Arbitrage and Valuation in the Market for Standard and Poor's Depositary Receipts.
This paper examines pricing in the market for depositary receipts, securities designed to track the performance of a stock index that trade like shares of stock. Arbitrage costs are low because these assets have low fundamental risk, low transactions costs, and high dividend yields. We find that Standard and Poor's Depositary Receipts (SPDRs), or spiders, do not trade at economically significant discounts, unlike closed-end mutual fund shares. Although individual investors invest much more heavily in SPDRs than in S&P 500 stock, investor sentiment is not an important determinant of the discount. The SPDRs redemption feature facilitates arbitrage so that sophisticated traders can take advantage of and eliminate mispricing. However, we also report a larger, economically significant discount for MidCap SPDRs. MidCap SPDRs are designed to track the performance of the S&P MidCap 400 index, an index of moderate capitalization firms, and are expected to have higher arbitrage costs. Finally, we find that SPDRs and Mi dCap SPDRs returns are not excessively volatile, also unlike closed-end funds.
Recently stock exchanges have introduced index derivative products that trade just like shares of stock. Because traded stock baskets are simple assets like closed-end mutual funds, they provide an ideal experiment to study pricing. These products are not actively managed, but rather track an existing stock index.  For example, in January 1993 the American Stock Exchange (AMEX) introduced Standard and Poor's Depositary Receipts (SPDRs), or spiders, designed to track the performance of the S&P 500 index.  The price of a depositary receipt should not deviate from its fundamental value as predicted by the level of the underlying index if all investors are rational. This paper examines whether depositary receipts trade at prices that reflect fundamental value.
Perhaps no question in finance has received greater attention than the extent to which asset prices reflect fundamental values. Keynes (1936) argued that markets are unstable and driven by waves of irrational psychology. In contrast, if markets are efficient, price reflects all information so that the profits made by acting on information do not exceed the costs of trading (Jensen, 1978). Accordingly, assets trade at prices that reflect their fundamental values and no arbitrage opportunity exists. However, the costs of trading are surely positive so that the extreme form of the efficient market hypothesis does not hold.
Even with rational traders in the market, an asset may be mispriced if traders have limited ability to take advantage of arbitrage opportunities. Significant arbitrage costs prevent rational traders from exerting sufficient price power to force prices to return to fundamental values (Shiller, 1984 and DeLong, Shleifer, Summers, and Waldmann, 1990). For example, arbitrage strategies based on mispricing may be restricted because of limits on short sale proceeds, the cost of portfolio rebalancing, and the possibility of forced liquidation (Lee, Shleifer, and Thaler, 1991). In a costly arbitrage framework with noise traders, Pontiff (1996) identifies factors that affect the profitability of arbitrage and, in turn, the magnitude of mispricing, Using a sample of closed-end mutual funds, Pontiff concludes that the magnitude of mispricing can be explained by various security characteristics, including how difficult the fund is to replicate, the security's dividend yield, and transaction costs. Although a closed-end fund is a very simple security that typically holds other publicly traded securities, these funds are perplexing, because they frequently trade at prices different from net asset value, i.e., market prices deviate from the actual value of the stock portfolio held by the fund. 
This paper studies the pricing efficiency of traded stock baskets and examines the impact of arbitrage costs in the pricing of these relatively new, but high volume, financial instruments. We investigate and compare pricing in the SPDRs and MidCap SPDRs markets.  MidCap SPDRs are designed in the same fashion as S&P500 SPDRs except that the Trust holds a portfolio of common stocks that closely tracks the performance of the S&P MidCap 400 Index, an index consisting of 400 moderate capitalization stocks. Shares of exchange listed stock portfolios have been actively traded since their introduction. In fact, SPDRs are commonly the most actively traded issue on the AMEX.  According to their sponsor, these depositary receipts "are securities that let you buy or sell an entire portfolio of stocks as easily as you do shares of a single stock" (PDR Services Corporation, 1996).  A share in a stock basket represents a unit of a trust and accumulated dividends are paid quarterly. An important and distinctive fe ature of the stock basket is that an investor who holds a prescribed number of units can redeem the units for the underlying stock. Despite the usefulness of traded stock baskets and their warm reception by investors, little research in finance has studied these securities. This paper pays particular attention to factors that should affect the profitability of arbitrage and, in turn, the extent of mispricing, if any.
Although the evidence suggests that closed-end funds are mispriced, there are clear differences between closed-end mutual funds and traded stock baskets. Traded stock baskets are not closed-end and the trusts can, and commonly do, issue new units each year. Furthermore, outstanding units of a stock basket can be redeemed for the actual underlying stock, unlike outstanding shares of a closed-end fund. As we argue subsequently, the redemption feature is particularly important when we attempt to evaluate the pricing efficiency of the market.
Closed-end funds and depositary receipts also have some common characteristics. Both trade on the open market, which means that their prices should reflect the forces of supply and demand, as well as underlying asset values. In addition, both are predominantly held by individual investors. If individual investors are noise traders who are subject to waves of optimism and pessimism, both closed-end funds and traded stock baskets may be underpriced (Zweig, 1973 and Lee, Shleifer, and Thaler, 1991).
