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February 5th, 2010, 12:54 AM
Stock market volatility is the systematic risk faced by investors who hold a market portfolio (e.g., a stock market index fund). Schwert (1989b) has undertaken an extensive study of stock market volatility, using historical data back to the 19th century. Some of his major findings are illustrated in Figure 1, which plots quarterly stock market volatility for the post-World War II period.1 The figure shows that volatility moves counter cyclically, exhibiting spikes during recessions. Also, stock market volatility tends to increase dramatically during financial crises (such as the 1987 stock market crash, the 1997 East Asia crisis, and the 1998 Russian bond default) and periods of uncertainty (such as the 1962 Cuban missile crisis). Moreover, volatility, once risen, shows some inertia in that it reverts only slowly to its previous, low level.
Although the causes of stock market volatility are not well understood, some authors suggest that elevated stock market volatility might reduce future economic activity. Schwert (1989a) argues that stock market volatility, by reflecting uncertainty about future cash flows and discount rates, provides important information about future economic activity. Campbell et al. (2001), citing work by Lilien (1982), reason that stock market volatility is related to structural change in the economy. Structural change consumes resources, which depresses gross domestic product (GDP) growth. Another link between stock market volatility and output rests on a cost-of-capital channel. That is, an increase in stock market volatility raises the compensation that shareholders demand for bearing systematic risk. The higher expected return leads to the higher cost of equity capital in the corporate sector, which reduces investment and output. Consistent with these hypotheses about the link between stock market volatility and economic activity, Campbell et al. (2001) show that—after controlling for the lagged dependent variable—stock market volatility has significant predictive power for real GDP growth. Moreover, these authors also show that stock market volatility drives out returns in forecasting output. This finding deserves discussion.
Finance theory suggests that stock market returns rather than volatility have predictive power for investment and output because stock market returns are a forward-looking variable that incorporates expectations about future cash flows and discount rates. Several studies have confirmed the predictive power of stock market returns for investment and output, among them Fama (1981), Fischer and Merton (1984), and Barro (1990). On the other hand, the finding of Campbell et al. about the predictive power of stock market volatility for future economic activity is new, but the authors do not provide a theoretical explanation for the evidence. In this article, I try to reconcile the results of Campbell et al. with earlier empirical evidence on the predictive power of stock market returns and finance theory.
I first use Merton’s (1973) Intertemporal Capital Asset Pricing Model (ICAPM) to illustrate the relation between stock market returns and volatility. I show that stock market returns, the difference between stock market returns and a risk-free rate, are positively correlated with one-period-lagged variance, but are negatively correlated with contemporaneous variance. These results have been well understood in the literature (e.g., Pindyck, 1988). Past variance relates positively to excess returns because it contains information about conditional variance or risk. The contemporaneous relation between excess returns and variance is negative because of a volatility feedback effect. That is, a positive innovation in variance today implies higher expected future variance and, therefore, higher expected future returns. For future expected returns to be higher, the innovation in variance must be accompanied by a drop in the stock market price index. Early authors (e.g., Pindyck, 1988; Turner, Startz, and Nelson, 1989; and Dueker, 1991) have found some support for this hypothesized risk-return relation. However, while Turner, Startz, and Nelson (1989) and Dueker (1991) impose no model restrictions on the coefficients of the variance terms, Pindyck (1988) finds that data reject these restrictions over some sample periods. In this paper, I find that (i) past stock market variance has significant forecasting ability for excess returns; (ii) the risk price is found to be positive and precisely estimated; and (iii) the model restrictions are not rejected by data
After establishing the relation between excess returns and variance, it is straightforward to explain why stock market volatility drives out returns in forecasting output. According to the q theory of investment, an increase in stock market variance reduces investment—and hence output—contemporaneously because it raises the cost of capital. Lamont (2000), however, argues that investment expenditures react to changes in the cost of capital with lags. Therefore, stock market variance is negatively correlated with future investment and output. For the same reason, excess returns are expected to correlate positively with future output because excess returns correlate negatively with variance. It should be noted that excess returns—unlike variance—are hampered in their predictive power for future output because excess returns correlate positively with past variance, which in turn correlates negatively with future output. Because of these opposing effects, the predictive power of excess returns for future output is not as strong as the predictive power of variance. However, if the positive relation between excess returns and past variance is controlled for (i.e., adding past variance to the forecasting equation), excess returns might become significant and might even drive out variance because variance provides no additional information beyond excess returns in forecasting output.
I replicate the Campbell et al. (2001) result— that excess stock market returns are statistically insignificant in predicting GDP growth if stock market variance is also included in the forecasting equation—for the period 1963:Q1 to 1997:Q4. However, as postulated, I find that excess returns change from insignificant to marginally significant when I control for the lagged variance in the forecasting equation, meanwhile stock market variance changes from significant to marginally significant. I also analyze two more sample periods. One sample covers the entire postwar period (1947:Q2 to 2000:Q4), while the other sample spans the longest available time period, ranging from 1885:Q4 to 2000:Q4. For these two sample periods, I find that excess returns actually drive out variance in forecasting output growth; moreover, only return terms are statistically significant if I also add past returns and past variance to the forecasting equation. Finally, the formal out- of-sample forecast test rejects the null hypothesis that excess returns provide no information about future GDP growth beyond what is contained in variance. These results should not be a surprise. As mentioned above, from the cost-of capital point of view, volatility contains no additional information beyond excess returns; however, excess returns contain additional information (e.g., information about future cash flows) beyond variance in forecasting output.
