) represents the present value of the deferred tax liability on the gain on the call option embedded in the SIGN when the S&P 500 appreciates at a 9.1% annual rate. The tax rate is 29.2% because, under current tax law, 60% of the gain or loss on an investment in options is taxed as long-term gain or loss (currently taxed at a 28% peak individual rate) and the remaining 40% is taxed as short-term gain or loss (currently taxed at a 31% peak individual rate), for a blended rate of 29.2% (= 0.6|28~ + 0.4|31~).

The total value of the tax arbitrage created by the SIGNs, based on a 9.1% annual rate of appreciation, is T = |T.sub.1~ + |T.sub.2~ = $0.11 + 0.09 = $0.20 per SIGN, or roughly two percent of the public offering price per SIGN.

Under the new proposed tax regulations, future issues of SIGNs would benefit only from the tax arbitrage on the call option component. The new proposed regulations, which would require investors to pay tax on the zero coupon bond component each year as the discount amortizes, would cut the tax arbitrage benefit roughly in half (from 2.0% to 0.9% of the value of each SIGN).

D. Value of the Reduction in Transaction Costs

The underwriting discount for the SIGNs amounted to $0.50 per SIGN, which the issuer, the Republic of Austria, paid out of its gross proceeds. For purposes of analyzing the impact of the creation of SIGNs on the transaction costs an investor would incur, I compare the relative transaction costs associated with (i) purchasing 1,000 SIGNs, which would have cost $10,000, and (ii) purchasing a Treasury strip with $10,000 principal amount and a portfolio that replicates the call option component of each SIGN. The expected transaction costs associated with a dynamic replication strategy are difficult to estimate. They depend importantly on such factors as the frequency with which the replicating portfolio is rebalanced, the average size of the rebalancing transactions (due to the economies of scale in securities transactions), and the class of investor involved (see Figlewski |7~). Building on the work of Leland |11~, Swidler and Diltz |22~ estimate that the after-tax transaction costs involved in dynamically replicating long-dated call options, called Scores, varied between 1.3% and 4.2% of the Score's price. For comparative purposes, I also estimated the transaction costs associated with rolling over a series of shorter-dated S&P 500 call option contracts.

The estimated value of the call option component is $2.30. If the dynamic replication transaction costs are between 1.3% and 4.2% of this estimated value, they amount to between $0.03 and $0.10 per SIGN. These estimates will tend to understate the transaction costs associated with dynamically replicating a 5.5-year call option on the S&P 500 if the Scores in Swidler and Diltz's sample had times to expiration less than 5.5 years (which they may have) because longer-dated options are more costly to replicate dynamically (see Leland |11~ and Swidler and Diltz |22~).

Next, I consider the rollover alternative. Simply rolling over shorter-dated options will not replicate a longer-dated option's return stream; such a strategy is riskier than purchasing the longer-dated option. I consider the rollover alternative in order to gauge the reasonableness of the $0.03 to $0.10 estimated transaction costs for dynamic replication. Each S&P 500 LEAPS contract represents 100 options. The strike price equals the value of the S&P 500 divided by 10. In contrast, the standard S&P 500 index options contracts, which also represent 100 options, have a strike price equal to the value of the S&P 500. Thus, the S&P 500 contract with strike price 335 and expiring February 1991 has an aggregate strike price of $33,500. The S&P 500 LEAPS contract with strike price 35 and expiring December 1993 has an aggregate strike price of $3,500. Consequently, an investor with $10,000 to invest could purchase either 1,000 SIGNs or one Treasury strip plus three S&P 500 LEAPS contracts but could not use standard S&P 500 option contracts for this purpose because they are not divisible.