Our results indicate that, unlike closed-end mutual fund shares, the S&P500 stock basket does not trade at economically significant discounts from the actual value of the portfolio of stocks held by the Trust. However, we report more significant mispricing for the MidCap 400 stock basket, because arbitrage costs are greater. Consistent with Pontiff's noise trader model, our results suggest that impediments to arbitrage explain a significant amount of mispricing in financial markets. Significant discounts are reported in closed-end fund markets, because the costs of arbitrage hinder profitable trades. When the limits to arbitrage are few, pricing is very efficient. Despite the fact that both closed-end funds and SPDRs are held predominately by individual investors, SPDRs prices are very close to fundamental values. Sophisticated traders take advantage of and eliminate mispricing in the SPDRs market. The SPDRs redemption feature is critical. Because they can be redeemed, fundamental value is realizable should SPDRs prices deviate too far from the value of the underlying index. In contrast, fundamental value is not easily realizable for a closed-end fund so that persistent, economically significant discounts are observed. We also find that SPDRs and MidCap SPDRs returns are not excessively volatile, unlike the returns to closed-end funds (Pontiff, 1997).
The paper proceeds as follows. In Section I, we discuss the role of arbitrageurs in eliminating mispricing and review the evidence relating to pricing efficiency. In Section II, we describe the market for depositary receipts and data used in the empirical investigation. In Section III, we present evidence on the pricing efficiency of traded stock baskets. In Section IV, we discuss the results and offer concluding remarks.
I. The Role of Rational Traders
Early studies of stock markets generally support the theory that market prices efficiently reflect publicly available information. In contrast, closed-end mutual funds typically sell at prices different from their net asset values (Malkiel, 1977, Hardouvelis, La Porta, and Wizman, 1994, and Pontiff, 1995). Though certainly not the only documented inconsistency with the efficient market hypothesis, the closed-end fund puzzle has received a great deal of attention because, unlike common stock and most other traded securities, the market price and the underlying asset value are observable. The mispricing frequently reflects a premium in fund value when the fund is first offered to investors, with the premium turning to a discount, on average, of 10% within 120 days of trading (Lee, Shleifer, and Thaler, 1991). Possible explanations for mispricing of closed-end fund shares include agency costs resulting from excessive management fees or poor expected future performance, illiquid or restricted assets, and tax liabilities on unrealized capital gains. However, these factors have not provided a satisfactory explanation of the closed-end fund puzzle (Lee, Shleifer, and Thaler, 1991).
According to an alternative to the efficient market hypothesis that has recently gained prominence, differential investor clienteles can have important effects on asset pricing (Black, 1986, De Long, Shleifer, Summers, and Waldman, 1990, and Lee, Shleifer, and Thaler, 1991)  Two assumptions are important. First, some investors, referred to as noise traders, are not fully rational and their behavior is affected by sentiment that does not derive from news about fundamental values. Second, arbitrage by rational investors is limited and risky. The rational traders form fully rational expectations about prices and, thus, are not subject to sentiment. But, arbitrage is limited by risk (Shleifer and Summers, 1990). Importantly, "arbitrage does not eliminate the effects of noise because noise itself creates risk" (De Long, Shleifer, Summers, and Waldman, 1990, page 705). In order to explain the closed-end fund puzzle, the noise approach also assumes that uninformed traders are more likely to trade and hold closed -end funds than the funds' underlying assets. Otherwise, identical sentiment would impact the prices of the funds and their assets and no mispricing would be expected. Recent research provides evidence that closed-end fund discounts measure investor sentiment and predict returns (Neal and Wheatley, 1998).
Noise trader models imply that if individual investors invest more heavily in depositary receipts than in stocks included in the underlying index, the traded stock basket will sell at a discount. In fact, as we document in the following section, individual investors invest much more heavily in SPDRs than in S&P500 stocks. Promotional information for the stock basket recognizes that investor sentiment may play a role in pricing. According to the distributor "since SPDRs trade in an open auction market on the floor of the American Stock Exchange, prices are affected by supply and demand as well as market volatility, sentiment and other factors" (PDR Services Corporation, 1996). Yet as we document subsequently, the market for SPDRs does not exhibit economically significant mispricing.
According to the standard textbook treatment, if a depositary receipt sells at a discount in a frictionless market, an arbitrageur would buy the underpriced depositary receipt and short sell the stocks in the underlying index. The arbitrageur would then redeem the depositary receipts, close out the short stock position, and realize a profit. Alternatively, an investor could buy and immediately redeem the depositary receipts and sell the shares received. This process continues until price pressure eliminates the discount. Arbitrage as described is a fundamental concept in economics and finance and it is commonly assumed that arbitrage opportunities do not persist for long. However, actual arbitrage strategies are more complicated than the usual textbook treatment suggests (Shleifer and Vishny, 1997). Frictions may prevent arbitrageurs from taking advantage of mispricing. For example, transactions costs (e.g., brokerage costs, bid-ask spreads) and holding costs (e.g., borrowing costs, limits on short sale proc eeds) may be significant.
Using a noise trader model, Pontiff (1996) identifies security characteristics that affect arbitrage profitability and the extent of mispricing.  First, the arbitrageur's risk is greater when it is more difficult to hedge the fundamental value of the arbitrage position. With greater fundamental risk mispricing is more likely to persist because the costs of arbitrage are greater. As discussed above, if SPDRs sell at a discount, an arbitrageur would buy the underpriced SPDRs and short sell S&P500 stocks. The costs due to portfolio rebalancing are not likely to be significant because the S&P500 index composition is fairly stable and portfolio changes are predictable. The telling aspect of the strategy is that there is no fundamental or resale risk.  The SPDRs redemption feature allows the arbitrageur to eliminate fundamental and resale price risk because the option gives the ability to immediately buy the underlying asset at current prices. Shleifer and Vishny (1997) also argue that arbitrage activity is likely to be greater in markets in which arbitrageurs can accurately measure and easily realize fundamental value. The SPDRs market is such a market. Arbitrage opportunities are easy to identify because the prices of S&P500 stocks are closely watched and current prices are readily available.  However, arbitrage opportunities may arise more often in the MidCap SPDRs market because the underlying index includes less visible, lower volume stocks.
