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Arbitrage and Valuation in the Market for Standard and Poor's Depositary Receipts.



Yisong S. Tian Tian
 or T'ien
(Chinese; “Heaven”)

In indigenous Chinese religion, the supreme power reigning over humans and lesser gods. The term refers to a deity, to impersonal nature, or to both.
 [*]

This paper examines pricing in the market for depositary receipts depositary receipt

A negotiable certificate that represents a company's publicly traded debt or equity. Depositary receipts are created when a company's shares or bonds are delivered to a depositary's custodian bank, which instructs the depositary to issue
, securities designed to track the performance of a stock index that trade like shares of stock. Arbitrage arbitrage: see foreign exchange.
arbitrage

Business operation involving the purchase of foreign currency, gold, financial securities, or commodities in one market and their almost simultaneous sale in another market, in order to profit from price
 costs are low because these assets have low fundamental risk, low transactions costs Transactions costs

The time, effort, and money necessary, including such things as commission fees and the cost of physically moving the asset from seller to buyer. Transcations costs should also include the bid/ask spread as well as price impact costs (for example a large sell
, and high dividend yields. We find that Standard and Poor's Noun 1. Standard and Poor's - a broadly based stock market index
Standard and Poor's Index
 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 determinant, a polynomial expression that is inherent in the entries of a square matrix. The size n of the square matrix, as determined from the number of entries in any row or column, is called the order of the 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 mid·cap  
adj.
1. Or or relating to corporations whose retained earnings and outstanding shares of common stock have a value between those of small cap companies and large cap corporations.

2.
 SPDRs. MidCap SPDRs are designed to track the performance of the S&P MidCap 400 index, an index of moderate capitalization capitalization n. 1) the act of counting anticipated earnings and expenses as capital assets (property, equipment, fixtures) for accounting purposes. 2) the amount of anticipated net earnings which hypothetically can be used for conversion into capital assets.  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 Closed-end fund

An investment company that issues shares like any other corporation and usually does not redeem its shares. A publicly traded fund sold on stock exchanges or over the counter that may trade above or below its net asset value. Related: Open-end fund.
.

Recently stock exchanges have introduced index derivative derivative: see calculus.
derivative

In mathematics, a fundamental concept of differential calculus representing the instantaneous rate of change of a function.
 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. [1] For example, in January 1993 the American Stock Exchange American Stock Exchange (AMEX)

Stock exchange in the U.S. Originally known as “the Curb,” it began as an outdoor marketplace in New York City c. 1850. It moved indoors to its present location in the Wall Street area in 1921.
 (AMEX AMEX

See: American Stock Exchange
) introduced Standard and Poor's Depositary Receipts (SPDRs), or spiders, designed to track the performance of the S&P 500 index. [2] 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 unstable,
adj 1. not firm or fixed in one place; likely to move.
2. capable of undergoing spontaneous change. A nuclide in an unstable state is called
radioactive. An atom in an unstable state is called
excited.
 and driven by waves of irrational ir·ra·tion·al
adj.
Not rational; marked by a lack of accord with reason or sound judgment.


irrational adjective Unreasonable, illogical
 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 Efficient Market Hypothesis

States that all relevant information is fully and immediately reflected in a security's market price, thereby assuming that an investor will obtain an equilibrium rate of return.
 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 Rebalancing

The process of realigning the weightings of one's portfolio of assets.

Notes:
For example, if your portfolio's proportion of stock has grown too large for your intended assets weightings and risk tolerance, you might rebalance by selling some stock and putting
, and the possibility of forced liquidation Forced Liquidation

An action taken by brokerage houses that offsets and closes all positions within delinquent customer accounts in order to reduce exposure.

Notes:
 (Lee, Shleifer, and Thaler THALER. The name of a coin. The thaler of Prussia and of the northern states of Germany is deemed as money of account, at the custom-house, to be of the value of sixty-nine cents. Act of May 22, 1846.
     2.
, 1991). In a costly arbitrage framework with noise traders Noise Trader

The term used to describe an investor who makes decisions regarding buy and sell trades without the use of fundamental data. These investors generally have poor timing, follow trends, and over-react to good and bad news.
, 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 rep·li·cate
v.
1. To duplicate, copy, reproduce, or repeat.

2. To reproduce or make an exact copy or copies of genetic material, a cell, or an organism.

n.
A repetition of an experiment or a procedure.
, the security's dividend yield, and transaction costs Transaction Costs

Costs incurred when buying or selling securities. These include brokers' commissions and spreads (the difference between the price the dealer paid for a security and the price they can sell it).
. Although a closed-end fund is a very simple security that typically holds other publicly traded securities, these funds are perplexing per·plex  
tr.v. per·plexed, per·plex·ing, per·plex·es
1. To confuse or trouble with uncertainty or doubt. See Synonyms at puzzle.