The commission on three S&P 500 LEAPs contracts amounts to approximately 3.76% of the market value of the contract.(13) The following calculation leads to a rough estimate of the transaction cost savings that would result, net of investor taxes at a 31% rate, from the introduction of SIGNs. The call option component of the SIGNs was valued at $2.30. Applying the 3.76% commission rate to the $2.30 market value of the embedded call option gives $0.086 per SIGN. The transaction cost is added to the investor's tax basis in the option contract, and the associated tax shield is realized at the time the option is sold or expires (through the decrease in gain or increase in loss for tax purposes, which is equal to the amount of the transaction cost added to the investor's tax basis). If it is assumed that the alternative to buying 1,000 SIGNs is to purchase a unit consisting of one Treasury strip and LEAPS contracts with an equivalent value of $2.30 (per SIGN) that would be rolled over at the end of three years, then the investor's present-value after-tax transaction costs associated with purchasing the LEAPS contracts, denoted |E.sub.1~, would amount to roughly

|Mathematical Expression Omitted~

assuming a 31% investor tax rate and a discount rate equal to the average after-tax yield to an individual investor at which Republic of Austria bonds maturing in approximately 5.5 years were trading. This value exceeds the $0.03 to $0.10 transaction cost range estimated earlier, which I noted might understate the cost of replicating a 5.5-year option. Accordingly, to be conservative, I use the $0.12 cost estimate in the balance of the paper.

The approximate transaction cost associated with purchasing a Treasury strip is $50 per $10,000 principal amount, or 0.5% of the principal amount. Each SIGN has principal amount of $10, implying a proportionate commission of $0.05, assuming the investor purchased 1,000 SIGNs. This cost would be amortized for tax purposes over the 5.5-year life of the SIGNs so that the present-value after-tax cost, denoted |E.sub.2~, is

|Mathematical Expression Omitted~

Purchasers of SIGNs in the secondary market would pay a transaction cost of $32 per round lot (100 SIGNs), or $0.32 per SIGN.(14) A purchaser of 1,000 SIGNs at $10 per SIGN would pay a transaction cost of $95, or $0.095 per SIGN. This cost is added to their tax basis, which generates a tax shield at the time the SIGNs are sold. There is an opportunity cost to the extent of the time value of money foregone. Assuming the purchase of 1,000 SIGNs, the present-value after-tax transaction cost, denoted |E.sub.s~, is |E.sub.s~ = $0,095|1-1/||1 + (1 - 0.31)0.0805/2~.sup.11~~ = $0.02 per SIGN, where I have discounted at the after-tax Republic of Austria zero coupon yield because the tax payment is assumed to be made at maturity.

The present-value after-tax transaction cost savings equals the difference between the present-value after-tax transaction costs associated with the Treasury-strip-with-LEAPS unit (|E.sub.1~ + |E.sub.2~) and the present-value after-tax transaction costs associated with the SIGNs (|E.sub.s~). The savings amount to E = |E.sub.1~ + |E.sub.2~ - |E.sub.s~ = $0.12 + 0.04 - 0.02 = $0.14 per SIGN, assuming a total investment of approximately $10,000 (i.e., 1,000 SIGNs). These savings are due to the relatively low cost of purchasing the call option when it is embedded in the SIGN.(15) Thus, the introduction of SIGNs permits investors to purchase options more cheaply than they could purchase exchange-traded options.

E. Value Potentially Attributable to Creation of a Longer-Dated Option

The creation of a new security can benefit investors if it reduces the impact of market imperfections or makes the capital markets more complete (see Van Horne |24~). As already noted, the returns generated by the 5.5-year call option component of the SIGNs can not be duplicated by rolling over a shorter-term position in either the standard S&P 500 option contract or the new S&P 500 LEAPS contract. Moreover, dynamic replication would be prohibitively expensive for at least some retail investors because of transaction costs. One of the potential sources of value attributable to the creation of the call option embedded in the SIGNs is the value to investors (principally retail investors) who desire a long-dated call option on the S&P 500 but cannot buy one in the over-the-counter market due to market imperfections, such as restricted market access, limitation on contract size, etc. SIGNs would potentially be even more valuable to those retail investors who would find it prohibitively expensive to dynamically replicate the long-dated call option because of transaction costs.

