Investment Theory and Risk Management, + Website

Benchmarking to the Market Portfolio

All our work to this point made no reference to the market portfolio, in this case, the S&P 500 return. It is common, however, to compare the return to an asset or a portfolio of assets to the return on the market. There are many reasons, foremost of which is that the return to the market represents the opportunity cost of portfolio under management. For example, the return to Port 2 in the monthly data (weekly data) is 3 percent (0.742 percent) with risk 5.1 percent (2.99 percent). Had we invested in the market portfolio instead, we would have a return of 1 percent (0.3 percent) with risk 2.6 percent (1.3 percent). Does this look like a favorable risk-return trade-off to you? It depends on your risk preferences, but the return per unit risk is 3 percent/5.1 percent on the monthly Port 2 versus 1 percent/2.6 percent on the monthly S&P. This is a Sharpe ratio and it favors Port 2, at least from a risk-adjusted return perspective.

What about risk at the security level? Obviously, we can compare volatilities (standard deviations). But is there a measure of security risk relative to benchmark risk? The CAPM provides this measure in the form of the asset's β:

Beta is a measure of the covariation in the asset's return to the market return, specifically:

Actually, it is a very intuitive concept; a β of one means that the two return series are perfectly ...