In addition to the level of fundamental risk, a security's dividend yield affects the magnitude of mispricing. Dividend payments reduce the capital necessary for the arbitrage position and, thus, holding costs (Pontiff, 1996). Holding costs are those that an arbitrageur is subject to every period a position is open. A dividend is not subject to mispricing even when a security is because, when a dividend is paid, investors receive its full value. Securities with large dividend yields have less mispricing because holding costs are lower. We compare the extent of mispricing in SPDRs and MidCap SPDRs. The two securities, though very similar, have different dividend yields with S&P500 SPDRs having the higher yield.
A final security characteristic that affects the magnitude of mispricing is the amount of transaction costs, i.e. costs that are incurred every time a transaction is made. A security with larger transaction costs will exhibit greater mispricing, because the arbitrageur must cover these costs before realizing a profit. Transaction costs are not expected to have a large influence on the pricing of the depositary receipts examined. In the S&P500 market, trading volume is substantial and transactions costs are relatively low, though trading in the MidGap market may entail greater cost. 
When noise trading plays a role in pricing, traded stock baskets may sell at a discount if they are held predominantly by individual investors. In addition to the other frictions discussed above, arbitrage may be limited because capital is required to take advantage of mispricing. The full proceeds from a short sale of stock are not available to the arbitrageur and the purchase of at least one creation unit (50,000 units) is required. For example, at our average sample SPDR price, the purchase of one creation unit would require just over $3 million in capital. However, taken together, the characteristics of SPDRs suggest that mispricing in the SPDRs market should be small, if any exists at all. SPDRs have low fundamental risk and small transactions costs. We compare pricing in the SPDRs and MidCap SPDRs markets because, though the two securities are very similar, they differ in two important respects. First, the S&P500 index is easier to mimic than the MidCap 400 index. The composition of the larger capitali zation index is more stable and the constituent securities are more actively traded. Second, the SPDRs have a higher dividend yield. Thus, the MidCap SPDRs have more fundamental risk and greater holding costs, and are expected to exhibit greater mispricing. Before empirically examining pricing efficiency, we describe the depositary receipts markets in the following section.
II. Description of the Market
The SPDR Trust commenced operations on January 22, 1993. It was formed by PDR Services Corporation, a wholly-owned subsidiary of the AMEX, in order "to provide investors with the opportunity to purchase units of beneficial interest in the Trust representing proportionate undivided interests in the portfolio of securities held by the Trust ... consisting of substantially all of the common stocks, in substantially the same weighting, as the component common stocks of the Standard and Poor's 500 Index" (SPDR Prospectus). SPDRs are designed to approximate 1/10th of the value of the S&P500 index so that the price falls in the range of a typical share of stock. SPDRs are listed on the AMEX, have ticker symbol SPY, and trade just like any other stock.
Quarterly dividends are paid on the last business day of April, July, October, and January with the ex-dividend date falling on the third Friday of March, June, September, and December. The cash dividend reflects a pro rata amount of regular cash dividends accumulated by the Trust during the preceding quarterly period. Accumulated Trust expenses are deducted and all dividends received by the Trust over a quarter are held in a non-interest bearing account.
Table I reports descriptive information for the SPDR market. Our sample includes data from the inception of the Trust in January 1993 through the end of December 1997. For each sample year we report the number of SPDRs outstanding, average daily SPDR trading volume, total dollar value of the Trust's assets, year-end net asset value per SPDR, and year-end value of the S&P500 index. The data shows that SPDRs are a marketing success. SPDRs are actively traded and investors have demanded more units over time. The preliminary evidence suggests that the Trust's portfolio approximates the S&P500 index as the year-end net asset value is very close to the year-end S&P500 value divided by 10.
SPDRs may be redeemed or created only in blocks of 50,000 units. Such a block is referred to as a creation unit. Redemptions are permitted only on an in-kind basis with a balancing cash component to equate the transaction to the net asset value on the date of the transaction. In addition, a cash redemption payment is made by the Trust, which is equal to a proportional amount of the dividends received for the quarter prior to the date of redemption, less expenses of the Trust and any accrued tax liabilities. The trustee also charges a transaction fee of $250 to $1,500 per creation unit created or redeemed in order to offset order-processing costs. Table II reports Trust transactions for each year in our sample period.  Included are the numbers and dollar amounts of SPDRs sold and redeemed. Note that the number and value of redemptions is significant.
The traders themselves are a final important aspect of the SPDRs market. In 1993, institutional investors held less than 5% of the SPDRs outstanding but by 1994 institutional holdings grew to 23%.  The increase in institutional interest in SPDRs tapered off at that time and in 1997 was 25%. By comparison, average institutional ownership in the stock composing the Trust was almost constant at 59% in 1993 and 1997.  In computing this average, we used the actual dollar investment in S&P500 stocks as reported in the Trust financial statements in order to appropriately weight each stock's institutional holdings. This evidence suggests that SPDRs are held primarily by individual investors and that there is a marked difference in the clienteles that hold SPDRs and S&P500 stocks.
