To understand why stock volatility varies from time to time, the relationship between the stock market and the macroeconomy must become transparent. While we learn that financial market data exhibit anomalies or stylized facts, we want to know what explains these facts; we also want models to be able to capture them.
This essay analyses the relation between the stock market and the macroeconomy. It consequently discusses two questions: why does stock volatility vary over time? Why is macroeconomic volatility a weak predictor of financial volatility while it is the opposite that seems to hold?
The stock market is linked with the macroeconomy through such macroeconomic variables as consumption, investment and production. Periods of bad macroeconomic activity such as during recessions volatility for stocks, exchange rates, and macroeconomic variables such as inflation, money growth, production and interest rates tend to be higher than in normal non-recessionary periods. Ludvigson (2001) document that expected stock returns vary at cyclical frequencies and with macroeconomic variables. Moreover, Schwert (1989) documents that financial volatility can predict macroeconomic volatility while macroeconomic volatility has little power, if at all any, in predicting financial volatility. Thus, stock markets are in constant interaction with the macroeconomy and yet there is a disconnect.
The price of a financial asset obeys the martingale property if its expected payoff conditional on information available at the beginning of period t equals to zero. That is, the expected future price of an asset given period t information equals to period t price. This implies that we may be able to predict stock prices. However, high-frequency–short-time horizon–data show that stock prices are unpredictable (Lux, 2009). This means, if, for example, the price of an asset went down yesterday, the price may go up, or down or (rarely) stay the same today. Yesterday’s information is almost useless in predicting today’s prices. This is a consequence of the finding that asset prices are “roughly” random walks. For stock return is the percentage of a change in stock prices, it follows that, over a short time horizon stock returns are also unpredictable.
However, over longer horizons and business cycles, variables such as dividend to term premium have a considerable power in predicting stock returns (Lettau and Ludvigson, 2001; Cochrane, 1999; Schwert, 1989). Lettau and Ludvigson (2001) use U.S. quarterly stock market data to study the role of fluctuations in the ratio of aggregate consumption to wealth for predicting stock returns. They find that the ratio of consumption to wealth forecasts stock returns.
That stock returns are predictable over a long horizon is of little, if any, practical use to an investor. Suppose that we could predict stock returns using macroeconomy variables such as the rate of interest, these variables are typically available for much longer periods–e.g., monthly–than the daily financial market data: interest rates and other real market data do not vary as much as stock returns. If stock price is a stochastic process, this process could be anything, and it may not have a closed-form solution.
Studies on stock volatility find that stock volatility is time-varying and past volatility predict future volatilities and this is more so in lags than in leads (e.g., Lux (2009); Cochrane (1999); Hamilton and Lin (1996); Schwert (1989)). This is because, contrary to the assumption of random walk behavior of stock returns, aggregate returns do not converge to the normal distribution as would be required by the central limit theorem. Returns exhibit “fat tails” and dependency on higher moments than the normal distribution (Lux, 2009). Thus, stock returns are not perfectly uncorrelated but tend to cluster in two extremes of tranquil–in good conditions such as non-recessionary–and turbulence–in bad conditions such as during recessions (Lux, 2009).
Traditional asset pricing models do not capture these stylized facts of financial market data. This means that they may underestimate price changes and hence asset risks. In times of unusually high volatility losses are incurred and turmoil in the financial markets may spill over into the macroeconomy. Economies are characterized by periods of booms (high growths and investments) and busts (low growths and investments). Stock return volatility is unusually high during recessions and typically persistent in non-recessionary periods. It is easy to see this relationship since the macroeconomy is essentially about saving, investment, consumption, marginal rates of substitution and marginal rates of transformation. Thus, just as much as it is necessary for asset pricing models to accurately capture these facts and hence financial volatility, macroeconomic modeling must also be able to predict when excess financial volatility may interfere with an otherwise healthy macroeconomy.
