Option trading and returns versus the 52‐week high and low

DOI: 10.1111/fire.12310

ORIGINAL ARTICLE

Option trading and returns versus the 52-week high and low

Siu Kai Choy1 Jason Wei2

1King's Business School, King's College London, London, UK

2Department of Management, University of Toronto Scarborough & Joseph L. Rotman School of Management, University of Toronto, Toronto, Ontario, Canada

Correspondence Jason Wei, Department of Management, University of Toronto Scarborough & Joseph L. Rotman School of Management, University of Toronto, 105 St. George Street, Toronto, Ontario M5S 3E6, Canada. Email: wei@rotman.utoronto.ca

Abstract We show that option traders suffer from the anchoring effect induced by the stock price's 52-week high or low. Specifically, (1) trading of all options decreases as the stock price approaches its 52-week high or low, (2) the buy?sell imbalance for calls decreases and that for puts increases as the stock price approaches its 52-week high, and the opposite occurs as the stock price approaches its 52-week low, and (3) the subsequent delta-hedged option returns for both calls and puts are higher as the stock price approaches its 52-week extreme.

KEYWORDS 52-week high or low, anchoring effect, option returns, underpricing

JEL CLASSIFICATION G14

1 INTRODUCTION

In technical analysis, the past high and low stock prices often serve, respectively, as resistance and support levels. For instance, Brock et al. (1992) demonstrate that investors treat the breaking of the resistance and support levels (defined as the maximum and minimum prices in the past 50, 150, and 200 days) as buy and sell signals. George and Hwang (2004) specifically examine the 52-week high and show that the stock price momentum can be explained by investors' reluctance in incorporating positive news when the stock price is near the 52-week high, a manifestation of the anchoring effect (Tversky & Kahneman, 1974). Driessen et al. (2012) take the idea to the options market and examine, among other things, the option-implied volatilities around the 52-week high and low (i.e., the extremes). They find that the implied volatility decreases when the stock price approaches the 52-week extremes, an indication of anchoring-induced sluggish incorporation of news into stock prices.

Driessen et al. (2012) do not examine option trading around the 52-week extremes. While they infer a possible underpricing of options from the decreasing implied volatility, they do not directly investigate the pricing of options.

Financial Review. 2022;1?36.

journal/fire

? 2022 The Eastern Finance Association. 1

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We complement their study by examining how option trading activities and option returns react to the stock price relative to its 52-week extremes.

We argue and show that the observed lower implied volatility does not unambiguously imply an anchoring effect, let alone predicting the overall impact on trading and option valuation. In that sense, our study goes beyond what Driessen et al. (2012) have already uncovered. We carry out independent investigations and offer new insights regarding the potential anchoring effect in option trading.

We develop three hypotheses around the potential anchoring effect. First, some option investors might be sluggish in incorporating new information as the stock price approaches its 52-week high or low and their delayed actions reduce the trading volume of both call and put options. However, those who react to new information and form different opinions (Choy & Wei, 2012) will trade more. We will see an overall decrease in trading only if the anchoring effect dominates. In the absence of an anchoring effect and/or if the differences of opinion dominate, we will see an overall increase in trading. This is our first hypothesis.

Second, the sluggish reactions to news imply less buying of calls and less selling of puts as the stock price approaches its 52-week high, and less buying of puts and less selling of calls as the stock price approaches its 52-week low. Therefore, we infer a decrease (increase) in the buy?sell imbalance for calls (puts) as the stock price approaches its 52-week high, and the reverse as the stock price approaches its 52-week low. This is our second hypothesis. The differences of opinion will affect buying and selling to the same extent and thus will not impact the buy?sell imbalance.

