Background
In the autumn of 1987, more precisely on October 19th, the world witnessed the unfolding of the first contemporary global financial crisis. A “cascade effect” of market distress led to the total crash of global stock exchanges within a matter of hours. In a single trading session in the United States, the Dow Jones Industrial Average (DJIA) decreased by 22.6 percent, a drop that remains the largest one-day decline in the history of the stock market. During this period, there was also the sharpest downturn in the market in the United States since the Great Depression.
By demonstrating the unprecedented extent to which financial markets throughout the world were intertwined and technologically interconnected on Black Monday, the events highlighted the concept of "globalization," which was still fairly new at the time. A number of notable reforms resulted from Black Monday, including provision for exchanges to temporarily pause trading if markets sell off rapidly. Furthermore, the Federal Reserve's response established a precedent for the central bank to use "liquidity" to mitigate financial crises in the future. Regulations and economists identified several probable causes following Black Monday: international investors were increasingly active in US markets in the preceding years, which accounts for some of the rapid share price appreciation prior to the crisis.
Portfolio Insurance
The events of October 19th, or what led up to that disastrous trading day, are often associated with rising interest rates and portfolio insurance. Many people believe rising rates played a fundamental role in the recession, but it did not.
The initial price decline triggers a vicious circle by causing portfolio insurers to sell, which causes further price declines, which cause portfolio insurers to sell again, and so on (indeed, the cascade effect we mentioned earlier). The lack of buyers aggravated the circumstances, leading softwares to lower prices more and more. Even though portfolio insurers appeared
more secured, it is generally believed that portfolio insurers themselves mainly contributed to the sell-off through the automatization of the sell order process.
The Black-Scholes model at the core of the portfolio insurance did not forecast the likelihood of a crash, since the random walk model indicates that a major one-day drop like this would not occur in a million years.
Black-Scholes model
The Black Scholes model assumes that stock prices follow a log-normal distribution, which ensures that they will never be negative, suggesting that extreme moves are less likely as the stock price approaches zero. Nevertheless, by looking at the relation between the mean and median, it is straightforward that this assumption has some flaws.
The original Black-Scholes model assumed constant volatility and log-normal price distributions. However, in reality empirical asset return distributions exhibit fatter tails due to market crashes being more common and significant than otherwise assumed in the model.
The median is the middle number, so the returns to the right of the median have a 50% chance of occurring. On the other hand, the mean is the average, which can be thought of as the expected return. As option prices are priced on expected returns, actual realized returns greater than the mean will be a profit, and vice versa.
As the median is less than the mean in a log-normal distribution, this implies that a trade is profitable less than 50% of the time. But it can be seen from empirical data that this is clearly wrong. Furthermore, this implies that every trade is likely to have a negative expected value, resulting in zero trades from any rational market participant.
In order for the distribution to be consistent with empirical evidence, the median needed to be greater than the mean. To achieve this, the log-normal function was skewed mathematically. This resulted in the birth of the volatility skew.
The market crash questioned the accuracy of the Black-Scholes model, and the “volatility smile” revealed that large market movements in prices are more plausible than the theory predicts. In graphical terms, a volatility smile represents the skewed pattern created when implied volatilities of multiple options contracts share the same expiration date.
A smile is recorded when out of the money or in the money options show higher implied volatility than that of at the money options, and the first volatility smile recorder in financial history was, indeed, in the aftermath of the Black Monday stock market crash.
Going back to the events of October 19th, the huge collapse can't be explained by a single cause. To understand the reasons for this dramatic event we must do a general and complex analysis of the wide-ranging economic situation. We have to understand what are the unusual factors which could generate and feed this drop. A lot of important economists identified in the portfolio insurance the main reason for the drop; in fact, this strategy had been growing rapidly in importance over the few years before the crash.
However, not all the studies consider portfolio insurance as the most important reason for the drop but in all of them it is considered an important factor.
The trigger factor was an unexpected high merchandise trade deficit which pushed interest rates to new high levels. Because of that, a lot of institutions employing portfolio insurance strategies started to sell and they triggered the "cascade effect" mechanism.
The portfolio insurance is a dynamic hedging technique, developed in order to limit the losses a portfolio could suffer from the drop in an index level, but without having to physically sell the stocks included in the index; thus, it relies entirely on derivatives contracts, mainly futures and options.
Why was this tool so used at the time?
