April 26, 2020

Did the stock market over-react to Covid-19?

In the previous post we saw that the Dividend Discount Model does a good job at explaining the level of stock prices before the Covid crisis. Today, we turn to the stock market crash caused by the coronavirus outbreak. After stock prices went down 30%, some commentators argued the market over-reacted. Let us review their arguments as well as counter-arguments using the Dividend Discount Model.

The DDM says that stocks are worth the present value of future dividends. When dividends are expected to grow at g=4% per year and the discount rate is k=6% per year split into a 2% risk-free rate and a 4% equity risk premium, stocks are worth 50 times the current dividend D:

P = D/(k-g) = D/(0.06-0.04) = 50*D

When Covid hit, investors revised their expectations regarding future dividends. Let us suppose that the impact of social distancing and lockdown rules is to reduce dividends in 2020 by half. The value of stocks should decrease by a half-year's worth of dividends, that is, 0.5*D. Since we started from P=50*D, this represents a 1% drop in stock prices. This is much less than the 30% market crash which actually happened. What are we missing?

We implicitly assumed that, after the health crisis is over we return to the path of dividends that would have prevailed absent Covid. This scenario is what economists call a V-shaped recovery. But this scenario might be too optimistic. We may well settle on a new trend below the pre-crisis trend. Let us now assume that not only dividends are cut in half in 2020, but we also lose one full year of economic growth: dividends after 2020 will be permanently 4% below what they would have been absent the crisis. Since stocks are worth the present value of dividends, such a partial recovery implies that stocks also loses 4% of their value. Adding this 4% loss to the half-year's worth of dividends lost in 2020, we have a 1%+4%=5% drop in stock prices, which is still much smaller than the actual crash.

Preliminary conclusion: The forecasted drop in dividends has a very hard time explaining the size of the crash. It is this reasoning that led some commentators to argue that the market over-reacted in the crisis.

But we omitted one key factor: we assumed throughout that the discount rate did not change. However, the crisis can increase the equity risk premium for two reasons. First, there is more risk due to uncertainty regarding the evolution of the health situation. Second, individuals become more averse to risk, because they fear for their jobs and savings and their health. Therefore, it requires a higher equity risk premium to make investors willing to buy stocks. Let's say the equity risk premium increases from 4% to 5%. Added to the 2% risk-free rate, we have a discount rate k=7%. The new stock price is therefore

P = D/(0.07-0.04) = 33*D

Since we started from P=50*P, this represents a 33% drop in the price. If we factor in the reduction in dividends, for instance in the partial recovery scenario which contributes an additional 5% drop in stock prices, we get a 38% crash.

Conclusion: Explaining the size of the crash requires to take into account changes in the discount rate, that is, changes in the expected return of the stock market. In other words, the crash may well predict higher expected stock returns going forward, but these returns are only in expectation (they are not for sure) and they reflect compensation for higher risk and higher risk aversion.

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