Third, the lower realized volatility due to the sluggish incorporation of new information might lead to a downwardbiased volatility forecast, which in turn leads to undervaluation of both calls and puts. This is a direct implication from the findings of Driessen et al. (2012). However, another factor is also at play, which leads to ambiguity in the overall valuation. Under the demand?pressure theory of Garleanu et al. (2009), the second hypothesis implies mispricing of calls and puts in the opposite direction (e.g., calls being undervalued, and puts being overvalued when the stock price approaches its 52-week high), albeit not unbridled due to the put?call parity. The demand?pressure effect and the volatility effect reinforce each other for calls (puts) when the stock price approaches its 52-week high (low), but they offset each other for calls (puts) when the stock price approaches its 52-week low (high). Translating prices into returns, when the stock price approaches its 52-week high (low), the subsequent delta-hedged returns are unambiguously higher for calls (puts); for the other two combinations--calls as the stock price approaches its 52-week low and puts as the stock price approaches its 52-week high--if the volatility effect dominates, we should see higher subsequent delta-hedged returns, and if the demand pressure effect dominates, we should see lower subsequent delta-hedged returns. The above constitutes our third hypothesis.

Sorting and regression analyses based on the buy?sell trading data from Cboe and the pricing data from OptionMetrics demonstrate a strong anchoring effect in both option trading and valuation. The empirical results are robust to various alternative specifications.

We make two contributions to the literature. We contribute to the broad literature of how the anchoring effect impacts asset prices. There are many studies on stocks (e.g., Brock et al., 1992; George & Hwang, 2004; Huddart et al., 2008), but the investigation of the anchoring effect in options is rare, with Driessen et al. (2012) being an exception. While they focus on implied volatility, we directly examine option trading and pricing. Moreover, as shown in the hypothesis discussion, their finding of lower implied volatility does not have unambiguous implications for trading, nor for valuation. Therefore, we both extend and complement Driessen et al. (2012).

We also contribute to the literature of option return determinants. The extant research shows that the deltahedged option returns are affected by volatility risk (Bakshi & Kapadia, 2003), idiosyncratic volatility (Cao & Han, 2013), the joint effect of mispricing and short-sale constraints (Ramachandran & Tayal, 2021), the level of illiquidity (Christoffersen et al., 2018), liquidity risk (Choy & Wei, 2020), and a host of stock market anomalies (Cao et al., 2022; Choy & Wei, 2022). We show that the delta-hedged option returns are also affected by the salient yet irrelevant 52week high or low of the stock price. Therefore, we demonstrate that option investors are also subject to behavioral biases.

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2 LITERATURE REVIEW, CONTRIBUTION, AND HYPOTHESIS DEVELOPMENTS

Our paper extends and contributes to two strands of literature: (1) the impact of investors' behavioral biases--the anchoring effect in particular--on trading and asset returns and (2) the cross-section determinants of delta-hedged option returns.

2.1 Anchoring effect

In their classic study, Tversky and Kahneman (1974) demonstrate the "anchoring-and-adjustment" heuristic, a cognitive bias in decision making. Simply put, an anchoring effect is the tendency for individuals to base their decisions on salient yet irrelevant factors. Take as an example the 52-week high or low of a stock price. Rationally speaking, whether the stock is attractive or not should solely depend on its current trading price relative to its intrinsic value; whether the current price is close to its 52-week extreme should be irrelevant. Yet, investors tend to take the past high or low as an anchor and make investment decisions accordingly.

While Brock et al. (1992) systematically examine how investors trade based on signals derived from the stock price breaking the maximum (resistance level) and minimum (support level) prices in the past 50, 150, and 200 days, George and Hwang (2004) are among the first to uncover the 52-week high anchoring effect. They postulate and show that the stock price momentum can be explained by investors' reluctance in incorporating positive news into stock prices when they are near the 52-week highs. In effect, they discover a positive relation between the ratio of the stock price over the 52-week high and the subsequent stock returns. George et al. (2018) rationalize this relationship with the q-theory of Hou et al. (2015).

Huddart et al. (2008) show that stock trading volume increases after the stock price crosses the 52-week high or low, and the heightened trading activity lasts for several weeks before settling back to the normal level. The postbreak, risk-adjusted returns are positive in the ensuing week and month. They attribute this to bounded rationality and the attention effect (Barber & Odean, 2008). Due to various constraints, investors are only able to pay attention to a selected group of stocks, especially when it comes to purchase decisions with a large choice set. Consequently, stocks with salient features (e.g., prices breaking the 52-week highs or lows) attract investors' attention, leading to more buying, which in turn results in higher trading volume and returns. They only focus on the postbreak volume and price.

