# Panic v numerical discipline in predicting Covid19’s market impact

“Investment ideas can spread like epidemics.” Robert Shiller in his Nobel Lecture “Speculative Asset Markets” 2013

Bob Shiller’s Nobel winning contribution was the observation that asset markets generally are too volatile relative to theoretical methods for pricing securities. The panicked reaction to Coronavirus 2019 (Covid19) seems no exception.

I have regularly been asked what Covid19’s impact on markets *should* be? This is a difficult question since there are many factors determining equilibrium asset prices. The interesting aspect of the current crisis is that everyone agrees that it is a purely temporary economic shock. Therefore the transitional dynamics of the initial market decline and the recovery path for asset prices are of primary interest. At the risk of simplifying the problem and betraying the traditions of market efficiency, let me make an attempt at articulating the immediate impact and transitional market dynamics.

Theoretically, the stock market measures the value of the capital stock. Capital combines with labour to produce output, output is paid to shareholders as dividend income which is then consumed. Covid19 has negatively impacted this production process by (i) depleting the labour force (death, sickness), (ii) causing the capital stock to sit idle for a few months as factories quarantine. Eventually all will return to normal but there will be a short term impact on stock prices from these temporary effects. Without boring our dear readers with the derivation of the following equilibrium result (1), the market impact, P’-P, of this temporary shock is close to the following,

P’-P = ∑(g’-g)/(1+risk premium)^(t+i))

where g’-g is the critical quantity measuring how far below short term growth g’ declines relative to the long run average. Thus, if the effect of the Coronavirus is to reduce global growth initially by, say, 1% over 1 quarter and this persists for a few quarters then the impact on stock prices, P’-P, should reflect this.

The interesting question is * quantifying* these qualitative effects. This requires a calibration of the Covid19’s impact on the economy. The virus has touched about 1 in 100,000 people Globally, quarantined about 1 in 500 for 14 days and permanently reduced the labour supply by just 1 in 5,000,000. Taking these facts together, the impact of quarantine on both the labour supply and shutting down production suggests to a short term cost to growth of around 0.5% this quarter and this may persist but decay for several subsequent periods. [At least, this is Goldman Sachs’ expert view!] Therefore, I set the initial growth shock at -0.5% and assume that the shock persists with a half life of one year.

The results of the model are shown in the two diagrams above. In each case the horizontal axis measures time in years. The vertical axis for the left hand diagram measures the percentage deviation of economic growth and stock prices from their long run trend. The vertical axis for the right hand diagram measures the Expected Return for stocks relative to long run average. The left hand diagram confirms one’s intuition whereby the impact on stock prices is about six times greater than the impact on economic growth. However, the striking finding is that the magnitude of the decline is predicted to be only 3% whereas we all know that the stock markets reacted more violently than this over the last week. The diagram also predicts a once-off fall in prices followed by a gradual recovery.

Turning to the right hand diagram, the once off decline in stock prices has a temporarily ** positive** impact on future expected returns. This occurs to induce investors to buy stocks and replenish the capital stock.

One can play with this model, specifying various magnitudes and lengths of time that output growth is affected, as well as introducing more reasonable elements of uncertainty with stochastic shocks (sometimes called Monte Carlo simulation), the result of which is a calibrated distribution of the range of outcomes for stock prices. Again, without boring the reader, I can confidently assert that after this statistical playtime is completed the prospect of predicting a 10% decline in stock prices as a consequence of the Covid19 is statistically zero. The conclusion is that standard models cannot predict the empirical realities for market outcomes.

So back to Professor Shiller. “Investment ideas can spread like epidemics” seems a good way to explain how the Covid19 epidemic has spread an investment idea that is sometimes labelled ‘panic’. A feature of the sell off over the past week has been the uniform disposal of equities without much regard for the sectors/countries most negatively affected by Covid19 let alone those pockets that may benefit. This is symptomatic of blanket de-risking of portfolios which means selling stocks to buy cash. Panic is more politely referred to as a Risk-Aversion shock which means that the prevailing rate of return on stocks becomes insufficient to satisfy investors, leading them to sell their stocks ever-more cheaply until the future expected rate of return looks sufficiently compensatory again. In the meantime, the index fund managers liquidate large blocks of securities to meet redemptions and this flows through into blanket selling.

That said, the theoretical models still have something to say about extremes and whether they can be justified. The calibrated model that we presented illuminates the ‘rational’ reaction given the model. At least this provides a cool head when panic sets in.

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(1). I calibrated a version of the Basic Neo-Classical model with Utility maximising representative agent, a Cobb-Douglas Production function and a well defined steady state. The near-steady state dynamics are calculated for a given shock process which causes economic quantities and asset prices to deviate from the steady state equilibrium, in response to which the system returns to its steady state gradually over time. Asset price responses are the forward looking summation of deviations of capital from its steady state position. The treatment of uncertainty in this analysis is fudged by appealing to notions of certainty equivalence. I apologise for this but, my friends, this is a blog not a dissertation.

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