Investment Theory and Risk Management, + Website

The Cost of Constraints

The CAPM is an equilibrium model in which investors’ supply and demand decisions defines the market portfolio, in which all investors possess identical information and preferences are mean variance optimizers, and for which there are no restrictions on selling. Restrictions make portfolios inefficient relative to the market portfolio. In reality, there are many practical instances of restrictions; institutional investors, for example, may face short-selling restrictions as risk controls and others (like you and me) may find it impractical to engage in short sales for a variety of reasons (brokerage fees, trade size limitations, and downside risk). These restrictions will necessarily push our portfolios off the efficient frontier.

The impact of no short-sales restrictions can be seen in the spreadsheet exercises for this chapter. In this application, we solve for the minimum variance portfolio subject to an additional restriction that all weights must be nonzero. The solution is not analytic as was the case for Port 1 and Port 2 given earlier. Instead, it is a search process requiring iteration toward a combination of asset weights that generate the minimum variance for a targeted return. In all cases, the risk on the no-shorts portfolio will be higher. If, for example, we refer to the sheet containing the monthly returns for our 10 firms and set the targeted portfolio return at 2.5 percent, we get the following minimum variance portfolio:

Port 2