Using the Shapley value of stocks as systematic risk

What is it about?

Systematic risk as expressed by the relative covariance of stock returns to market returns is an essential measure for pricing risky securities. Although very much in use, in recent years the concept has become marginalized because of the difficulties that arise in estimating beta. As an alternative, I propose using the Shapley value from game theory to quantify the relative risk of a security in an optimal portfolio. The underlying idea is that since portfolios can be viewed as cooperative games played by assets aiming for minimize risk, with the Shapley value, investors can calculate the exact contribution of each risky asset to the joint payoff. For a portfolio of three stocks, I exemplify the Shapley value when risk is minimized regardless of portfolio return. Then, I compute the Shapley value of stocks and indices for optimal mean-variance portfolios using daily returns for the years 2016-19. This procedure reveals the risk attributes allocated to securities in optimal portfolios. Last, Shapley values are analyzed and compared to standard beta estimates to determine the ranking of assets with respect to pertinent risk and return.

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Photo by NeONBRAND on Unsplash

Photo by NeONBRAND on Unsplash