Irrational Exuberance and Option Smiles

Disagreement among investors is pervasive. Some investors see a trend and predict continuation; others see the same trend and predict reversal. Some investors overreact; others underreact. I explain how disagreement can and does cause markets to be inefficient. And I argue that option markets are particularly vulnerable in this respect; the “volatility smile” associated with index options is one manifestation of inefficiency stemming from heterogeneous beliefs. As part of the argument, I discuss an event study about “irrational exuberance,” the term Alan Greenspan, chair of the U.S. Federal Reserve Board, used in late 1996 to describe stock market sentiment. To study this event, I combined the information gleaned from option-pricing data with other information about market sentiment to assess the impact of heterogeneous beliefs on market efficiency. Do investors overreact, as the evidence on long-term reversals suggests? Or do they underreact, as the evidence on short-term momentum suggests? The truth is that some investors overreact and others underreact. Some observe a recent trend in security prices and predict continuation; others observe the same trend and predict reversal. Because markets serve to aggregate disparate beliefs, this issue is important for market efficiency. For example, some scholars argue that because investors overreact about as often as they underreact, markets are efficient.I explain how investor disagreement can and does cause markets to be inefficient. I argue that option markets are particularly vulnerable in this respect. Even when the strength of bullish opinion is matched by that of bearish opinion, bulls overbid the prices of index call options and bears overbid the prices of index put options. The result is mispricing at both ends of the exercise-price spectrum. The effect is a pronounced “volatility smile”—that is, the volatilities associated with intermediate exercise prices are lower than at the extremes, both low and high, which is a common characteristic in index option pricing.When a market trend has been conspicuous, individual investors tend to predict continuation of the trend but professional investors tend to predict reversal. For this reason, the study described here focused on the latter part of 1996, when the uptrend in market prices was particularly notable. In fact, the trend was so salient that on December 5, 1996, in a remark that gained worldwide attention, Alan Greenspan, the chair of the U.S. Federal Reserve Board, used the term “irrational exuberance” to describe U.S. stock market sentiment. I show that during November 1996, not all investors were irrationally exuberant; in fact, disagreement among investors was strong—and prices were inefficient.To study efficiency of the market and investor sentiment in November and December of 1996, I used indicators to track the sentiment of advisory newsletter writers, individual investors, and option traders. For tracking option trader sentiment, I obtained daily data of implied volatilities and estimated the time series of risk-neutral probabilities for all S&P 500 Index options traded from June through December of 1996. For each listed S&P 500 option, I obtained the price, date, and time of the last trade, the bid price, the ask price, and trading volume. I also obtained the closing price of the S&P 500 and the prevailing three-month U.S. T-bill rate. I focused on the December 1996 options because they expired about two weeks after Greenspan's irrational exuberance remark.By and large, I found that bullish sentiment among newsletter writers and individual investors was above average and rising during November. During the course of the month, the option volatility smile intensified, which suggests that differences of opinion were growing.I also found that traders in index options were becoming increasingly pessimistic as the S&P 500 rose during the course of the month. In theory, the risk-neutral probabilities associated with call options are the same as those associated with puts. But during the latter part of November, the risk-neutral probabilities derived from calls were markedly different from the probabilities derived from puts and indicated growing trader pessimism. The character of the risk-neutral probabilities also suggests that arbitrage was not fully carried out at the time, so arbitrage profits were possible.