With the strike price of the S&P 500 option contract at 336.69, the standard contract size would be 100 times the index value, or $33,669, which corresponds to approximately 3,367 SIGNs based on the $10 public offering price. The minimum denomination for a Treasury strip is $10,000 principal amount, which corresponds to 1,000 SIGNs. An individual investor who wished to invest only a few thousand dollars would, of course, derive a benefit from SIGNs due to the indivisibility of both Treasury strips and standard S&P 500 option contracts. Only in this limited sense has the creation of SIGNs given rise to investment opportunities that did not previously exist. The benefit is due to market imperfections in the form of limited (small) investor access to the over-the-counter options markets, the indivisibility of exchange-traded options contracts, and the transaction costs retail investors would incur in implementing a dynamic replication strategy.

The new S&P 500 LEAPs contract has mitigated the impact of these imperfections in two ways: (i) the time to expiration of exchange-traded options has been extended, and (ii) the contract size is just one-tenth of the contract size for the standard S&P 500 options contracts. Nevertheless, the minimum size of a Treasury-strip-with-call-option transaction would involve buying $10,000 principal amount of Treasury strips, and SIGNs would permit even smaller (embedded) zero coupon bond purchases.

Returning to Equation (1), the SIGNs were sold to investors at a price of V = $10.00. I have estimated values for B, C, T, and E. Based on those values, Equation (1) implies a value for R, the value, if any, attributable to creating an investment alternative that is not otherwise available to the investors who purchased the SIGNs. From Equation (1), the implied value of R is

R = V - (B + C + T + E) = $10.00

- (6.48 + 2.30 + 0.20 + 0.14) = $0.88

for investors who could afford to purchase 1,000 SIGNs. For these investors, as well as for larger investors, SIGNs are inferior to the alternative of buying Treasury strips and S&P 500 call options, unless the value they attribute to being able to purchase a 5.5-year call option on the S&P 500 instead of having to replicate one dynamically is at least $0.88.

For investors who could not afford to purchase even 1,000 SIGNs, the tax savings T would still have value but because there is no close substitute for SIGNs, it is not meaningful to attribute any transaction cost savings to SIGNs in this case. For these investors, the implied value of R is

R = V - B - C - T = $10.00 - 6.48 - 2.30 - 0.20 = $1.02.

The value that might be attributable to reducing the impact of market imperfections, in particular, permitting smaller transactions to take place in S&P 500 call options, amounts to approximately $1.02 per SIGN, or 10.2% of the market value of each SIGN.

The estimated value for R was calculated as a residual based on the observed initial offering price V = $10.00 and the values estimated for B, C, T, and E. The estimated value of R will therefore include the effect of any mispricing that might have occurred. Chen and Sears |5~ found mispricing in the case of a similar financial instrument, SPINs, during the four-month period immediately following their issuance. I investigate the possibility of mispricing in Section IV.

III. Sensitivity Analysis

The upper panel of Exhibit 4 shows the sensitivity of the value of the call option component to the stock price volatility |Sigma~ and the dividend yield q. The volatilities implied in the S&P 500 call option prices on January 28, 1991, were between 16.95% and 19.02%. I used a somewhat wider range in Exhibit 4. The 3.3% dividend yield is toward the low end of the historical range. The dividend yield for the S&P 500 has typically been in the range from 3% to 6% |19~. Within the indicated ranges for |Sigma~ and q, the value of the embedded call option varies between $1.35 and $2.52. Adding the $6.48 value of the zero coupon bond component, the combined value of the debt and equity components of the SIGNs is between $7.83 and $9.00, significantly lower than the $10.00 price at which the Republic of Austria SIGNs were offered to investors.