2. To make confusedly intricate; complicate.
, 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. [3]

This paper studies the pricing efficiency Pricing efficiency

Also called external efficiency; a market characteristic that prices at all times fully reflect all available information that is relevant to the valuation of securities.
 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. [4] 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. [5] According to according to
prep.
1. As stated or indicated by; on the authority of: according to historians.

2. In keeping with: according to instructions.

3.
 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 PDR

A trademark for Physicians' Desk Reference, a group of reference books containing drug listings, especially one for prescription drugs.


PDR 
 Services Corporation, 1996). [6] A share in a stock basket represents a unit of a trust and accumulated dividends Accumulated dividend

A dividend that has reached its due date, but is not paid out. See: Cumulative preferred stock.


accumulated dividend

See dividends in arrears.
 are paid quarterly. An important and distinctive fe ature of the stock basket is that an investor who holds a prescribed pre·scribe  
v. pre·scribed, pre·scrib·ing, pre·scribes

v.tr.
1. To set down as a rule or guide; enjoin. See Synonyms at dictate.

2. To order the use of (a medicine or other treatment).
 number of units can redeem redeem v. to buy back, as when an owner who had mortgaged his/her real property pays off the debt. The term also refers to paying the amount due and all charges after a foreclosure (due to failure to make payments when due) has begun.  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 re·deem  
tr.v. re·deemed, re·deem·ing, re·deems
1. To recover ownership of by paying a specified sum.

2. To pay off (a promissory note, for example).

3.
 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 pre·dom·i·nant  
adj.
1. Having greatest ascendancy, importance, influence, authority, or force. See Synonyms at dominant.

2.
 held by individual investors. If individual investors are noise traders who are subject to waves of optimism and pessimism pessimism, philosophical opinion or doctrine that evil predominates over good; the opposite of optimism. Systematic forms of pessimism may be found in philosophy and religion. , both closed-end funds and traded stock baskets may be underpriced un·der·price  
tr.v. un·der·priced, un·der·pric·ing, un·der·pric·es
1. To price lower than the real, normal, or appropriate value.

2.
 (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 IMPEDIMENTS, contracts. Legal objections to the making of a contract. Impediments which relate to the person are those of minority, want of reason, coverture, and the like; they are sometimes called disabilities. Vide Incapacity.
     2.
 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 hin·der 1  
v. hin·dered, hin·der·ing, hin·ders

v.tr.
1. To be or get in the way of.

2. To obstruct or delay the progress of.

v.intr.
 profitable trades. When the limits to arbitrage Limits to arbitrage is a theory which assumes that restrictions placed upon funds, that would ordinarily be used by rational traders to arbitrage away pricing inefficiencies, leave prices in a non-equilibrium state for protracted periods of time.  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 relating to relate prepconcernant

relating to relate prepbezüglich +gen, mit Bezug auf +acc 
 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 in·con·sis·ten·cy  
n. pl. in·con·sis·ten·cies
1. The state or quality of being inconsistent.

2. Something inconsistent: many inconsistencies in your proposal.
 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 ob·serv·a·ble  
adj.
1. Possible to observe: observable phenomena; an observable change in demeanor. See Synonyms at noticeable.

2.
. 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 Agency Costs

The costs resulting from an agent performing services for a principal.

Notes:
Agency costs are generally the commissions earned by agents.
See also: Agency Problem, Agent, Principal



Agency costs
 resulting from excessive management fees or poor expected future performance, illiquid Illiquid

An asset or security that cannot be converted into cash very quickly (or near prevailing market prices).

Notes:
A house is a good example of an illiquid asset.
See also: Cash, Liquidity



Illiquid

In the context of finance.
 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 prominence /prom·i·nence/ (prom´i-nins) a protrusion or projection.

frontonasal 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) [7] 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 textbook Informatics A treatise on a particular subject. See Bible.  treatment, if a depositary receipt sells at a discount in a frictionless market Frictionless Market

A theoretical trading environment where all costs and restraints associated with transactions are non-existent.

Notes:
The advent of discount brokers and their low commissions has brought the market closer to a frictionless state.
, an arbitrageur Arbitrageur

A type of investor who attempts to profit from price inefficiencies in the market by making simultaneous trades that offset each other and capture risk-free profits.
 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 Frictions

The "stickiness" involved in making transactions; the total process including time, effort, money, and tax effects of gathering information and making a transaction such as buying a stock or borrowing money.
 may prevent arbitrageurs from taking advantage of mispricing. For example, transactions costs (e.g., brokerage costs, bid-ask spreads Bid-Ask Spread

The amount by which the ask price exceeds the bid.

