Beyond Greed and Fear

by Hersh Shefrin

  You will observe that 20 billion years is longer than a century. Yet in this century we have observed the 1929 crash, the 1987 crash, and the October 1989 minicrash. In other words, option traders seriously underestimated the probability of a crash. So the challenge is how to reconcile the volatility values we observe with a higher probability of crash events.

  The solution is to replace lognormality with a distribution that has a fatter lower tail and is skewed to the left. The high implied volatilities associated with low exercise prices are picking up that fat tail. In other words, the prices of the options are much higher than occur in a Black-Scholes setting, not because of higher volatility but because of skewness. Crashes simply occur more frequently than the Black-Scholes lognormal framework admits.

  So what causes crashes? Robert Shiller (1993b) reports the results of a survey he ran within days of the 1987 crash to try and answer this question. What he discovered was the absence of fundamental news to trigger the decline. No precipitating news event sparked the fall. The most frequent response by investors was that “the market was overvalued.” I translate that as sentiment.

  Implied Volatility as a Forecasting Variable

  Linda Canina and Stephen Figlewski (1993) argue that implied volatility is neither a good predictor of future volatility nor a good reflection of past volatility. If so, this suggests that investors are not very good at forecasting market volatility.

  Before examining some evidence, recall one of the lessons discussed in chapter 5, concerning the character of efficient forecasts. The point was that forecasts should be less volatile than the variable being forecast. But for many people, their predictions are about as variable as the series they are trying to predict, because their predictions are guided by representativeness.

  With this in mind, consider the average of the implied volatilities of call options with exercise prices between 900 and 995. Figure 19-3 below shows how the average implied volatility moved over the period April 17, 1997, through May 19, 1998. This was a time when the S&P 500 moved from 768 to over 1100, crossing 1000 on February 2, 1998. The figure also includes a curve of subsequent S&P 500 volatility, measured over a moving window of forty trading days. For each date, the implied volatility curve shows the market’s forecast of future

  Figure 19-3 Comparison Implied Volatility, 900 Calls versus Subsequent Realized Volatility

  Does implied volatility serve as an efficient forecast for subsequent actual volatility? In an efficient market, it would. Given the smile or sneer pattern, we need to figure out which implied volatility to use. The most common choice of implied volatility is the one associated with at-the-money call options. During the period shown in the chart, implied volatility was higher than actual volatility for most of the time. It is also very volatile itself: efficient forecasts tend to be less volatile than the variable being forecast. Representativeness tends to induce excessive volatility in forecasts. volatility, whereas the subsequent volatility curve shows what volatility turned out to be over the next forty trading days.

  Recall that a forecast should fluctuate less than the variable whose value is being predicted. Does the implied volatility curve in figure 19-3 fluctuate too much relative to actual volatility? I leave that one to you.

  Index Options and Market Swings

  David Bates (1991) suggests that in 1987, investors’ fears of a crash could be perceived in index option prices. For comparable exercise prices, he found considerably higher put-option implied volatilities than call-option implied volatilities. This led him to construct what he called a “crash premium.”

  The summer of 1998 was another interesting period when it comes to the way index option prices reflect investors’ concerns. By the end of August 1998, the S&P 500 had declined almost 20 percent, relative to the all-time high it reached just six weeks earlier. Wall Street Journal writer Suzanne McGee suggested that one reason for the stock sell-off might have been the high cost of index options. She also mentions the role that index options played in the 1987 crash, a point to which I return. She wrote:

  In past sell-offs, market participants and analysts have worried that derivative products, designed to protect individual portfolios, have in fact exacerbated market declines. During the stock market crash of October 1987, for instance, money managers seeking to protect their holdings aggressively sold stock index futures even as the market slid, sending indexes to new lows that in turn triggered still more selling.

  But this sell-off is different. Some market participants believe it was the absence, rather than the presence, of the right kind of derivative products at an affordable price that made a sell-off almost inevitable.

  “By the time Monday arrived, volatility had gone up so much that it was far, far too expensive to buy put options,” says Scott Fullman, option-market strategist at Swiss American Securities in New York. …

  On July 31, when the index closed at 1120.7, investors could buy the right to sell the index at 1010 in or before the third week of September for only $10. That means they could lock in 10% downside for about 1% of the index’s value for a period of seven weeks.

  By the time the dust settled late Monday, the S&P 500 had fallen to 957.50, below the 1010 strike price, and the option’s premium had soared to $68. Yesterday, as the market rebounded, the premium fell back to only $33. Still, to lock in seven weeks’ worth of 10% downside protection from yesterday’s S&P 500 close would cost $18, or nearly 18% almost double levels of a month ago.8

  What does Suzanne McGee’s discussion mean in terms of implied volatilities? The implied volatilities associated with a 10 percent decline had gone from under 30 percent to over 40 percent.