The design of MidCap SPDRs is very similar to that of SPDRs. The total MidCap Trust investment was $496,761,298 as of September 30, 1997, approximately one-tenth of that of the S&P500 SPDRs Trust. MidGap SPDRs are constructed to track the performance of the S&P MidCap 400 index, a broadly based index consisting of publicly traded stock in a representative segment of middle capitalization companies. The MidCap SPDRs Trust began operations on April 27, 1995. The number of MidCap SPDRs required for a creation unit is 25,000 and the value of the depositary receipts is 1/5th of the value of the index. A comparison of pricing in the SPDRs and MidCap SPDRs markets allows us to examine the impact of various security characteristics on pricing efficiency.
Although the characteristics of the two depositary receipts are very similar, the MidCap index is likely to have higher arbitrage costs. Because the S&P500 index consists of larger companies, it is easier to replicate than the S&P MidCap 400 index and, thus, MidCap SPDRs may have higher fundamental risk. In addition, larger transactions costs are generally associated with smaller firms. Finally, the dividend yield on the S&P MidCap 400 index is lower than that of the S&P500 index. Since MidGap SPDRs commenced trading, the underlying index has provided a yield of 1.85% whereas the S&P500 index has yielded 2.42% since SPDRs began trading. These differences suggest that mispricing in the MidCap SPDRs market may exceed that in the SPDRs market.
III. Pricing Efficiency in Depositary Receipts Markets
In order to examine pricing efficiency and the impact of arbitrage costs, we estimate and compare the extent of mispricing in SPDRs and MidCap SPDRs. Assuming the Trusts successfully track the underlying indexes and, for the moment, ignoring the effect of dividends, we expect the prices of the depositary receipts to closely track their underlying indexes. Otherwise, profitable arbitrage strategies would be suggested. We also compare the volatility of depositary receipts returns to the variability of their underlying index returns. As Pontiff (1997) shows, if investors are rational, the variances of the two returns should be equal.
In order to examine pricing efficiency, we first examine the percentage discount. For the S&P500 depositary receipts, the mispricing measure is computed as (S&P500 - SPDR)/S&P500*100, where S&P500 is the level of the Standard and Poor's 500 index and SPDR is ten times the closing price of Standard and Poor's Depositary Receipts. The SPDR price and dividend data are from the CRSP daily database and the S&P500 index and dividend data are from Standard and Poor's Corporation through the DRI database.  Although calculation of the discount appears to be straightforward, consideration of dividends introduces a complication.
The cash flows from purchasing (or short selling) the S&P500 stock portfolio and SPDRs differ, even if the Trust's management excels at rebalancing the portfolio at low cost to reflect changes in the index. An investor who purchases the S&P500 portfolio receives dividends as they are paid, whereas an investor who purchases a SPDR receives accumulated dividends, without interest, at the end of the quarter. Thus, when we compare the price of the S&P500 portfolio to the price of a SPDR, we must recognize the differences in the cash flow stream. The value of the index reflects all future dividends paid on the constituent stocks. In addition to these dividends, the SPDR price reflects dividends paid and accumulated since the last SPDR ex-dividend date. To appropriately compare S&P500 and SPDR values, we compute an adjusted SPDR price by deducting the dividend accumulated since the last ex-dividend date from the SPDR price. [16,17] We refer to the discount calculated using this SPDR series as the adjusted measure. In addition, when a company leaves the index capital gains distributions are held by the Trust and paid at year-end. Thus, the adjusted price also appropriately reflects these distributions. For SPDRs, there was only one small capital gains distribution during the sample period.
The SPDR redemption option affirms the appropriateness of adjusting the SPDR price series prior to estimating the extent of mispricing, if any. Owners of SPDRs in creation unit blocks can redeem their units for the underlying securities with a cash payment reflecting accrued dividends. Upon redemption, the value of a SPDR to its holder is the current value of the component stocks plus accrued dividends, again suggesting that a comparison of the unadjusted SPDR price to the S&P500 index level is inappropriate. Instead the SPDR price less accrued dividends should track the index.
Figure 1 illustrates the percentage daily discount for the unadjusted SPDRs series over the sample period. The figure shows that there is considerable variation in the discount over time. However, as compared to discounts reported for closed-end funds, which can exceed 25%, the SPDR discount does not appear to be substantial. Though discounts are observed, there appears to be a negative mean, or premium, on average. As the figure also clearly shows, a distinct seasonal pattern in the unadjusted discount is evident. This pattern appears to be related to the quarterly pattern of dividend accumulation and payment, rather than to a purely monthly seasonal.
Recognition of the importance of dividend cash flows and the redemption option are key to understanding this seasonal pattern. As discussed earlier, a significant number of SPDR units are redeemed each year. Upon redemption, the holder receives dividends accrued up to the redemption date, rather than a prorated amount related to dividends that will be paid over the time remaining in the quarter. Figure 2 shows the percentage daily discount using the adjusted SPDR. The seasonal pattern is not evident. The discount appears to vary randomly overtime and falls mostly in the range of -0.5% to 1.0%. 
Previous evidence suggests that closed-end funds trade at a premium when first offered. After approximately 120 days this premium turns to a discount (Lee, Shleifer, and Thaler, 1991). No such reversal was evident in the discount for SPDRs. Statistical examination of Figures 1 and 2 are not suggestive of a shift in the mean discount overtime. Examinations of the percentage (unadjusted and adjusted) discounts in MidCap SPDRs result in similar conclusions.