Notes:
For example, if the bid price is $20 and the ask price is $21 then the "bid-ask spread" is $1.
) 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. [8] 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 resale n. selling again, particularly at retail. In many states a "resale license" or "resale number" is required so that the state can monitor the collection of sales tax on retail sales.


RESALE.
 risk. [9] 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. [10] 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 Trading volume

The number of shares transacted every day. As there is a seller for every buyer, one can think of the trading volume as half of the number of shares transacted. That is, if A sells 100 shares to B, the volume is 100 shares.
 is substantial and transactions costs are relatively low, though trading in the MidGap market may entail entail, in law, restriction of inheritance to a limited class of descendants for at least several generations. The object of entail is to preserve large estates in land from the disintegration that is caused by equal inheritance by all the heirs and by the ordinary  greater cost. [11]

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 SPDR

The Standard and Poor's depositary receipt. This is a tracking stock which trades like an index mutual fund which follows the S&P 500. It trades continuously.


SPDR

See Standard amp; Poor's Depositary Receipt (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 CONSTITUENT. He who gives authority to another to act for him. 1 Bouv. Inst. n. 893.
     2. The constituent is bound with whatever his attorney does by virtue of his authority.
 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 pro·por·tion·ate  
adj.
Being in due proportion; proportional.

tr.v. pro·por·tion·at·ed, pro·por·tion·at·ing, pro·por·tion·ates
To make proportionate.
 undivided interests undivided interest n. title to real property held by two or more persons without specifying the interests of each party by percentage or description of a portion of the real estate.  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 Ticker Symbol

An arrangement of characters (usually letters) representing a particular security listed on an exchange or otherwise traded publicly. When a company issues securities to the public marketplace, it selects an available ticker symbol for its securities which investors
 SPY SPY. One who goes into a place for the purpose of ascertaining the best way of doing an injury there.
     2. The term is mostly applied to an enemy who comes into the camp for the purpose of ascertaining its situation in order to make an attack upon it.
, 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 Ex-dividend date

The first day of trading when the buyer of a stock is no longer entitled to the most recently announced dividend payment ( i.e. the trade will settle the day after the record date, too late for the buyer to appear on the shareholder record and receive the dividend.
 falling on the third Friday of March, June, September, and December. The cash dividend reflects a pro rata [Latin, Proportionately.] A phrase that describes a division made according to a certain rate, percentage, or share.

In a Bankruptcy case, when the debtor is insolvent, creditors generally agree to accept a pro rata share of what is owed to them.
 amount of regular cash dividends accumulated ac·cu·mu·late  
v. ac·cu·mu·lat·ed, ac·cu·mu·lat·ing, ac·cu·mu·lates

v.tr.
To gather or pile up; amass. See Synonyms at gather.

v.intr.
To mount up; increase.
 by the Trust during the preceding quarterly period. Accumulated Trust expenses are deducted de·duct  
v. de·duct·ed, de·duct·ing, de·ducts

v.tr.
1. To take away (a quantity) from another; subtract.

2. To derive by deduction; deduce.

v.intr.
 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 e·quate  
v. e·quat·ed, e·quat·ing, e·quates

v.tr.
1. To make equal or equivalent.

2. To reduce to a standard or an average; equalize.

3.
 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 proportional

values expressed as a proportion of the total number of values in a series.


proportional dwarf
the patient is a miniature without disproportionate reductions or enlargements of body parts.
 amount of the dividends received for the quarter prior to the date of redemption, less expenses of the Trust and any accrued ac·crue  
v. ac·crued, ac·cru·ing, ac·crues

v.intr.
1. To come to one as a gain, addition, or increment: interest accruing in my savings account.

2.
 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. [12] 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 Institutional Investor

A non-bank person or organization that trades securities in large enough share quantities or dollar amounts that they qualify for preferential treatment and lower commissions.
 held less than 5% of the SPDRs outstanding but by 1994 institutional holdings grew to 23%. [13] The increase in institutional interest in SPDRs tapered ta·per  
n.
1. A small or very slender candle.

2. A long wax-coated wick used to light candles or gas lamps.

3. A source of feeble light.

4.
a.
 off at that time and in 1997 was 25%. By comparison, average institutional ownership in the stock composing com·pose  
v. com·posed, com·pos·ing, com·pos·es

v.tr.
1. To make up the constituent parts of; constitute or form:
 the Trust was almost constant at 59% in 1993 and 1997. [14] In computing computing - computer  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.