In the article, I investigate the empirical link between stock market returns and volatility, analyze their relative forecasting power for output, and offer some concluding remarks.
Although the causes of stock market volatility are not well understood, some authors suggest that elevated stock market volatility might reduce future economic activity. Schwert (1989a) argues that stock market volatility, by reflecting uncertainty about future cash flows and discount rates, provides important information about future economic activity. Campbell et al. (2001), citing work by Lilien (1982), reason that stock market volatility is related to structural change in the economy. Structural change consumes resources, which depresses gross domestic product (GDP) growth. Another link between stock market volatility and output rests on a cost-of-capital channel. That is, an increase in stock market volatility raises the compensation that shareholders demand for bearing systematic risk. The higher expected return leads to the higher cost of equity capital in the corporate sector, which reduces investment and output. Consistent with these hypotheses about the link between stock market volatility and economic activity, Campbell et al. (2001) show that—after controlling for the lagged dependent variable—stock market volatility has significant predictive power for real GDP growth. Moreover, these authors also show that stock market volatility drives out returns in forecasting output. This finding deserves discussion.
Finance theory suggests that stock market returns rather than volatility have predictive power for investment and output because stock market returns are a forward-looking variable that incorporates expectations about future cash flows and discount rates. Several studies have confirmed the predictive power of stock market returns for investment and output, among them Fama (1981), Fischer and Merton (1984), and Barro (1990). On the other hand, the finding of Campbell et al. about the predictive power of stock market volatility for future economic activity is new, but the authors do not provide a theoretical explanation for the evidence. In this article, I try to reconcile the results of Campbell et al. with earlier empirical evidence on the predictive power of stock market returns and finance theory.
I first use Merton’s (1973) Intertemporal Capital Asset Pricing Model (ICAPM) to illustrate the relation between stock market returns and volatility. I show that stock market returns, the difference between stock market returns and a risk-free rate, are positively correlated with one-period-lagged variance, but are negatively correlated with contemporaneous variance. These results have been well understood in the literature (e.g., Pindyck, 1988). Past variance relates positively to excess returns because it contains information about conditional variance or risk. The contemporaneous relation between excess returns and variance is negative because of a volatility feedback effect. That is, a positive innovation in variance today implies higher expected future variance and, therefore, higher expected future returns. For future expected returns to be higher, the innovation in variance must be accompanied by a drop in the stock market price index. Early authors (e.g., Pindyck, 1988; Turner, Startz, and Nelson, 1989; and Dueker, 1991) have found some support for this hypothesized risk-return relation. However, while Turner, Startz, and Nelson (1989) and Dueker (1991) impose no model restrictions on the coefficients of the variance terms, Pindyck (1988) finds that data reject these restrictions over some sample periods. In this paper, I find that (i) past stock market variance has significant forecasting ability for excess returns; (ii) the risk price is found to be positive and precisely estimated; and (iii) the model restrictions are not rejected by data
After establishing the relation between excess returns and variance, it is straightforward to explain why stock market volatility drives out returns in forecasting output. According to the q theory of investment, an increase in stock market variance reduces investment—and hence output—contemporaneously because it raises the cost of capital. Lamont (2000), however, argues that investment expenditures react to changes in the cost of capital with lags. Therefore, stock market variance is negatively correlated with future investment and output. For the same reason, excess returns are expected to correlate positively with future output because excess returns correlate negatively with variance. It should be noted that excess returns—unlike variance—are hampered in their predictive power for future output because excess returns correlate positively with past variance, which in turn correlates negatively with future output. Because of these opposing effects, the predictive power of excess returns for future output is not as strong as the predictive power of variance. However, if the positive relation between excess returns and past variance is controlled for (i.e., adding past variance to the forecasting equation), excess returns might become significant and might even drive out variance because variance provides no additional information beyond excess returns in forecasting output.
I replicate the Campbell et al. (2001) result— that excess stock market returns are statistically insignificant in predicting GDP growth if stock market variance is also included in the forecasting equation—for the period 1963:Q1 to 1997:Q4. However, as postulated, I find that excess returns change from insignificant to marginally significant when I control for the lagged variance in the forecasting equation, meanwhile stock market variance changes from significant to marginally significant. I also analyze two more sample periods. One sample covers the entire postwar period (1947:Q2 to 2000:Q4), while the other sample spans the longest available time period, ranging from 1885:Q4 to 2000:Q4. For these two sample periods, I find that excess returns actually drive out variance in forecasting output growth; moreover, only return terms are statistically significant if I also add past returns and past variance to the forecasting equation. Finally, the formal out- of-sample forecast test rejects the null hypothesis that excess returns provide no information about future GDP growth beyond what is contained in variance. These results should not be a surprise. As mentioned above, from the cost-of capital point of view, volatility contains no additional information beyond excess returns; however, excess returns contain additional information (e.g., information about future cash flows) beyond variance in forecasting output.
In the article, I investigate the empirical link between stock market returns and volatility, analyze their relative forecasting power for output, and offer some concluding remarks.