Portfolio Design: A Modern Approach to Asset Allocation

ALTERNATIVE APPROACHES TO OPTIMIZATION

In 1974, William Sharpe published an article that turned the portfolio optimization problem around. Usually portfolio optimization asks what portfolio weights would be chosen given a set of expected returns. Instead, Sharpe (1974) asked what expected returns would lead an investor to hold the set of assets that this investor has chosen. Sharpe used the portfolios of a large investment firm as an illustration.8 He calculated the expected returns that were consistent with the portfolio chosen by this firm. These expected returns might prove to be surprisingly high or low to the firm. This would then give the firm a basis for modifying its initial portfolio choice.

Sharpe’s insight later led to the Black and Litterman (1992) method for analyzing portfolios. Black and Litterman asked a different question than did Sharpe. They asked what expected returns would be necessary for investors to hold the assets available in the market. Instead of using historical returns for optimization, Black and Litterman generate equilibrium expected returns that are consistent with the weights of each asset in the market.

To see the intuition behind the Black-Litterman method, consider a simple example. Suppose that the only assets in the world were U.S. large-cap value and growth stocks. Russell defines the Russell 1000 Growth and Value Indexes so that they have equal market capitalization weights. But growth stocks have lower returns than value stocks. And, over ...