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Sharpe Ratio, Alpha or Geometric Mean?

| | Posted in: Big Ideas, Mutual/Hedge Funds

What is the single best performance metric an investor can use to rank performances of competing portfolios (such as mutual funds)? In his September 2016 paper entitled “Measuring Portfolio Performance: Sharpe, Alpha, or the Geometric Mean?”, Moshe Levy compares Sharpe ratio, 5-factor (market, size, book-to-market, profitability, investment) alpha and geometric mean return as portfolio performance metric. The widely used Sharpe ratio is optimal when return distributions are normal and the investor can borrow at the lending (risk-free) rate without limit for leverage. However, asset return distributions may not be normal, investors generally borrow at an interest rate above the risk-free rate and Federal Reserve Regulation T restricts borrowing to 100% of an investor’s initial capital. Moreover, investors typically restrict themselves to much lower borrowing levels. His methodology is to compare the ranking of a set of actual equity mutual funds under realistic assumptions based on each of the three metrics with the ranking produced by utility maximizing allocations for each fund paired with the risk-free asset. The better the ranking produced by the metric aligns with the utility maximization ranking, the better the metric. His baseline assumption is that actual annual borrowing rate is 3.5% above the lending rate. For robustness, he considers several levels of investor risk aversion in determining utility maximization and other gaps between borrowing and lending rates. Using theory, monthly returns for 10,145 U.S. domestic equity mutual funds, the risk-free (lending) rate and returns for the five Fama-French factors during July 2005 through June 2015, he finds that:

  • With borrowing limited to 100% of capital and a borrowing rate 3.5% higher than the lending rate:
    • Sharpe ratio ranking of mutual funds differs from that produced by utility maximization for an investor with typical risk aversion. An investor using Sharpe ratio in this way does not usually pick one of the best funds.
    • 5-factor alpha ranking of mutual funds is worse at picking the best funds than Sharpe ratio.
    • Geometric mean return ranking usually picks one of the best funds.
  • For a typically risk-averse investor, borrowing constraint thresholds for choosing geometric mean over Sharpe ratio are:
    • A limit on borrowing of less than 120% of initial capital invested.
    • An annual borrowing rate that is over 1.6% higher than the lending rate.
  • Findings are largely robust for different levels of risk aversion. However, investors who are more (less) risk-averse than the typical investor, bear a lower (higher) penalty for using Sharpe ratio rather than geometric mean return to rank the mutual funds.
  • Fund rankings produced by different return measurement intervals are generally more stable for geometric mean return than for Sharpe ratio.

In summary, evidence indicates that, for investors with typical borrowing constraints, the geometric mean is much better at ranking portfolios (mutual funds) than both Sharpe ratio and multi-factor alpha.

Cautions regarding findings include:

  • The analysis presented is not about predicting fund performance. Rather, it employs all the data in the sample period to rank funds in testing the best simple way to measure fund performance. An investor would not know the ranking during the sample period. In other words, geometric mean return is useful for picking funds only if past performance persists to a material degree.
  • Some investors may be able to borrow at cheaper interest rates than tested, making Sharpe ratio more competitive with geometric mean return.
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