A. Data

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 CRSP Collaborative Research Support Program (USA)
CRSP Collaborative Research Support Program
CRSP Center for Research in Security Prices
CRSP Center for Research in Security Prices
 daily database and the S&P500 index and dividend data are from Standard and Poor's Corporation through the DRI See Digital Research.  database. [15] Although calculation of the discount appears to be straightforward, consideration of dividends introduces a complication complication /com·pli·ca·tion/ (kom?pli-ka´shun)
1. disease(s) concurrent with another disease.

2. occurrence of several diseases in the same patient.


com·pli·ca·tion
n.
.

The cash flows from purchasing (or short selling Short Selling

The selling of a security that the seller does not own, or any sale that is completed by the delivery of a security borrowed by the seller. Short sellers assume that they will be able to buy the stock at a lower amount than the price at which they sold short.
) 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 To perform mathematical operations or general computer processing. For an explanation of "The 3 C's," or how the computer processes data, see computer.  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 Redemption date

The date on which a bond matures or is redeemed.


redemption date

The date on which a debt security is scheduled to be redeemed by the issuer. The redemption date is the scheduled maturity date or, if applicable, a call 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%. [18]

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 suggestive of Decision making adjective Referring to a pattern by LM or imaging, that the interpreter associates with a particular–usually malignant lesion. See Aunt Millie approach, Defensive medicine.  a shift in the mean discount overtime. Examinations of the percentage (unadjusted and adjusted) discounts in MidCap SPDRs result in similar conclusions.

Analogous analogous /anal·o·gous/ (ah-nal´ah-gus) resembling or similar in some respects, as in function or appearance, but not in origin or development.

a·nal·o·gous
adj.
 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. [19] 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 Rational pricing is the assumption in financial economics that asset prices (and hence asset pricing models) will reflect the arbitrage-free price of the asset as any deviation from this price will be "arbitraged away".  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. [20] 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 In statistics, the average amount a number varies from the average number in a series of numbers.

(statistics) standard deviation - (SD) A measure of the range of values in a set of numbers.
 of the discount, as well as a t-test of the null hypothesis null hypothesis,
n theoretical assumption that a given therapy will have results not statistically different from another treatment.

null hypothesis,
n
 that the mean discount is zero and an F-test of the null hypothesis of equal mean discount in SPDRs and MidCap SPDRs. [21] Importantly, inference (logic) inference - The logical process by which new facts are derived from known facts by the application of inference rules.

See also symbolic inference, type 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. [22] Trading commissions can easily account for this discrepancy DISCREPANCY. A difference between one thing and another, between one writing and another; a variance. (q.v.)
     2. Discrepancies are material and immaterial.
. [23] Index arbitrage Index Arbitrage

An investment strategy that attempts to profit from the differences between actual and theoretical futures prices of the same stock index. This is done by simultaneously buying (or selling) a stock index future while selling (or buying) the stocks in that index.
 studies provide further insight into arbitrage profitability. Estimates of the total costs of index arbitrage between cash index and futures markets futures market, a commodity exchange where contracts for the future delivery of grain, livestock, and precious metals are bought and sold. Speculation in futures serves to protect both the developers and the users of the commodities from unfavorable and unpredictable  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. [24]

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. [25]

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 Wilcoxon test

a test used in statistics to compare paired data. Has the advantage of incorporating the size of the difference between the two sets of data in the comparison.
 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 ar·gu·a·ble  
adj.
1. Open to argument: an arguable question, still unresolved.

2. That can be argued plausibly; defensible in argument: three arguable points of law.
. 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 con·tra·dict  
v. con·tra·dict·ed, con·tra·dict·ing, con·tra·dicts

v.tr.
1. To assert or express the opposite of (a statement).

2. To deny the statement of. See Synonyms at deny.
 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 pre·dom·i·nant  
adj.
1. Having greatest ascendancy, importance, influence, authority, or force. See Synonyms at dominant.

2.
 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 Large Trader

A futures trader who holds or controls a single position that is equal to or greater than the CFTC specified reporting levels.