Analogous to the SPDRs data discussed above, we obtained price and index data for MidCap SPDRs from the CRSP and DRI databases. For these depositary receipts, the percentage discount is computed as (S&P400 -- MidCap SPDR)/S&P400* 100, where S&P400 is the level of the Standard and Poor's MidCap 400 index and MidCap SPDR is five times the closing price of Standard and Poor's Midcap 400 Depositary Receipts. Again to appropriately compare index and depositary receipt prices, we must compute an adjusted price by deducting the dividends accumulated since the last ex-dividend date from the MidCap SPDRs price. Because dividends for the MidCap 400 index are not available on a daily basis, we used the weekly dividend yield to approximate the daily dividend.  Further, because capital gains distributions are held by the Trust when a company leaves the index until year-end, the adjusted price also reflects these distributions. For MidCap SPDRs, there were fairly large capital gains distributions in 1996 and 1997, whi ch have significant impact on the adjusted price.
B. Rational Pricing in Depositary Receipts Markets
Table III reports summary statistics for the percentage discount each day since introduction of the two depositary receipts: January 1993 through December 1997 for the SPDRs and April 1995 through December 1997 for the MidCap SPDRs.  The discount is calculated using two SPDR series: unadjusted and adjusted to reflect the accrued dividends that would be paid on redemption. The table reports the mean, median, maximum, minimum, and standard deviation of the discount, as well as a t-test of the null hypothesis that the mean discount is zero and an F-test of the null hypothesis of equal mean discount in SPDRs and MidCap SPDRs.  Importantly, inference depends on proper adjustment of the SPDRs series for accrued dividends.
The mean SPDRs discount without adjustment is actually a significant premium. However, given the different dividend payment patterns for SPDRs and the stocks underlying the S&P500 index portfolio, adjustment for dividends is appropriate. With adjustment for accumulated dividends, we find a statistically significant discount in the pricing of SPDRs (t=4.01). Whether the discount is economically significant is another question altogether. A discount of 0.0686% translates into a dollar amount of only 41 cents, or for a round-lot trade of SPDRs of $4.10.  Trading commissions can easily account for this discrepancy.  Index arbitrage studies provide further insight into arbitrage profitability. Estimates of the total costs of index arbitrage between cash index and futures markets range from 0.31 to 1.0% of index value (MacKinlay and Ramaswamy, 1988, Chung, 1991, and Neal, 1996). Even with moderate arbitrage costs, the average mispricing of 0.0686 percent does not indicate the existence of profitable arbitr age opportunities. 
Similarly, the average unadjusted (adjusted) discount in MidCap SPDRs is 1.0363 (1.3167) and, with a t-statistic of 21.72 (47.69), the discount is statistically significant at the 0.01 level. Unlike the SPDRs discount, the MidCap SPDRS mispricing appears to be economically significant. The discount of 1.32% translates into a dollar amount of $64.97 for a round-lot trade. However, although it is significant, mispricing of 1.32% is substantially lower than that observed for closed-end mutual funds, which is, on average, 10%.
Table III also provides a comparison of the percentage discount across SPDRs and MidCap SPDRs. The characteristics of the two depositary receipts are very similar, though the MidCap index is likely to have higher arbitrage costs. Because the S&P500 index consists of large companies with high trading volume, it is easier to replicate than the S&P MidCap 400 index and, thus, MidCap SPDRs likely have higher fundamental risk. Arbitrage involves more risk if the fundamental value of the position is difficult to hedge. In addition, larger transactions costs are generally associated with smaller firms. Finally, the dividend yield on the S&P MidCap 400 index is lower than that of the S&P500 index. Since MidCap SPDRs commenced trading, the underlying index has provided a yield of 1.85% whereas the S&P500 index has yielded 2.42% since SPDRs began trading. These differences suggest that mispricing in the MidCap SPDRs market will exceed that in the SPDRs market. Referring to Table III, we see greater mispricing in the M idCap SPDRs market as compared to the SPDRs market, as expected, and this difference is statistically significant with an F-statistic of 1,189.66 (3,397.67) for the unadjusted (adjusted) series. 
Table IV provides the results of an examination of absolute pricing efficiency in SPDRs and MidCap SPDRs markets. Pontiff (1996) argues that the absolute value of the discount is the proper measure of mispricing because arbitrage costs are related to the magnitude of mispricing, rather than its level. For SPDRs, the absolute percentage discount is computed as \S&P500 - SPDR\/[S&P500.sup.*]100, where S&P500 is the level of the Standard and Poor's 500 index and SPDR is ten times the closing price of Standard and Poor's Depositary Receipts. Similarly, for MidCap SPDRs, the absolute percentage discount is computed as \S&P400 - MidCap SPDR\/[S&P400.sup.*]100, where S&P400 is the level of the Standard and Poor's MidCap 400 index and MidCap SPDR is five times the closing price of Standard and Poor's Midcap 400 Depositary Receipts. As in the earlier examination of pricing efficiency, the absolute discount is calculated using two SPDR series: unadjusted and adjusted to reflect accrued dividends and capital gains dist ributions. The table reports the mean, median, maximum, minimum, and standard deviation of the absolute discount, as well as a t-test of the null hypothesis that the mean absolute discount is zero and a Wilcoxon test of the null hypothesis of equal median absolute discounts across SPDRs and MidCap SPDRs markets.
The results reported in Tables III and IV lead to similar inferences. The statistically significant absolute discounts in Table IV indicate mispricing in SPDRs and MidCap SPDRs, though whether the mispricing leads to arbitrage opportunities is arguable. After adjustment for accrued dividends, the extent of mispricing in SPDRs is only 0.1395%, which for around lot SPDR trade translates into $8.39. Transactions costs may exceed the possible profits generated from trade.