  At the beginning of the excerpt, McGee describes the sale of stock index futures during the crash of 1987. This instance provides a dramatic illustration of assumption risk. Money managers had purchased “portfolio insurance,” a synthetic put option that in theory replicates an actual put option through a dynamically adjusted combination of Treasury bills and a short position in index futures. But in the crash of 1987, the unanticipated volume led to major problems with order execution, thereby preventing the synthetic put from being properly formed.

  Overreaction

  I interviewed soybean trader Sheldon Natenberg about the volatility of implied volatility. His response was instructive: “Markets in general tend to overreact. This is probably true of implied volatility as well. Part of volatile volatility is psychological. But it also has to do with weaknesses in the model.”

  Jeremy Stein (1989) studied whether the index option market tends to overreact. Specifically, he asked whether long-term options overreact to short-term shocks. For example, a sudden unexpected move in the market may lead to an increase in the implied volatility of options that expire in the month or so. But by the law of averages, the impact on options that expire many months away should be much less. In fact, the longer the time to expiration, the closer the implied volatility should be to the long-term historic volatility of 20 percent.

  What does the implied volatility curve look like for long-term options? In May 1998, the longest available options on the S&P 500 expired in December 1999. Figure 19-4 shows the implied volatilities at various exercise prices. Notice that with the exception of the 750 calls, the remaining volatility pattern is quite flat.9 This pattern is typical for LEAPS, including the dip at the left.

  Are implied volatilities for LEAPS stable or do they move too quickly in response to short-term events? This is the essence of the overreaction question. Consider a comparison between the implied

  Figure 19-4 S&P 500 Implied Volatility, December 1999 Calls

  The pattern for long-term option volatilities tends to be much flatter than the pattern for options expiring in the short term. For very long options, implied volatilities should hover around mean historical volatility. Overreaction occurs if long-term volatilities react to financial news in a comparable way as their short-term counterparts. volatilities for the June 1998 calls and Decembe
r 1999 calls for two dates, roughly one month apart.

  On April 21, 1998, the S&P 500 closed at 1126.7. On that date, implied volatility for an at-the-money June call was 19 percent, while implied volatility for the December 1999 LEAPS was about 21 percent. One month later, on May 19, the S&P 500 was a little lower at 1109.52, and implied volatility for an at-the-money June call had fallen to 17 percent. But as we saw in figure 19-4, the implied volatility for December 1999 LEAPS had climbed 2 percent, to 23 percent.

  Because the long-term volatilities moved in the opposite direction from their short-term counterparts, I am not sure I would call this an instance of overreaction. But by the same token, I wouldn’t call the long-term implied volatilities stable. I should mention that the overreaction issue raised by Stein has produced something of a controversy. A study by Diz and Finucane (1993) using a different time period claims to find no evidence of overreaction.

  Using Options to Measure Sentiment

  Is there evidence of sentiment in option trading? Natenberg suggests that unlike the case of futures, where traders are content to make the bid-ask spread, “option traders try to create positions that are consistent with their opinions.”

  The call-put ratio (CPR) is defined as the ratio of open daily call volume to open daily put-option volume. Users of the CPR, mostly technical analysts, believe that when investors become more optimistic, option traders increase their holding of call options relative to put options. Hence, they believe that an abnormally high reading of this index signals considerable optimism. In other words, they believe that the CPR is a sentiment indicator, just like the Bullish Sentiment Index discussed in chapter 6.

  As they do with the Bullish Sentiment Index, technical analysts treat the CPR as a contrarian indicator. In his book on technical analysis, Thomas Meyers (1989, 1994) states that a buy signal is generated when the inverse of the CPR, the put/call ratio, exceeds 0.55.10 Billingsley and Chance (1988) argue that the put/call ratio is in fact positively correlated with returns, thereby supporting the claims advanced by technical analysts.

  Consider two questions. First, does the recent evidence support the claim that the CPR is a contrarian indicator? Second, what drives the CPR?

  Figure 19-5 Call/Put Ratio and the Subsequent Gains in the S&P 500 Index, January 1995–November 1998

  Some technical analysts believe that when investors are unduly optimistic, they buy more call options than put options. As a result, analysts treat the ratio of open calls to open puts as a sentiment index, believing that extreme sentiment tends to be unwarranted. In other words, that when the call/put ratio is low, the market subsequently tends to rise. The chart plots the subsequent percentage change in the S&P 500 against the call/put ratio. The gain in the S&P 500 is measured as 1 plus the change. On the whole, the two series tend to move inversely.

  Figure 19-5 displays the comovement of the call/put ratio and the gain to the S&P 500 over the subsequent 60-day period. The subsequent movement (60 days later) is vertically aligned with the value of the CPR. When we look at figure 19-5, it does seem that when the call/put ratio goes up, the S&P 500 subsequently turns down.11 Hence the evidence does support the claim that the CPR is a contrarian indicator.

  The second question asks about the determinants of the call/put ratio. For example, when we looked at the Bullish Sentiment Index, we found that its value was largely driven by past movements in the market. The Bullish Sentiment Index is an excellent predictor of the past. Is the same true for the call/put ratio? Yes, because technical analysts are trend followers.