The lower panel of Exhibit 4 indicates the sensitivity of the value of the tax arbitrage to different rates of S&P 500 appreciation based on the range of call option values calculated in the upper panel. The value of the tax arbitrage is sensitive to the appreciation rate but is not particularly sensitive to variation in |Sigma~ or q. The value of the tax arbitrage is between $0.14 and $0.40 per SIGN for annual appreciation rates between 6% and 18%. Adding the value of the tax arbitrage to the combined value of the debt and equity components of the SIGNs gives a range of $7.97 (= 7.83 + 0.14) to $9.40 (= 9.00 + 0.40), still significantly below the initial public offering price.

Based on the $10.00 initial public offering price, investors would have found it cheaper to buy a Treasury strip and dynamically replicate the 5.5-year call option, provided the present value of the after-tax transaction costs was less than $0.60 (= 10.00 - 9.40), which is more than four times the transaction cost savings I estimated. Nevertheless, Figlewski's |7~ results imply that at least for some retail investors, dynamic replication would not have been a cost effective alternative to the SIGNs. As noted at the beginning of the paper, the SIGNs were marketed principally to retail investors.

IV. Price Behavior of SIGNs in the Secondary Market

This section investigates the price behavior of SIGNs between their issuance and December 31, 1992. Chen and Sears |5~ found that SPINs went through a seasoning process. During the four months immediately following their issuance, the market price of the SPINs exceeded the price predicted by their model by between 4.93% and 5.86% (depending on which version of their model is used). Thereafter, the market price and the predicted price were within one percent of one another over a period of several months (until the October 1987 crash).

I used the model developed in this paper to estimate values for B, C, T, and E in Equation (1) for the last trading day of each month between February 1991 and December 1992. The 23 month-end values of B + C + T + E, together with the value $9.12 estimated as of the January 28, 1991 initial offering date, are plotted in Exhibit 5 along with the closing SIGNs price for each of those trading days. Data concerning Republic of Austria bond yields, Treasury yields, the value of the S&P 500, the annual dividend yield on the S&P 500 portfolio, the volatility of the rate of return on the S&P 500, and the price of the SIGNs were obtained from Bloomberg, L.P.

The predicted value of the SIGNs was 8.80% below the market price on January 28, 1991. At the end of February 1991, the predicted value was $9.84, which differed from the $10.00 market price by only 1.60%. At the end of March 1991, the predicted value was $10.03, which slightly exceeded the $10.00 market price. Thereafter, the predicted value and the market price approximate one another and fluctuate similarly. Over the February 1991-December 1992 period, the end-of-month predicted value exceeded the end-of-month market price by 2.03% on average.(16)

The price behavior of the SIGNs in relation to the predicted prices suggests that investors may have initially overvalued the SIGNs but that the mispricing was eliminated within roughly one to two months. However, an alternative explanation is also possible: Only a comparatively small number of investors placed a positive value on having investment opportunities previously unavailable to them because of option contract indivisibilities, and the demand for SIGNs from this source was fully satisfied in the initial offering and in the secondary market during the first two months of trading. In any case, the subsequent trading behavior of the SIGNs suggests that after the first two months of trading, R = 0, and hence that the value of the innovation should be attributed primarily to the value of the tax arbitrage it created (measured by T) and to the reduction in after-tax transaction costs it made possible (measured by E).

V. Measuring the Arbitrage Gain Realized by the Republic of Austria

The $0.50 underwriting discount per SIGN was paid by the Republic of Austria. The prospectus for the SIGNs disclosed that the Republic of Austria would use approximately 30% of the net proceeds of the SIGNs issue to hedge its contingent S&P 500 liability |16, p. S-5~. The net proceeds per SIGN amounted to $9.50. The cost of the hedge amounted to approximately $2.85 (= 0.3 x 9.50), leaving proceeds net of hedging costs amounting to $6.65. I calculated earlier that the bond component of each SIGN was worth $6.48. Hence, if the Republic of Austria could purchase a matching 5.5-year call option on the S&P 500 for $2.85, it would perfectly hedge its contingent liability and realize a riskless arbitrage profit of $0.17 (= 6.65 - 6.48) per SIGN. Put somewhat differently, the profit of $0.17 per SIGN would effectively reduce the Republic of Austria's cost of issuing 5.5-year zero coupon debt to r that solves

6.65 = 10/|(1 + (r/2)).sup.11~ r = 7.56% per annum

for a saving of 49 basis points per annum relative to the 8.05% per annum cost of a conventional zero coupon issue.