Stock volatility over time
Schwert (1989) analyses the relationship between stock market volatility and time-varying economic variables–macroeconomic volatility, economic activity, financial leverage, and stock trading activity–over the period between 1857 and 1987. He finds that during this period the estimated standard deviation varied between two and twenty percent. This variability affected business cycle variables such as capital movement and consumption. During the Great Depression between 1929 and 1939 the volatility of many economic variables, such as inflation, money growth, and industrial production, was unusually high. He documents that stock market volatility increases during recessions and with financial leverage, and is correlated with interest rate and corporate bond return volatility. The ex ante volatility of market returns appears to significantly (and negatively) affect risk-averse investors.
The stock price in Schwert (1989) is defined as the “discounted present value of expected future cash flows to stockholders.” To see how macroeconomic activity affect stock return volatility, Schwert (1989) assumes, for simplicity, that the discount rate is constant over time. Then, the conditional variance will be proportional to the conditional variance of the expected future cash flows, meaning that there is a proportional relationship between the uncertainty in expected future macroeconomic conditions and stock return volatility. Reasoning like this, Schwert (1989) sees the reason why macroeconomic data can help explain why stock return volatility varies over time.
It is sufficient to report the most important findings in Schwert (1989):
- Stock return volatility is high in times of stock market crashes, during recessions and is persistent in other times. There is a strong relationship between stock market
volatility and the state of the economy. - Lagged stock volatility is the “most important” predictor of current stock volatility. Lagged bond return volatility are stronger predictors of current stock volatility than
short-term interest volatility. Stock return volatility is a poor predictor of interest rate volatility. - Stock return volatility can not predict inflation volatility. There is no strong relationship between inflation or money growth volatility and the stock return volatility.
Stock return volatility can predict the base growth rate volatility. - Macroeconomic volatility is not sufficient to account for future stock return volatility. The reverse is, however, true: you can use financial volatility to predict macroeconomic
volatility.
What do we draw from these findings? It is no surprise that lagged stock volatility is the strongest predictor of current stock volatility. It is a vindication of the stylized fact of financial market data that stock returns are not truly independent and identically (i.i.d) normally distributed. On aggregation they do not converge to normal distribution, but tend to converge to this for long horizons. They exhibit volatility clustering. These facts as has been discussed in the introduction section have been known at least as early as the 1960s (Lux, 2009). We can explain the findings in items (1), (3) and (4) based on frequency of data. While data for variables such as inflation, and growth are typically available monthly, stock return data are “high-frequency.” This high-frequency of data makes the stock market react quickly on new unexpected information. It vindicates the “market outcome” that financial markets are informational efficient, as Lux (2009) and Cochrane (1999) document, in that all currently available information is already incorporated in evaluating the price of the asset in question and stock prices change only because of new unexpected information.
For an investor in the stock market chooses different levels of investment and consumption, we must understand what macroeconomic factors affect risks on stock returns. And for stock market crashes may spill over into the macroeconomy and possibly drive it into a recession, we must understand what stock market factors affect the macroeconomy
References
Cochrane, John H. 1999. “New Facts in Finance.” Economic Perspectives, , (QIII): 36–58.
Hamilton, James D., and Gang Lin. 1996. “Stock Market Volatility and the Business Cycle.” Journal of Applied Econometrics, 11(5): 573–593.
Lettau, Martin, and Sydney Ludvigson. 2001. “Consumption, Aggregate Wealth, and Expected Stock Returns.” The Journal of Finance, 56(3): 815–849.
Lux, Thomas. 2009. “Stochastic Behavioral Asset Pricing Models and the Stylized Facts.” In Handbook of Financial Markets Dynamics and Evolution. Handbooks in Finance, , ed.
Kalus Reiner Schenk-Hoppé Thorsten Hens, Chapter 3, 161–215. North-Holland.
Schwert, G William. 1989. “Why Does Stock Market Volatility Change over Time?” Journal of Finance, 44(5): 1115–53.
