Efficiency in index options markets and trading in stock baskets

Abstract

Researchers have reported mispricing in index options markets. This study further examines the efficiency of the S&P 500 index options market by testing theoretical pricing relationships implied by no-arbitrage conditions. The effect of a traded stock basket, Standard and Poor’s Depository Receipts (SPDRs), on the link between index and options markets is also examined. We find that pricing efficiency within option markets improves but there is little evidence to support the hypothesis that a stock basket enhances arbitrage across markets. When transactions costs and short sales constraints are included, very few violations of inter-market pricing relationships such as put–call parity are reported. However, violations of within market pricing relationships such as the box spread remain frequent. Extensive analysis suggests that the results are robust.

Introduction

The no-arbitrage principle is a powerful tool in the pricing of financial assets because it does not rely on strong assumptions about traders' behavior or market price dynamics. The principle simply assumes that if riskless profit opportunities exist, arbitrageurs enter the market and quickly eliminate the mispricing. Arbitrage is critical to ensure market efficiency because it forces asset prices to return to their fundamental values. In some situations, market frictions limit arbitrage so that arbitrageurs cannot take advantage of the profit opportunities presented by mispricing. For example, in a market with capital constraints, arbitrageurs may be ineffective in their attempts to move the market toward an efficient state if they cannot raise the capital necessary to form the riskfree portfolio (Shleifer and Vishny, 1997).

Some earlier studies report evidence of mispricing of index call and put options in the US (Evnine and Rudd, 1985, Chance, 1986, Chance, 1987) and Canada (Ackert and Tian, 1998), though arbitrage may be limited due to liquidity risk (Kamara and Miller, 1995). Liquidity risk arises from the possibility of an adverse price movement before a desirable trade can be executed. If options are priced inefficiently, an arbitrage transaction requires trade in multiple assets and, in the case of index options, one of these assets is itself a stock portfolio consisting of many assets. Thus, mispricing may not be an indication of market inefficiency because the asset underlying the options is not easily or costlessly reproduced. To arbitrage from mispriced stock index options, an investor may need to replicate the index, i.e., the investor may need to buy or sell a basket of stocks that is perfectly correlated with the index. This can be difficult and costly even for large investors.

In the 1990s, stock exchanges introduced index derivative products that replicate stock baskets and trade just like any other share of stock. These exchange-traded funds are not actively managed and are designed to track an existing stock index. For example, since March 1990 investors in Canada are able to trade Toronto Index Participation Units (TIPs) which are constructed to track the performance of the Toronto 35 index. In the United States, the American Stock Exchange (AMEX) introduced Standard and Poor’s Depository Receipts (SPDRs), or spiders, in January 1993. This index derivative product is designed to replicate the S&P 500 stock index. Efficiency should be enhanced with the introduction of these traded stock baskets because market participants can easily replicate the asset underlying index option contracts.

The objective of this study is to empirically examine the efficiency of the market for S&P 500 index options. Earlier studies find frequent violations of theoretical option pricing relationships. In addition to providing new results on the efficiency of the S&P 500 index options market, our study extends this research by examining the effect of a traded stock basket on the effectiveness of information exchange between index and option markets and on option market efficiency. We investigate whether index options are priced correctly relative to one another by testing theoretical pricing relationships implied by no-arbitrage conditions, both before and after the inception of SPDRs trading. These no-arbitrage conditions place bounds on possible call and put option prices (boundary conditions, call and put spreads, and convexity) and imply relative pricing relationships between put and call option prices (put–call parity, box spread). We compare the number and size of violations in S&P 500 index option relations before and after the introduction of SPDRs. Significant violations of pricing relations across option and stock markets (boundary conditions and put–call parity) after the introduction of SPDRs indicate market inefficiency if arbitrage based on these violations can be executed with relatively low cost and effort with the trading of a stock basket. Other arbitrage relations we examine are independent of the stock price (box, call, and put spreads and convexity). These tests provide insight into how the efficiency of the options market has evolved over time and are not dependent on simultaneous data from options and stock markets (Ronn and Ronn, 1989).

All of the pricing relationships we examine are independent of an option pricing model so that no assumptions concerning the process underlying the stock price are required. Thus, empirical tests of these types of relationships are true tests of market efficiency instead of joint tests of market efficiency and model specification. We adjust for discrete dividend payments and recognize the limits that transaction costs, including the bid–ask spread, and short sales constraints place on arbitrage. We conduct additional analysis to investigate the sensitivity of our results. We use both nonparametric tests that are free of distributional assumptions and parametric tests. We conduct ex ante tests to investigate whether arbitrage opportunities persist and examine the effect of index futures trading on the link between option and stock markets. Finally, in addition to examining option market efficiency and the impact of SPDRs trading, we investigate whether no-arbitrage violations are systematically related to time, the term to maturity, movements in the stock market, or liquidity risk.

Since SPDRs were first offered in 1993, the product has become one of the most actively traded issues on the AMEX. SPDRs are exchange-traded funds that represent an interest in a trust with accumulated dividends paid quarterly. The cash dividend reflects a pro rata amount of regular cash dividends accumulated by the trust during the preceding quarterly period. SPDRs are designed to approximate 1/10th of the value of the S&P 500 index, so that trading prices will fall in the range of a typical stock. An investor who holds a prescribed number of SPDRs may actually redeem them for the underlying stock at any time. This feature is particularly important because it reduces liquidity risk and facilitates arbitrage (Ackert and Tian, 1999). With this stock basket, investors can trade a single security that represents a diversified portfolio of the corporations in the S&P 500 index.²

The results reported subsequently indicate significant mispricing of call and put options both before and after the introduction of SPDRs. However, once transaction costs are included in the analysis, we report substantially fewer violations in boundary conditions and put–call parity over the entire sample period, consistent with earlier research by Kamara and Miller (1995). We find that inequality violations disappear once short-sales restrictions are recognized for those relationships that require short sales, as did Kamara and Miller. However, as they note, the results continue to suggest the possibility of unexploited arbitrage opportunities for traders who own the asset.

When we recognize these limits to arbitrage, we do not observe a significant reduction in the median boundary or put–call parity violations after SPDRs are introduced. Thus, the impact of SPDRs trading is limited in practical terms because of the significance of other trading costs including commissions, bid–ask spreads, and short sales constraints. We also report a decrease in violations of relationships that are independent of the stock price (box, call, and put spreads and convexity) suggesting an improvement in the pricing of options relative to each other.

The remainder of the paper is organized as follows. In Section 2 we review the evidence concerning the efficiency of index option markets. In Section 3 we describe our methodology. The data employed in our examination of option market efficiency and the empirical results are described in Section 4. Section 5 reports the results of additional analysis into the determinants of violations of pricing relations. The final section provides discussion of the results and concluding remarks.