VI. Conclusions

The quick response by the Internal Revenue Service to the introduction of SIGNs reflects its concern about the potential for tax arbitrage. The Internal Revenue Service has become increasingly vigilant in recent years in trying to spot securities innovations whose principal rationale is tax arbitrage. In the case of SIGNs, the tax arbitrage represents approximately $0.20 per SIGN, or 2.0% of the value of each SIGN, and a total of $2.0 million for the entire Republic of Austria issue. The change in tax treatment, had it applied to the Republic of Austria issue, would have reduced the value of the tax arbitrage by approximately $1.1 million.

Returning to the two questions posed at the beginning of the paper: (i) the Republic of Austria issued SIGNs in order to take advantage of an opportunity to earn an arbitrage profit, and (ii) SIGNs were innovative in the sense that they gave rise to a tax arbitrage, enabled an investor to avoid the transaction costs associated with dynamically replicating a 5.5-year call option on the S&P 500, and created an opportunity for small investors to purchase long-term S&P 500 call options that is not otherwise available to them due to market imperfections. SIGNs also represent a good example of how a new security can yield attractive returns to an innovator who takes advantage of an opportunity to create a tax arbitrage or reduce the impact of market imperfections.

1 Finnerty |8~ and Tufano |23~ describe a range of securities innovations that typify the process of securities innovation.

2 Debt instruments sold in the United States typically have a principal amount of $1,000. The $10 denomination is designed to appeal to retail investors. While the issue was lead managed by Goldman Sachs & Co., the three co-managers, Dean Witter Reynolds Inc., Oppenheimer & Co., Inc., and A.G. Edwards & Sons. Inc., are all nationally recognized securities firms with a strong retail business (i.e., individual investors as opposed to financial institutions). Also, the underwriting spread was $0.50 per SIGN, or 5% of the public offering price, which is the size of spread typically observed in the equity market rather than in an institutional debt offering.

3 This section is based on discussions with tax consultants at Deloitte & Touche, New York, NY, and tax counsel at Howard, Darby & Levin, New York, NY.

4 As of April 16, 1993, the IRS still had not issued final regulations.

5 The preliminary prospectus specified a zero coupon issue. Press reports indicated that investors objected to the zero coupon structure. Salomon set a two percent coupon but raised the strike price of the embedded call option to compensate for the two percent coupon |18~.

6 As of December 31, 1992, total open interest in the S&P 500 LEAPS amounted to 20,692 call option contracts (versus 318,484 contracts for the standard S&P 500 call option) and 112,479 put option contracts (versus 396,804 contracts for the standard S&P 500 put option). The difference in dollar value of open interest is even greater because each LEAPS contract is based on one-tenth of the value of the S&P 500 whereas each standard S&P 500 contract is based on the full index value.

7 The bond price was obtained from Bloomberg, L.P., which obtains its pricing data from Merrill Lynch Capital Markets.

8 Prior studies have come to conflicting conclusions regarding the accuracy of Black-Scholes options pricing (see Black |1~, MacBeth and Merville |12~, and Rubinstein |17~).

9 The parameter values used in this estimation were S = 33.607, X = 35.00, t = 2.8904 years (to December 18, 1993), q = 0.033, r = 0.0722, and observed price = $4.75. Note that the S&P 500 LEAPS contracts are based on one-tenth of the value of the S&P 500.

