The Benchmark Error Problem with Global Capital Markets

Abstract

the University of Notre Dame at the time h s article was written. D uring the late 1970s and early 1980s, Richard Roll in several articles voiced concern with the testing of the Capital Asset Pricing Model (CAPM), as well as with use of the model to evaluate investment performance (Roll [1977, 1978, 1980, 19811). Roll referred to t h s latter problem as a benchmark error, because the practice has been to compare the performance of a portfolio manager to the performance of an unmanaged portfolio of equal risk. The benchmark typically has been a security market index adjusted for risk, where the risk measure is the one implied by the CAPM (i.e., beta). Roll shows that if the benchmark employed in this evaluation is mistakenly specified, you cannot measure the performance of portfolio managers properly. An inappropriate proxy for the market portfolio (benchmark) can have two effects. First, the systematic risk measures (beta) computed for individual assets and for alternative portfolios will be wrong, because the betas are derived using an inappropriate proxy for the market portfolio. Second, the security market line (SML) derived to measure the relative risk-adjusted performance of alternative portfolios d be misspecitied because the SML. is then the line h m the risk-free return through an improperly specified proxy for the market portfolio. Roll shows that, assuming the proxy used to represent the market portfolio of risky assets is not as mean-variance efficient as the “true” market portfolio, it is possible that the performance of a portfolio using the inappropriate SML would be considered superior,