Finally, we compare the volatility of returns on depositary receipts to that of the underlying index. Pontiff's (1997) results contradict the efficient market hypothesis because, on average, his sample of closed-end funds have monthly return variances that are 64% larger than net asset value return variances. If investors rationally price funds based on expected fundamental values, the variances of the two returns should be equal. Thus, if the log variance ratio of monthly returns for closed-end funds to net asset value exceeds one, a fund's return is excessively volatile. Following Pontiff, if the log variance ratio of returns for a depositary receipt to the underlying index is greater than one, the returns to the traded stock basket are excessively volatile and prices do not rationally reflect fundamental value. For SPDRs, the volatilities are extremely close. Instead of observing excess volatility as Pontiff did, we find that the SPDRs volatility is actually slightly less than the volatility of the S&P500 index returns using monthly adjusted returns. The estimated SPDR volatility is 0.43% less than the S&P500 volatility (i.e., the log variance ratio is just less than one). For the MidCap SPDRs, slight excess volatility exists with the monthly adjusted returns variance 1.26% larger than the volatility of the underlying index returns. Higher excess volatility is consistent with higher arbitrage costs in the MidCap SPDRs market.
The results reported above suggest that the characteristics of SPDRs result in a very small discount and economically insignificant mispricing. However, significant mispricing in MidCap SPDRs markets is indicated. In addition, volatility estimates are very close to predictions based on the efficient market hypothesis for both S&P500 and MidCap SPDRs. Consistent with Pontiff's (1996) arguments, the magnitude of SPDRs mispricing is low, because arbitrage costs are low. SPDRs have little fundamental risk, high dividend yield, and low transactions costs, all of which enhance the pricing efficiency of the market.
VI. Discussion and Conclusion
One of the basic concerns of corporate finance is raising capital for new investment. Well-functioning financial markets are critical because these markets facilitate the allocation of capital to its most productive uses. This paper examines the functioning of the market for Standard and Poor's Depositary Receipts, units of trusts that are designed to replicate the S&P500 and MidCap 400 indexes. We find no economically significant mispricing in the S&P500 SPDRs market, though prices in the MidCap SPDRs market deviate more significantly from fundamental value.
Our evidence suggests that these new and actively traded securities are priced relatively efficiently in the market, particularly in comparison to closed-end funds. Consistent with our expectations, we report a larger discount for MidCap SPDRs. These depositary receipts likely have higher arbitrage costs due to higher fundamental risk, higher transactions costs; and lower dividend yields. Further, the results suggest that investor sentiment does not have an important role in SPDRs pricing despite the fact that SPDRs are held predominantly by individual investors. Sias (1997) provides insight into this finding. In his study of the role of institutional investors in closed-end fund pricing, Sias concludes that the importance of institutional investors in the market is not accurately reflected in ownership statistics. Instead he finds that the average percentage of trading volume by institutions is seven times their ownership. If institutional investors are rational traders in the SPDRs market, they may make th e marginal trades that eliminate mispricing.
Although we cannot argue that news about fundamental value is the only force that moves asset prices, arbitrage appears to successfully eliminate the effect of noise traders in the SPDRs market. However, economically significant mispricing is reported in the market for MidCap SPDRs. Although the MidCap index has a higher dividend yield, the redemption feature should minimize the impact of dividend capture. Differences in pricing efficiency across the two markets are likely explained by differences in fundamental risk. Arbitrage of mispricing is easier when fundamental value is easily and accurately measured. Because of the immense coverage and interest in S&P 500 firms, uncertainty about SPDRs' fundamental value is extremely low.
Economically significant discounts in S&P500 SPDRs prices do not arise even though the predominant holders of SPDRs are individual investors who may be subject to waves of optimism and pessimism. Investors with large holdings can redeem SPDRs and actually receive the underlying stock. This feature of the SPDRs market facilitates arbitrage as it minimizes fundamental and resale price risk. Thus, even if noise traders hold SPDRs, rational traders drive prices because, for these large traders, the limits to arbitrage are few.
The views expressed are those of the authors and not necessarily those of the Federal Reserve Bank of Atlanta or the Federal Reserve System. The authors thank Bryan Church, Doug Emery, Shane A. Johnson, and two anonymous referees for helpful comments, Cheryl Anderson Brown for editorial assistance, and Kendra Hiscox and Shalini Patel for research assistance.
(*.) Lucy F. Ackert is Professor at Michael J. Coles College of Business, Kennesaw State University and Visiting Scholar at the Federal Reserve Bank of Atlanta. Yisong S. Tian is Associate Professor at Schulich School of Business, York University.
(1.) We focus specifically on traded stock baskets that are not actively managed. However, we recognize that some brokerage firms offer unit investment trusts (UITs) to investors. There are significant differences between the traded stock baskets on which we focus and these UITs. Unit investment trusts offered by brokerage firms commonly include stocks that are chosen strategically or to provide exposure to a particular sector of the market. They typically involve commission costs in addition to trust operating expenses. Another important difference between traded stock baskets and these unit investment trusts is that it can be difficult for an investor to track the performance of the UITs. The UITs are not traded and investors cash out positions at the net asset value. Finally, UITs commonly have a fixed maturity of one to five years. By comparison, SPDRs have a fixed maturity of the first to occur of 1) the year 2118 or 2) 20 years after the death of 11 individuals named in the Trust agreement.
(2.) Similarly, in March 1990 the Toronto Stock Exchange (TSE) introduced Toronto Index Participation Units (TIPs), a traded stock basket designed to replicate the Toronto 35 index. Another example is DIAMONDS, which were introduced in January 1998 by the AMEX and are benchmarked on the Dow Jones Industrial Average.
