Understanding the Capital Asset Pricing Model: Kelly trading and market equilibrium

What is it about?

The award winning Capital Asset Pricing Model describes the asset allocation of a market in equilibrium. Our contribution is to describe the path taken to reach the equilibrium. We show that mean-variance efficient traders dynamically choose portfolio strategies that force the instantaneous asset-asset correlations towards a saddle point. This saddle point satisfies the fundamental equation of CAPM.

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Photo by Anne Nygård on Unsplash

Photo by Anne Nygård on Unsplash

Why is it important?

CAPM is often read from risk to return: estimate beta from historical covariance and use it to infer the required return. Our results show that equilibrium may also run in the opposite direction. Expected returns determine Kelly portfolio demand, and the resulting trading changes volatilities and correlations until a CAPM-consistent covariance relation is reached. Historical beta is therefore an outcome of a past equilibrium, not automatically a structural input for forecasting the future cost of equity.