  Summary

  All three behavioral themes can be identified in option markets. This chapter explained how options are used and priced, and how they reflect sentiment.

  Usage: Covered-call writing is the most popular option-trading strategy among individual investors. Its popularity largely stems from frame dependence, especially the ability to segregate gains and achieve a psychological counterbalance for losses on the underlying stock. As I indicated, the connection between option premiums and cash dividends is very important for investors inclined to write covered calls.

  Pricing: Heuristic-driven bias leads to a smile effect that distorts the connection between implied volatility and actual volatility. The implied volatilities attached to index options with low exercise prices are unrealistically high. Rubinstein (1995) uses the term crashophobia to describe one aspect of this effect. Just as other markets do, option markets exhibit overreaction, a consequence of representativeness. Most academic scholars believe that option prices are determined by arbitrage and that therefore prices are free from the influence of sentiment. The behavior of implied volatilities relative to actual volatilities suggests the contrary.

  Sentiment: The call/put ratio does appear to capture a key aspect of sentiment. Moreover, the evidence supports an inverse relationship between the call/put ratio and subsequent movements in the market.

  Chapter 20 Commodity Futures: Orange Juice and Sentiment

  The frantic hand signals that commodity traders use in the trading pits suggests that prices are extremely volatile. Is this impression accurate?

  From the perspective of market efficiency, the question about volatility boils down to whether commodity prices overreact to the flow of new material information. From the outside, it is often difficult to judge how germane the flow of information actually is. However, in a very clever article, Richard Roll (1984) suggests that we can use one commodity market to evaluate those information flows. That commodity is orange juice concentrate, where the most relevant fundamental variables that change on a day-to-day basis are the weather around Orlando, Florida, and the supply of oranges from Brazil.

  There are many kinds of players in the market for orange juice concentrate:

  • large fruit companies such as UniMark,

  • beverage companies like Tropicana and Coca Cola (maker of Minute Maid orange juice),

  • large funds speculating on the direction of commodity prices,

  • “paper guys”—traders in the ring who handle orders from account executives or trade for their own accounts, and

  • those in search of what orange juice trader Frank Tesoriero calls a “cheap coffee analogy.”1

  The bottom line is that heuristic-driven bias by these traders causes the price of orange juice concentrate to be excessively volatile relative to the underlying fundamentals. In other words, sentiment impacts the market for concentrate. Usually, excess volatility is a manifestation of trader overreaction, either to news that has occurred or to the absence of news altogether.

  This chapter discusses the following:

  • the institutional structure of the concentrate market

  • the importance of Orlando weather

  • the volatility of prices for orange juice concentrate

  • four short cases about the reaction of concentrate prices to changes in Florida weather, events in Brazil, and nothing at all

  The Institutional Structure of the Market for Orange Juice Concentrate

  Orange juice concentrate is traded on the floor of the New York Cotton Exchange. At any one time there are usually nine futures contracts being traded, with the delivery dates being two months apart. For example, on July 26, 1997, contracts were available for delivery in September 1997, November 1997, January 1998, and so on up through January 1999. A single contract is for 15,000 lbs. of orange solids, standardized by concentration (termed “degrees Brix”). Prices are quoted in cents per pound. For example, on July 26, 1997, the closing price for the March 1998 contract was 82.55¢ per pound.

  Why Florida Weather Is So Important

  What makes orange juice futures so special, as far as studying volatility is concerned, is that almost all of the U.S. orange crop—more than 98 percent—used to manufacture concentrate is grown in a single geographic location: near Orlando, Florida. As we shall see later, oranges grown in Brazil are also used to make orange juice concentrate. However, the important point is that this high
ly localized production enables us to track much of the key information flows about the supply of oranges.

  With the current technology, natural conditions impair producers from making short-term adjustments to capacity. Why? Because it takes between five and fifteen years before a newly planted orange tree is mature enough to produce fruit. So most of the time, markets will witness little day-to-day variation in the supply of oranges to the market.

  Orange juice concentrate is, of course, the key ingredient in orange juice, be it fresh or frozen. So, it is reasonable to expect that the retail price of orange juice would play a key role in the price of concentrate. The factors that drive the retail price of orange juice tend to be quite stable—consumer tastes, consumer incomes, the different ways to consume orange juice, and the prices of substitute products such as apple juice. Roll reports that these factors do not exhibit a lot of day-to-day variation.

  So, where does this leave us? Demand conditions appear to be quite stable. The retail price of orange juice is quite stable. Production capacity is quite stable. How about Florida weather?

  The most critical weather events for a citrus crop are freezes. A severe freeze can destroy the entire crop. In fact, an 1895 freeze not only destroyed the crop, but also killed almost every tree. Today, advances in technology have made Florida citrus trees more resistant to freezing temperatures. However, several successive days of below-freezing temperatures can still wreak havoc on the crop. The harvesting of oranges occurs from autumn through early summer. A freeze will damage fruit, prompting trees to drop significant amounts prematurely.