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Estimation of
the European
Equity Model

European Bond
and Currency Markets
in Anticipation of
Monetary Union


Volatile Markets
BARRA Models

Part One:
The Case for
the Market Neutral

BARRA announces new
managing director of
research

The BARRA Brainteaser
for Winter 1999

Solution for the Fall 1998
Brainteaser

Volatile Markets and BARRA Models

by Neil Gilfedder and Kenneth Hui

The U.S. equity markets were sharply negative in August, 1998. That, perhaps, is the bad news. The good news is that BARRA’s US E-3 model performed remarkably well. In this article, we will assess the scale of August’s market movement, and then look at how well the US E-3 model explained, forecast, and reacted to it.

How unusual was August? The graph below illustrates the distribution of monthly total returns of the S&P 500 from January, 1973 through September, 1998. Over that period, the mean monthly return was 1.00%, and the standard deviation was 4.47%. As a result, August’s return of -14.4% was a 3.2-standard-deviation (or 3.2-sigma) event. The graph also shows that there have been four 3-standard-deviation events since 1973. In other words, 3-sigma events occurred 1.3% of the time during the 309-month period considered.

FIGURE 1: S&P 500 Returns, 1973-1998

If the S&P 500’s total returns followed a normal distribution, we’d expect to see 3-sigma events occurring 0.26% of the time. The returns, in fact, are somewhat "fat-tailed" (or have positive kurtosis), implying that big events occur more frequently than they would under a normal distribution. Active returns, however, do tend to follow a normal distribution.

Given that August was a significant and unusual month, how did the model do at explaining its market movement? The model uses 65 common factors (13 risk indices and 52 industries) to explain asset returns. The proportion of variance in return explained by the variance in the common factors is measured by the R-squared. In August, the R-squared was 80%, compared with a historical average of 32.8%. The R-squared will tend to be higher when there is major market movement, because the co-movement of stocks will dominate the movement of stocks relative to other stocks, and this co-movement is largely explained by the model’s common factors. The high R-squared is nevertheless an indication that the model’s factors provide a good ex-post explanation of August’s events.

FIGURE 2: Factor Returns vs Beta, August 1998

The predicted betas also performed well. Predicted beta is a measure of the degree to which assets co-vary with the market. Assets with higher betas should decline more when the market declines. In August, this happened: the higher-beta risk indices and industries had larger negative returns than did lower-beta factors. This is illustrated in the following graph.

Finally, how unexpected was August’s market-movement? And how did the model react? The model’s forecast of the S&P 500’s volatility is based on an extended GARCH time-series regression. This methodology results in a model that responds quickly to large events in the market. Hence, the forecasts better reflect the historical observation that markets tend to become more volatile after large downturns and less volatile after large upturns. Going into August, the predicted volatility was 14.76%. In other words, the return was predicted to be in the range of ± 14.76% per year (or ± 4.26% per month) with approximately a two-thirds probability. After August, the forecast volatility rose to 17.33% in response to the downturn, exhibiting the responsiveness of GARCH models. As the markets became less turbulent in subsequent months, the forecast volatility fell. Going into January, 1999, the predicted volatility of the S&P 500 was 13.95%

Large-scale market movements are difficult to predict, but investors who use BARRA’s U.S. equity risk model have an advantage. The model’s powerful common factors, which explain much of the movement, enable those investors to expose themselves only to risks similar to their benchmark’s, and hence, not to stray far from the benchmark’s returns. In addition, the model is quick to react to changes in the market, thus allowing investors to react swiftly and take altered market conditions into account.