(3.) Net asset value is computed by dividing total reported asset value less liabilities by the number of shares outstanding. After the closed-end fund shares are initially issued, all trades are between shareholders at prices determined by supply and demand. In contrast, shares in open-end funds are traded between the fund and shareholder at the net asset value.
(4.) Throughout the remainder of the paper, unless we specifically refer to the security as MidCap SPDRs, SPDRs should be interpreted in the narrow sense as meaning S&P500 SPDRs rather than in the broad sense as any depositary receipt.
(5.) For example, on July 30, 1998 SPDR volume was 7,680,500 shares though the number of units traded often exceeds 10 million. By comparison, the second and third most active AMEX issues on that day were Hanover Direct Inc. and Viacom Inc. with volumes of 2,499,900 and 1,124,800, respectively.
(6.) In addition to facilitating participation in the market by large and small investors, hedging and arbitrage strategies are easier to implement with a traded stock basket. Furthermore, these stock baskets may enhance market efficiency if they allow for more effective information transfer across stock and derivatives markets. The evidence concerning the impact of stock basket trading on market efficiency is mixed. Park and Switzer (1995) conclude that TIPs trading seems to have enhanced the efficiency of the Canadian index futures market. However, in their study of the impact of TIPs trading in the Canadian options market, Ackert and Tian (1998) conclude that the evidence does not support improved efficiency across stock and stock index options markets.
(7.) The investor sentiment hypothesis is not universally accepted. See, for example, Swaminathan (1996) and Chen, Kan, and Miller's (1993) comment on the work of Lee, Shleifer, and Thaler (1991) and their response (Chopra, Lee, Shleifer, and Thaler, 1993).
(8.) In addition to the three factors discussed subsequently, Pontiff (1996) argues that mispricing increases with increases in interest rates. He regresses the average absolute discount for his sample of funds on the level and change in the Treasury bill rate and finds that the discount increases with both. when we regressed the absolute value of the SPDR discount on the level and change in interest rates, the coefficient estimates were not significantly different from zero. Note that Pontiff's dependent variable is a cross-sectional average so that his analysis may provide more power with which to test the hypothesis. As many depositary receipts have only recently been offered by exchanges for trading, we did not have a cross-section of these securities with a sufficient time series available for analysis.
(9.) An alternative arbitrage strategy involves buying and immediately redeeming the SPDRS and then selling the shares received. Although this strategy requires no short sale of stock, some resale risk is involved because stock prices may move before the arbitrageur has the opportunity to sell the shares.
(10.) In the case of closed-end mutual funds, there is likely to be less arbitrage activity. Although fundamental value can be measured with little difficulty, it is not easily realizable. Shares in closed-end funds are not redeemable and must be sold in the open market. As a result, a sizable discount may persist over a prolonged period of time resulting in increased fundamental risk to arbitrageurs.
(11.) Although it is costly for an investor to replicate the S&P500 particularly with rebalancing, the index can be replicated fairly easily and inexpensively with S&P500 futures.
(12.) A comparison of Tables I and II reveals that in 1993 the number of SPDRs sold and outstanding differs by 150,000 or three creation units. This difference reflects the seed shares when the Trust was formed. Conversations with officials of the trustee indicated that, basically, the Trust started with 150,000 shares when trading commenced in 1993. Thus, the net asset value per SPDR is correctly computed for 1993 by dividing the total net asset value by 9.9 million. In subsequent years, the number of SPDRs outstanding is equal to the number outstanding the previous year, plus SPDRs sold, less SPDRs redeemed, plus SPDRs issued to satisfy dividend reinvestment.
(13.) Institutional ownership data is obtained from the June issue of the Standard and Poor's Stock Guide and the Spring issue of Moody's Stock Guide. Both issues were used to ensure complete, accurate information. Lee, Shleifer, and Thaler (1991) also get institutional ownership data from Standard and Poor's.
(14.) Information on institutional holdings was included in the stock guides for all stock issues as reported in note 13 with the exception of NextLevel Systems, Inc. NextLevel is the largest of three companies formed by the split of General Instrument Corporation in 1997, 50 we used institutional ownership data reported for General Instrument. Excluding this company does not change the 1997 average of 59%.
(15.) SPDRs trading concludes at 4:15 p.m., whereas trading of the S&P500 index's component stocks closes at 4:00 p.m.. Thus, the SPDR and S&P500 closing prices are not strictly synchronous. If the two closing prices differ significantly because a great deal of information is released in this 15 minute period, we would expect to find high correlation between changes in the S&P500 and lagged changes in SPDR prices. However, the contemporaneous correlation for daily data is 0.999, whereas the correlation between changes in the index and lagged changes in SPDRs prices is small (0.001). Although there is a potential for bias, the correlation results provide evidence that the effect of the 15-minute trading time differential is minimal. Further evidence that the 15 minute differential has little impact is provided by our examination of cash index-futures and SPDR-futures arbitrage. The S&P500 futures market closes at 4:15 p.m., as does the SPDRs market. Following Neal (1996) we compared mispricing using a cost of carry model. With transactions costs conservatively estimated at 0.3%, there are no violations for either cash index-futures or SPDRs-futures arbitrage relationships during our sample period.
(16.) Because the Trust accumulates dividends without interest, we do not incorporate the time value of money.
(17.) We discovered several omitted SPDR dividends in the CRSP database. After confirming that these were errors, we calculated the quarterly dividends using dividend payments on the component stocks. We compared the available SPDR dividends reported in CRSP to our computed values to ensure the accuracy of our method.