Because it represented a technological innovation of the theory of dynamic trading strategies. The development of technology was fundamental for the invention of portfolio insurance which can be dated from the Black-Scholes option pricing paper of 1973, which showed how to create a synthetic option by a dynamic trading strategy involving a share of stock and cash. The first time that was used was in 1780 and after this, its use in investment had a really rapid growth.
Portfolio insurance has been a real fad but studying it in detail one can realize that in reality it has not spread regularly. In fact, its use tended to be stable until 1985, at which it began to increase rapidly. If investors were responding instantaneously to information, we should have seen portfolio insurance come in with a bang in 1972 (when first drafts of the Black-Scholes paper were circulated, and when it was very clear how to create a synthetic option).
However, the cascading effect that was triggered in 1987 after a first weekly collapse that then led to Black Monday is not only due to portfolio insurance. In fact, through analysis and surveys addressed to the population after the collapse and to those who had predicted the drop, it was seen that in most of them there was a bad feeling about a possible collapse due in particular to the fact that the American market was continuously in rise for the past 5 years and many thought that the market was overpriced and that a collapse was inevitable.
Moreover, a fair part was also concerned about the high US debt. So, as soon as there was the first weekly drop in October 1987, many saw it as a first sign of the imminent collapse and began to sell, taken by fear, triggering the process that led to the black Monday.
Why did it fail?
The question is then, why portfolio insurance strategies were not effective during October 1987. To answer this question, we must analyze the preconditions on which the strategy itself relies on, that are:
1. Low transaction costs
2. Price continuous markets.
Both those preconditions were not met during the 1987 crisis, in particular in spot, futures and options markets bid-ask spread widened substantially, and thus it was more costly to dynamically hedge the positions, significantly lowering the performance of the strategy. In addition to this, on October 19th, we had the most significant one-day drop in price of the DJIA, which went down by more than 22%. Without getting too much into the mathematical definition, a price-continuous market refers to a market where price movements are way smoother than a 22% drop in a single day. Further going into the intra-day movements, the changes in value of the most important market indices occurred so rapidly that it was almost impossible to execute the necessary number of future transactions during those times.
We have now seen how the market affected the performance of portfolio insurance strategies, the question remains on whether this strategy affected the market during the Black Monday, and if so to what extent.
The research carried out by Mark Rubenstein in 1988 (Portfolio Insurance and the Market Crash, Financial Analysts Journal Jan. - Feb. 1988, Vol. 44) analyzes the main factors contributing to the crash; according to the authors’ view, “Any investor who unexpectedly reduced his holding of stocks, shorted stocks, covered long future positions or increased open sold futures position on October 19th contributed to the crash”. As in any market crash, the “cascade effect” is what eventually determines whether the crash will happen or not. Therefore, what was the role played by portfolio insurers in this cascade effect? Rubenstein points out that portfolio insurers accounted for about 12% of the dollar change in net sold position on Black Monday, and it is difficult to say if such a percentage of market share is substantial to define the portfolio insurance strategies as the cause of the market crash.
In addition to this, we must remember that the higher the transaction costs, the lower the trades a portfolio insurer would execute, and thus the hedging strategy in a market where transaction costs are high would stop before the full hedged that would be otherwise implemented. The author suggests a list of potential causes for the crash, such as:
1. The unjustified and unprecedented rapid rise in market prices over the years before the crash. This would indeed lead to a bubble that eventually has to crash.
2. The Dow’s decline over the two months before the crash, that left many investors ready to liquidate some of their position.
3. The fear of increasing interest rates and a resurgence of inflation
4. Failures of the market
This last point is particularly interesting, as the author suggests that the market itself, and its inefficiency in handling large numbers of actors playing at the same, lead to a lack of trust in the system itself. The NYSE’s SUPER DOT (the electronic system used to execute orders at the time) experienced a massive mechanical failure because of the system overload, which led the system to be even more loaded because investors were placing additional orders to cash their positions.
The author addresses another main point, that is the fact that the crash was international in scope, while the portfolio insurance market played a small role in foreign (with respect to the U.S.) markets. In addition to this, after the crash there was a prolonged increase in volatility, for which it is difficult to blame the portfolio insurance strategies. Thus, in the authors’ view, other and more important factors have been at work at the time.
In conclusion, we can say that Cascade effects of portfolio insurance might be one important factor, but the simple story does not settle the issue, a large role during the ’87 market crash was played by investors’ behavior.
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