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AbstractWhen constructing portfolios, practitioners must take opportunity cost into account and view returns as excess, not total returns. Using total returns in a means–variance optimization—a remarkably common error—introduces a bias that will cause "optimal" portfolios to overweight domestic cash securities at the expense of higher‐risk instruments and instruments invested abroad. The original work on modern portfolio theory made little mention of excess versus total returns in optimization in part because the theory assumed one was only choosing between risky assets and that all of the assets were denominated in the same currency. Thus, those who refer to the original version of the theory could easily misapply it when considering assets in different currency zones. This paper seeks to demonstrate the problems and biases inherent in using total returns versus excess returns in means–variance optimization.

AbstractIn order to meet their financial goals, investors, whether institutions or individuals, must make asset allocation decisions by balancing their return targets with their tolerance for volatility, their liquidity requirements, and time horizons. Yet even optimal mixes of investments with regard to time horizon, liquidity, and volatility levels are sometimes not adequate to achieve the return objectives of a firm or an individual. Using leverage scales up both returns and risks, introducing the potential for default. When using leverage, either as a fund manager or as an investor into a fund, fully understanding the potential for default is absolutely necessary. Using standard measures of risk and return can be very misleading. Sharpe ratios and information ratios can lead the investor into a state of unwarranted comfort with respect to the probability of losing more than is acceptable. Many traditional measures of risk do not deal with this problem correctly. This paper takes a barrier option theoretic approach to analyzing the potential for losses and the potential for the leveraged investor to be knocked‐out of his position even under circumstances of perfect knowledge of the end return. Thus, it demonstrates the necessity of a more rigorous approach to understanding the risk of any particular style of investment, particularly when dealing with hedge funds.