Notes:
Reporting levels, which require either the firm or the large trader to provide the necessary reporting documentation, change
, 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 The Federal Reserve Bank of Atlanta is responsible for the 6th District of the Federal Reserve, which covers Alabama, Florida, Georgia, and parts of Louisiana, Mississippi, and Tennessee.  or the Federal Reserve System. The authors thank Bryan Church, Doug Emery emery: see corundum.
emery

Granular rock consisting of a mixture of the mineral corundum (aluminum oxide, Al2O3) and iron oxides such as magnetite (Fe3O4) or hematite (Fe2O3).
, 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 Kennesaw State University, commonly known as Kennesaw State, is a public, coeducational university and is part of the University System of Georgia. It is located in Kennesaw, an unincorporated community in Cobb County, Georgia, United States, approximately 20 miles north of  and Visiting Scholar A visiting scholar, in the world of academia, is a scholar from an institution who visits a receiving university that hosts him where he or she is projected to teach (visiting professor), lecture (visiting lecturer), or perform research (visiting researcher  at the Federal Reserve Bank of Atlanta. Yisong S. Tian is Associate Professor at Schulich School of Business, York University York University, at North York, Ont., Canada; nondenominational; coeducational; founded 1959 as an affiliate of the Univ. of Toronto, became independent 1965. .

(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 Operating expenses

The amount paid for asset maintenance or the cost of doing business, excluding depreciation. Earnings are distributed after operating expenses are deducted.
. 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 Toronto Stock Exchange (TSE)

Canada's largest stock exchange, trading approximately 1,200 company stocks and 33 options.
 (TSE See Tokyo Stock Exchange.

TSE

1. See Tokyo Stock Exchange (TSE).

2. See 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 Dow Jones Industrial Average

The best known U.S. index of stocks. A price-weighted average of 30 actively traded blue-chip stocks, primarily industrials including stocks that trade on the New York Stock Exchange.
.

(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 Open-End Fund

A mutual fund that continues to sell shares to investors, and will buy back shares when investors wish to sell.

Notes:
Open-end funds have no limit to the number of shares they can issue. The majority of mutual funds are open end.
 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 Small investor

An individual person investing in small quantities of stock or bonds. This group of investors makes up a minimal fraction of total stock ownership.


small investor 
, 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 derivatives markets are the financial markets for derivatives. The market can be divided into two, that for exchange traded derivatives and that for over-the-counter derivatives. . 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 Index Futures

A futures contract on a stock or financial index. For each index there may be a different multiple for determining the price of the futures contract.

Notes:
For example, the S&P 500 index is one of the most widely traded index futures contracts in the U.S.
 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 coefficient /co·ef·fi·cient/ (ko?ah-fish´int)
1. an expression of the change or effect produced by variation in certain factors, or of the ratio between two different quantities.

2.
 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 re·deem  
tr.v. re·deemed, re·deem·ing, re·deems
1. To recover ownership of by paying a specified sum.

2. To pay off (a promissory note, for example).

3.
 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 Redeemable

Eligible for redemption under the terms of an indenture.
 and must be sold in the open market. As a result, a sizable siz·a·ble also size·a·ble  
adj.
Of considerable size; fairly large.



siza·ble·ness n.
 discount may persist over a prolonged pro·long  
tr.v. pro·longed, pro·long·ing, pro·longs
1. To lengthen in duration; protract.

2. To lengthen in extent.
 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 Years, The

the seven decades of Eleanor Pargiter’s life. [Br. Lit.: Benét, 1109]

See : Time
 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 Reinvestment

Using dividends, interest and capital gains earned in an investment or mutual fund to purchase additional shares or units, rather than receiving the distributions in cash.

1. In terms of stocks, it is the reinvestment of dividends to purchase additional shares.
.

(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 Refers to events that are synchronized, or coordinated, in time. For example, the interval between transmitting A and B is the same as between B and C, and completing the current operation before the next one is started are considered synchronous operations. Contrast with asynchronous. . 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 con·tem·po·ra·ne·ous  
adj.
Originating, existing, or happening during the same period of time: the contemporaneous reigns of two monarchs. See Synonyms at contemporary.
 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 mul·ti·ply 1  
v. mul·ti·plied, mul·ti·ply·ing, mul·ti·plies

v.tr.
1. To increase the amount, number, or degree of.

2. Mathematics To perform multiplication on.
 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 See parametric modeling, parametric symbol and PTC.  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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A numerical guide to investor feeling toward the securities markets that is constructed to determine whether certain segments of the investment community are bullish or bearish.
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Chopra, N., C. M. C. Lee, A. Shleifer, and R. H. Thaler, 1993, "Yes, Discounts on Closed-End Funds Are a Sentiment Index," Journal of Finance 48(2), 801-808.

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A form of market risk associated with the investment decisions of noise traders. The higher the volatility in market price for a particular security, the greater the associated noise trader risk

Notes:
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internationalization - internationalisation
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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.
Publication:Financial Management
Geographic Code:1USA
Date:Sep 22, 2000
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