(18.) Though not included, for comparative purposes we examined the discount at the end of each month using unadjusted and adjusted SPDRs and the patterns are similar. We also examined monthly data constructed using beginning of month prices. Again inferences are unaffected.
(19.) To do so, we multiplied the weekly yield by the current index value and divided by five. This calculation assumes that the yield is constant over the days of the week and to the extent that the yield is nonconstant, the calculated daily dividend is not a perfect estimate. However, the dividend adjustment adds to the discount so that the bias should not affect inferences.
(20.) Conclusions are similar using monthly observation intervals.
(21.) In addition to the statistics reported in Tables III and IV, we conducted non-parametric tests because the distributions are non-normal. We performed tests of the hypothesis that the median discount is zero and two-sample Wilcoxon tests to compare the discounts in SPDRs and MidCap SPDRs. The non-parametric test statistics are all significant at the 0.01 level and inferences are consistent with those reported in the paper based on parametric tests.
(22.) The average SPDR price times ten for our sample period was 601.41, which when multiplied by 0.000686 gives 41 cents. A round-lot of SPDRs is considered to be 100 units so we multiplied again by 10 to get the mispricing of $4.10 on a round-lot basis.
(23.) Even the least expensive method of trading through the Internet has a minimum brokerage fee of about S 14.95.
(24.) Discrete price increments may further limit an arbitrageur's ability to take advantage of small price discrepancies.
(25.) These F-tests use the full sample for both series. We also compared mispricing in SPDRs and MidCap SPDRs for concurrent periods (April 1995 through December 1997) and inferences are similar.
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Descriptive Information for the SPDR Market
The table reports summary information for Standard and Poor's 500 Depositary Receipts (SPDRs) including the number of units outstanding, average daily trading volume, total trust investment, and net asset value per unit at year-end. The table also reports the year-end value of the S&P500 stock index.
Percentage Daily Discount in Unadjusted SPDRs
The figure shows the percentage discount in SPDRs each day for January 1993 through December 1997. The percentage discount measures the extent to which SPDRs are mispriced and is computed as (S&P500 -- SPDR)/S&P500* 100, where S&P500 is the level of the Standard and Poor's 500 index and SPDR is ten times the closing price of Standard and Poor's Depositary Receipts. The discount is calculated using the SPDR series that is not adjusted for accumulated dividends.
Percentage Daily Discount in Adjusted SPDRs
The figure shows the percentage discount in SPDRs each day for January 1993 through December 1997. The percentage discount measures the extent to which SPDRs are mispriced and is computed as (S&P500 - SPDR)/S&P500*100 where S&P500 is the level of the Standard and Poor's 500 index and SPDR is ten times the closing price of Standard and Poor's Depositary Receipts. The discount is calculated using the SPDR series that is adjusted for accumulated dividends.
Pricing Efficiency in the SPDRs and MidCap SPDRs Markets
The table reports summary statistics for the percentage discount each day in the SPDRs and MidCap SPDRs markets since their introduction: January 1993 through December 1997 for the SPDRs and April 1995 through December 1997 for the MidCap SPDRs. For SPDRs, the percentage discount measures the extent to which SPDRs are mispriced and is computed as (S&P500 -- SPDR)/S&P500 [*] 100, where S&P500 is the level of the Standard and Poor's 500 index and SPDR is ten times the closing price of Standard and Poor's Depositary Receipts. Similarly, for MidCap SPDRs, the percentage discount is computed as (S&P400 -- MidCap SPDR)/S&P400 [*] 100, where S&P400 is the level of the Standard and Poor's MidCap 400 index and MidCap SPDR is five times the closing price of Standard and Poor's Midcap 400 Depositary Receipts. The discount is calculated using two SPDR series: unadjusted and adjusted to reflect accrued dividends and capital gains distributions. The table reports the mean, median, maximum, minimum, and standard deviation of the discount, as well as a t-test of the null hypothesis that the mean discount is zero and an F-test of the null hypothesis of equal mean discounts across SPDRs and MidCap SPDRs markets.
Absolute Pricing Efficiency in the SPDRs and MidCap SPDRs Markets
The table reports summary statistics for the absolute percentage discount each day in the SPDRs and MidCap SPDRs markets since their introduction: January 1993 through December 1997 for the SPDRs and April 1995 through December 1997 for the MidCap SPDRs. For SPDRs, the absolute percentage discount measures the extent to which SPDRs are mispriced and is computed as \S&P500 - SPDR\/S&P50O* l00, where S&P500 is the level of the Standard and Poor's 500 index and SPDR is ten times the closing price of Standard and Poor's Depositary Receipts. Similarly, for MidCap SPDRs, the absolute percentage discount is computed as \S&P400 -- MidCap SPDR\/S&P400* 100, where S&P400 is the level of the Standard and Poor's MidCap 400 index and MidCap SPDR is five times the closing price of Standard and Poor's Midcap 400 Depositary Receipts. The absolute discount is calculated using two SPDR series: unadjusted and adjusted to reflect accrued dividends and capital gains distributions. The table reports the mean, median, maximum, mini mum, and standard deviation of the absolute discount, as well as a t-test of the null hypothesis that the mean absolute discount is zero and a Wilcoxon test of the null hypothesis of equal median absolute discounts across SPDRs and MidCap SPDRs markets.
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|Author:||Ackert, Lucy F.; Tian, Yisong S.|
|Date:||Sep 22, 2000|
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