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5/5/04
Alex Castaldo: Price Down, Volatility Up, Why?

Long ago in 1976 Fischer Black reported that implied and historical volatilities of individual stocks go up when the stock prices go down. He considered price changes over a fairly long interval (weeks or months). He noted that the effect could be quite pronounced. The explanation he proposed was "the leverage effect". [Studies of Stock Price Volatility Changes. Proceedings of the 1976 Meetings of the American Statistical Association, Business and Economics Statistics Section, pp. 177-181]

In 1982 Christie published a paper on the subject, with a similar finding. Volatility increases when prices are down and when interest rates are high. [Christie, A. (1982). The stochastic behavior of common stock variances. Journal of Financial Economics 10, 407 432]

The Leverage Effect

In the Corporate Finance literature it is generally accepted (both theoretically and empirically) that the volatility of a stock increases with increasing leverage. Leverage is defined as D / (D+E) where D is the amount of Debt and E is the market value of the company's stock. Often when we think of increasing leverage we imagine that the company issues more debt (D increases), but it can also occur if E decreases. Why does the vol increase? Intuitively if E is very small the company is near insolvency and its stock price has a strong response to news (positive or negative) hence the high volatility.

The problem with this explanation (as Christie already saw) is that the effect is not large enough to explain the volatility changes that we see. And even companies with little or no debt experience volatility increases.

The same phenomenon occurs with stock indexes (eg. S&P500) and their implied volatilites (eg. VIX). We are all familiar with the fact that VIX usually rises on a day in which S&P is down substantially. If anything the data show that stock index volatilities are MORE RESPONSIVE to price drops than the volatilities of individual stocks, which is also difficult to square with the Leverage Effect explanation.


An alternative explanation involves portfolio insurance. It is thought that some institutions wish to reduce their exposure when stock prices go down. For example a pension fund may need X billion dollars to pay retirement benefits. At the present time the value of the fund's portfolio is greater than this, but as it decreases towards X the fund may want to reduce its exposure to equities so as to be sure not to go below; it can do this either through the purchase of puts or through dynamic hedging strategies. If a lot of investors act this way (and we don't know if that is true or not), then it would have the macro effect of increasing the volatility of the S&P as its price went down.

An advantage of this explanation is that it is consistent with the observed difference between individual stocks and indexes. Institutions are interested in hedging their entire portfolio, not individual stocks.

A weak point is that we don't know who these portfolio insurers are and why they would predominate over the investors who wish to increase their exposure as stock prices go down. So the explanation is somewhat ad hoc.


In conclusion the case that price down implies volatility up is well established empirically, but there is no agreement in the literature as to why this happens. The two leading explanations have been presented.

 

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