Researchers have also examined the anchoring-induced behavioral biases in other settings. Baker et al. (2009) show that the 52-week high is frequently used by both bidders and targets in an M&A setting. An offering price set below the 52-week high is considered unattractive by the target, but the bidder may view such a price already generously inflated. In the earnings announcement setting, Birru (2015) confirms both the lower price expectation and the underreaction to news as stock prices approach their 52-week highs. Similarly, George et al. (2015) show that the postearnings announcement drift (PEAD) is mostly explained by the 52-week high--investors' anchoring prevents them from reacting to extreme earnings news in a timely fashion, leading to prolonged price effects after the announcement. Finally, Li et al. (2020) show that firms avoid undervaluation of their stocks by undergoing stock splits when the price is approaching its 52-week high.

To our best knowledge, there are only two studies that link the 52-week extremes to options. Manohar and Ngene (2018) demonstrate that the spread between implied volatilities of put and call options can predict future stock returns around 52-week highs and lows, which they argue is driven by informed option traders. Our study is largely inspired by Driessen et al. (2012) who examine the option implied volatilities, stock betas, and return volatilities around the 52-week highs and lows. They find that both the implied volatility and beta decrease when the stock price

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approaches the 52-week high or low, and that the stock return volatility increases after the stock price breaks the 52-week high or low.1

While they find an increase in stock trading as the stock price approaches and subsequently breaks its 52-week high or low, they do not examine option trading. Likewise, while they infer potential underpricing of options from the decrease in implied volatility, they do not directly investigate the potential mispricing of options. In fact, it turns out that one cannot make unambiguous predictions, based on the findings of Driessen et al. (2012), of either the option trading pattern or the mis-valuation. Therefore, not only do we confirm their findings, we also complement their study by examining how option trading activities and option returns are affected by the distance between the current stock price and its 52-week high or low.2

2.2 Cross-section determinants of hedged returns

Our study also contributes to the strand of literature that investigates the determinants of option returns. In the Black?Scholes world, delta-hedged returns should equal the risk-free rate. However, Bakshi and Kapadia (2003) find negative delta-hedged returns (after subtracting the risk-free rate), which they attribute to volatility risk. Other researchers show that option returns are also related to such factors as implied volatility (Goyal & Saretto, 2009), idiosyncratic volatility (Cao & Han, 2013), risk-neutral skewness (Bali & Murray, 2013), the joint effect of mispricing and short-sale constraints (Ramachandran & Tayal, 2021), the illiquidity level (Christoffersen et al., 2018), liquidity risk (Choy & Wei, 2020), variance risk premium (Han & Zhou, 2017), and a host of stock market anomalies (Cao et al., 2022; Choy & Wei, 2022). Our study is similar to Choy and Wei (2022) in nature. Kumar et al. (2021) show that daily winner and loser stocks substantially underperform other stocks after they acquire the attention-grabbing status. Choy and Wei (2022) investigate whether a stock's winner/loser status also affects its option returns. Analogously, motivated by the findings about the impact of the 52-week highs and lows on stock returns (e.g., George & Hwang, 2004), we investigate whether a stock's 52-week high or low affects option returns. We demonstrate that option investors trade less when the stock price approaches or breaks the 52-week high or low and their sluggish reactions to news make options mis-valued. Therefore, option investors are also subject to the anchoring effect.

2.3 Hypotheses

As shown by Driessen et al. (2012) and Huddart et al. (2008), investors' behavior after the stock price breaks its 52-week high or low is largely driven by the attention effect. Since our focus is on the anchoring effect, we only study option trading and returns before or during the stock price breaks its 52-week high or low. To this end, following George and Hwang (2004) and George et al. (2018), we define our key variable as the ratio of the current stock price over its 52-week high: price-to-high or PTH in short. Price-to-low (PTL) is defined analogously. When the stock price is approaching its 52-week high, PTH increases and achieves its maximum value of one when the stock price is equal to the 52-week high. On the other hand, PTL is above one and achieves its minimum value of one when the stock price reaches its 52-week low. For ease of exposition, we put a negative sign in front of PTL so that when PTH or PTL increases, the stock price is approaching its previous extremes.