10 The estimated implied volatilities by contract were 17.67% (February 1991 at 335), 19.02% (March 1991 at 335), 16.95% (February 1991 at 340), 18.57% (March 1991 at 340), and 18.84% (June 1991 at 340). I used the 17.98% estimate because the S&P 500 LEAPS contract expires much later than these other contracts and therefore seems more appropriate. Alternatively, I could have employed the implicit weighting scheme outlined by Whaley |25~ to weight the various implied volatilities, but using the simple estimate seemed more appropriate for the reason just given.

11 The Republic of Austria had three publicly traded coupon-bearing issues that were scheduled to mature around the time the SIGNs are scheduled to mature. These three issues and their yields to maturity on January 28, 1991, were: (i) 7 3/4% due May 8, 1996 yielding 8.54% per annum semiannually compounded, (ii) 7 3/4% due February 18, 1997 yielding 8.34%, and (iii) 9 1/4% due June 28, 1996 yielding 8.21%. All prices and yields were obtained from Bloomberg, L.P. The average of these three yields, 8.36%, was used to discount the stream of tax liabilities, |L.sub.1~(t), in Equation (3).

12 |T.sub.2~ is a random variable whose expected value depends upon the path-dependent values of the call option component of the SIGN. The expected value of |T.sub.2~ might be roughly estimated, for given expected return and volatility, in the following manner. The Black-Scholes option pricing model implicitly assumes a lognormal diffusion process. Given expected rate of return |Mu~ = 12.4%, volatility |Sigma~ = 17.98%, and continuous dividend yield q = 3.3%, the rate of share price appreciation for any time interval of length t will be distributed approximately normal with mean (|Mu~ - q)t and variance ||Sigma~.sup.2~t. The share prices and call option prices corresponding to the five rates of appreciation (|Mu~- q)t, (|Mu~- q)t|+ or -~|Sigma~|square root of t~ and (|Mu~ - q)t|+ or -~2|Sigma~|square root of t~ can be determined for each time t = 1, 2, 3, 4, 5 and 6 from this distribution. By approximating the normal distribution discretely and estimating |T.sub.2~ for each of the five rates of appreciation, I estimated the expected value of |T.sub.2~ to be approximately $0.09, the same value estimated by considering only the expected rate of share price appreciation (9.1% per annum). Details of the calculation are available from the author.

13 The estimated commission rates quoted in this paper were obtained from Pershing Securities, a subsidiary of Donaldson Lufkin & Jenrette. The commission on the three contracts is calculated as $35 plus 0.013 multiplied by the market value of the contracts, if the market value is under $3,000. The fractional component decreases for transaction sizes greater than $3,000. On January 28, 1991, the December 1993 LEAPS 35 contract was quoted at $4.75 per underlying option, implying a total market value of $475 per contract. The commission is $35 + 0.013(3)(475) = $53.53 for the three contracts, or 3.76% (= 53.53/1425) of the market value of the three contracts.

14 Calculated as $25 plus 7/10 of 1% of the value of the transaction.

15 If instead it is assumed that the investor would roll over a position in the standard six-month S&P 500 contract, the commission would amount to

approximately 2.75% of the value of the transaction for one contract. But each standard S&P 500 option contract has an aggregate strike price equal to 100 times the S&P 500. If it is assumed that the investor would be able to purchase sufficient SIGNs to obtain an aggregate call option component equivalent to one standard S&P 500 contract, then the 2.75% commission rate would be achievable. If the strike price of the S&P 500 contract is 335, for example, the investor would have to be able to purchase 3,350 SIGNs, at an aggregate cost of $33,500. Applying the 2.75% commission rate to the $2.30 market value of the embedded call option gives $0.063 per SIGN. The stream of after-tax transaction costs associated with rolling over the six-month options every six months has a present value of

|Mathematical Expression Omitted~

The transaction cost savings amount to E = $0.42 + 0.04 - 0.02 = $0.44 per SIGN, which represents 88% of the gross underwriting commission. In establishing the price at which to sell the SIGNs, the underwriters would presumably try to price the SIGNs so as to recover the underwriting spread from investors. If so, this analysis suggests that the underwriters of the Republic of Austria SIGNs issue viewed the rollover of standard S&P 500 option contracts, rather than S&P 500 LEAPS, as the most appropriate benchmark, perhaps because of the very thin trading to date in the S&P 500 LEAPS contracts.

