May 28

Sharpe ratio beats the newcomers - FRM learning objectives "in the news"

by David Harper, CFA, FRM, CIPM

FRM |

In the just released Financial Analyst Journal (FAJ), Martin Eling's published "Does the measure matter in the mutual fund industry?" He examines the relative performance of three categories of return/risk metrics. In addition to a refreshing finding, it is a nice list of return/risk metrics. For the FRM candidate specifically, your study includes: Sharpe ratio, drawdown (common in hedge funds), Sortino, VaR and conditional VaR (aka., ES).

His finding, in a nutshell, is that none of the fancy metrics beat the Sharpe. Outcomes by rank order do not vary by metric. "The choice of performance metric does not critically influence the relative evaluation of funds.", he says. IMO, Kappa 3 was too clever by half and had this coming.

He compare Sharpe ratio (excess return/sample volatility) to three categories of measures:

  • Lower partial moments of orders. These try to correct for a flaw in volatility: it treats upside just like downside. So, the metrics here correspond to three moments: Omega (1st), Sortino (2nd), and Kappa 3 (3rd). In the FRM, we review Sortino as the second moment is the variance. So, the Sortino is a measure of semi-variance or semi-deviation (i.e., dispersion of returns but only those below some threshold)
  • Drawdowns: variations on some measure of maximum loss over a period of time. These are intuitive measures. I think of them as "take my breath away metrics:" in its worst loss, how much did the fund draw down and take investors breath away, in a bad way.
  • Value at risk (VaR) variations. See next.

The VaR variations include:

  • Standard VaR. Here the return/risk metric is the Sharpe ratio except substitute VaR for standard deviation: = (return-riskless rate)/VaR
  • Conditional VaR. The expected loss conditional on the loss exceeding VaR: E[loss| loss < VaR]. For example, if VaR = -10%, what is the expected (average) loss among only those outcomes that are less than -10%? Also called expected shortfall (ES)  if we ignore a subtle distinction between continuous/discrete distributions
  • Modified VaR: An adjustment of VaR to handle non-normality. If VaR = (-mean)+[(volatility)(scale by confidence)(scale by time)], the Modified VaR increases the (scaled by confidence). For example, at 95% confidence, = NORMSINV(1-95%) = -1.645. But modified VaR will give back -1.654*(multiplier) where the multiplier is a function of skew and kurtosis; such that if skew = 0 and excess kurtosis = 0, modified VaR = VaR.

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