Calibrating Risk Preferences with Generalized CAPM Based on Mixed CVaR Deviation

Abstract

The generalized Capital Asset Pricing Model based on mixed CVaR deviation is used for calibrating risk preferences of investors protecting investments in S&P500 by means of options. The corresponding new generalized beta is designed to capture tail performance of S&P500 returns. Calibration is done by extracting information about risk preferences from option prices on S&P500. Actual market option prices are matched with the estimated prices from the pricing equation based on the generalized beta. In addition to the risk preferences, an optimal allocation to a portfolio of options for the considered group of investors is calculated. I Introduction The Capital Asset Pricing Model (CAPM, see Sharpe (1964), Linther (1965), Mossin (1966), Treynor (1961, 1962)) after its foundation in the 1960’s became one of the most popular methodologies for estimation of returns of securities and explanation of their combined behavior. This model assumes that all investors want to minimize risk of their investments, and all investors measure risk by the standard deviation of return. The model implies that all optimal portfolios are mixtures of the Market Fund and risk free instrument. The Market Fund is commonly approximated by some stock market index, such as S&P500. An important practical application of the CAPM model is the possibility to calculate hedged portfolios uncorrelated with the market. To reduce the risk of a portfolio, an investor can include additional securities and hedge market risk. The risk of the portfolio in terms of CAPM model is measured by “beta”. The value of beta for every security or portfolio is proportional to the correlation between its return and market return. This follows from the assumption that investors have risk attitudes expressed with the standard deviation (volatility). The hedging is designed to reduce portfolio beta with the idea to protect the portfolio in case of a market downturn. However, beta is just a scaled correlation with the market and there is no guarantee that hedges will cover