16 The predicted value begins to exceed the market price persistently beginning in March 1992. For the 23-month period, February 1991 to December 1992, the 2.03% average differential is significant at the 0.05 level (t = 2.23).

References

1. F. Black. "Fact and Fantasy in the Use of Options," Financial Analysts Journal (July-August 1975), pp. 36-41, 61-72.

2. F. Black and M. Scholes, "The Pricing of Options and Corporate Liabilities," Journal of Political Economy (May-June 1973), pp. 637-654.

3. D.M. Chance and J.B. Broughton, "Market Index Depository Liabilities: Analysis, Interpretation, and Performance," Journal of Financial Services Research (December 1988), pp. 335-352.

4. A.H. Chen and J.W. Kensinger, "An Analysis of Market-Index Certificates of Deposit," Journal of Financial Services Research (July 1990), pp. 93-110.

5. K.C. Chen and R.S. Sears, "Pricing the SPIN," Financial Management (Summer 1990), pp. 36-47.

6. K.S. Choie and F. Novomestky, "Replication of Long-Term with Short-Term Options," Journal of Portfolio Management (Winter 1989), pp. 17-19.

7. S. Figlewski, "Options Arbitrage in Imperfect Markets," Journal of Finance (December 1989), pp. 1289-1311.

8. J.D. Finnerty, "Financial Engineering in Corporate Finance: An Overview," Financial Management (Winter 1988), pp. 14-33.

9. J. Hull, Options, Futures, and Other Derivative Securities, Englewood Cliffs, NJ, Prentice-Hall, 1989, Ch. 6.

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14. R.C. Merton, "Theory of Rational Option Pricing," Bell Journal of Economics and Management Science (Spring 1973), pp. 141-183.

15. "Proposed Regulation 1.1275-4(g)," Standard Federal Tax Reports, Commerce Clearing House, February 28, 1991, p. 57,679-2.

16. Republic of Austria, Stock Index Growth Notes ("SIGNs") due August 15, 1996, prospectus, January 28, 1991.

17. M. Rubinstein, "Nonparametric Tests of Alternative Option Pricing Models Using All Reported Trades and Quotes on the 30 Most Active CBOE Option Classes from August 23, 1976 through August 31, 1978," Journal of Finance (June 1985), pp. 455-480.

18. Salomon Inc, 2% Standard & Poor's 500 Index Subordinated Notes, prospectus, August 21, 1986.

19. Security Price Index Record, New York, Standard & Poor's Corporation, 1990, p. 119.

20. "SPX LEAPS - Contract Specifications," Chicago, Chicago Board Options Exchange, 1990.

21. Stocks, Bonds, Bills, and Inflation: 1990 Yearbook, Chicago, Ibbotson Associates, 1990.

22. S. Swidler and J.D. Diltz, "Implied Volatilities and Transaction Costs." Journal of Financial and Quantitative Analysis (September 1992), pp. 437-447.

23. P. Tufano, "Financial Innovation and First-Mover Advantages," Journal of Financial Economics (December 1989), pp. 213-240.

24. J.C. Van Horne, "Of Financial Innovations and Excesses," Journal of Finance (July 1985), pp. 621-631.

25. R. Whaley, "Valuation of American Call Options on Dividend-Paying Stocks: Empirical Tests," Journal of Financial Economics (March 1982), pp. 29-58.

John D. Finnerty is a Professor of Finance at Fordham University and a General Partner with McFarland Dewey & Co., New York, New York.

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Title Annotation: | Security Design Special Issue; stock index growth notes |
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Author: | Finnerty, John D. |

Publication: | Financial Management |

Date: | Jun 22, 1993 |

Words: | 8996 |

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