Our first hypothesis links the potential anchoring effect to option trading. Option trading can be motivated by either new information (e.g., Pan & Poteshman, 2006) or differences of opinion (Choy & Wei, 2012), or both. Upon

1 For completeness, we replicate tab. III in Driessen et al. (2012). We are able to confirm the results under approaching (i.e., when the stock price is approaching its 52-week high or low) in their sample period of 1996?2008. Moreover, we find similar and stronger results in the later sample period of 2008?2018. 2 In fact, there are numerous studies that examine other behavioral biases among option investors. For instance, Liu et al. (2021) examine herding, disposition effect, and overtrading in the context of market liquidity versus volatility.

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the arrival of new information, regardless of its positive or negative nature, the trading of both call and put options could increase--the heightened trading by the informed and those who have different interpretations of the news. However, in the presence of an anchoring effect, the net effect on trading is ambiguous.

On one hand, the decrease in implied volatility in both call and put options as the stock price approaches its 52week high or low (observed by Driessen et al. (2012)) implies a potential anchoring effect, namely, option investors trade less as the current stock price approaches its previous extreme. For instance, as the stock price approaches its 52-week high, positive information is not compounded into the current price in a timely fashion, and investors tend to scale back trading while waiting for the new trading signal--the breaking of the 52-week high. The same logic applies when the stock price is approaching its 52-week low. On the other hand, investors less prone to the anchoring effect but more likely to form different opinions from the stock price movement will trade more. Therefore, the net effect on trading depends on which phenomenon dominates. The above can be summarized in the following hypothesis:

Hypothesis 1: As the stock price approaches its 52-week high or low, that is, as PTH or PTL increases, the trading of both call and put options could increase or decrease. If the anchoring effect dominates, then we should see a decrease in trading; if there is no or a weak anchoring effect, then the effect of differences of opinion dominates and we should see an increase in option trading.

The potential anchoring effect allows us to further delineate trading along the lines of buying versus selling. Three essential elements shall assist us in further delineations. First, investors become bullish when they receive positive information and bearish when they receive negative information. Second, a bullish or bearish view can be traded upon with alternative option positions. For instance, a bullish investor could either buy a call option or sell a put option. Third, the reverse also applies. For example, if investors perceive less positive information than usual, they will buy fewer calls and sell fewer puts. With the above in mind, we can make the following predictions. When the stock price approaches its 52-week high, the incorporation of positive information into stock and option prices is delayed, leading to less buying of calls and less selling of puts. As a result, other things being equal, the buy?sell imbalance of calls should go down and that of puts should go up. Similarly, when the stock price approaches its 52-week low, the slow incorporation of negative information leads to less buying of puts and less selling of calls. Therefore, all else being equal, the buy?sell imbalance of calls should go up and that of puts should go down. This leads us to the following hypothesis:

Hypothesis 2: If there is an anchoring effect in option trading, then we should observe the following: as the stock price approaches its 52-week high, the buy?sell imbalance of calls should decrease and that of puts should increase; as the stock price approaches its 52-week low, the buy?sell imbalance of calls should increase and that of puts should decrease.

Driessen et al. (2012) observe a decline in the implied volatility as the stock price approaches its 52-week high or low, but if the lower implied volatility accurately reflects the ex ante volatility, then options are not undervalued. On the other hand, an undervaluation could ensue if option investors use a volatility forecasting model, which heavily relies on the recently realized volatility (e.g., Model 11 in Bekaert & Hoerova, 2014). In this case, the volatility forecast is derived from an artificially lower realized volatility caused by the slow incorporation of new information due to the anchoring effect.

However, the biased volatility forecast is not the only channel leading to a potential mis-valuation. Demand pressure also plays a role. Garleanu et al. (2009) postulate that the net positive demand from investors would push up option prices due to risk-averse market makers' inability to perfectly hedge their positions. The flipside of this argu-

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