Portfolio analysis is essentially a statistical technique. However, because the ‘‘true’’ population parameters for the input data (expected returns, variances, and covariances) are unobservable, sample statistics must be estimated. Thus, the efficient portfolios generated by portfolio analysis are no better than the statistical input data on which they are based.
The single-index factor model assumes that the co-movement between stocks is due to a single common influence or index. Casual observation of stock prices reveals that when the market goes up (as measured by any of the widely available stock market indexes), most stocks tend to increase in price, and when the market goes down, most stocks tend to decrease in price.
Factor models are applied by portfolio managers to analyze the potential returns on a portfolio of risky assets, to choose the optimal allocation of their funds to different assets and to measure portfolio risk. The theory of linear regression-based factor models applies to most portfolios of risky assets, excluding options portfolios but including alternative investments such as real estate, hedge funds, and volatility, as well as traditional assets such as commodities, stocks, and bonds.
