Management of Financial Risk | Sharpe Ratio; Calmar Ratio: Pain to Gain Ratio

Management of financial riskThere are many risk metrics one can use to evaluate, the performance of a fund manager. The risk metric that has become the standard for judging fund manager risk performance is the Sharpe Ratio.  The Sharpe Ratio – A ratio developed by Nobel laureate William F. Sharpe to measure risk-adjusted performance. The Sharpe Ratio tells us whether a portfolio’s returns are due to astute investment decisions or a result of excessive risk taking. The Sharpe Ratio is calculated by subtracting the risk-free rate – The theoretical rate of return of an investment with zero risk – from the rate of return for a portfolio and dividing the result by the standard deviation of the portfolio returns.  Even though the Sharpe Ratio is an excellent ratio to measure fund managers’ performances it has its flaws:s:

1.) The Sharpe ratio can’t distinguish between upside volatility and downside volatility.   For example say that we have fund returns for two managers below in diagram 1.

Fund Manager A has a Sharpe Ratio of 0.349 and Fund Manager B has a Sharpe Ratio of 0.3043 from the monthly returns in the year of 2011.  Fund Manager has a large upside volatility swing in the month of September but the Sharpe Ratio can’t distinguish between the upside or downside volatility which penalized Fund Manager B.

 2.) The Sharpe Ratio can’t tell the difference between intermittent losses and consecutive losses.  Looking again at Diagram 1 Fund Manager A has three consecutive months of negative returns generating a maximum drawdown of 12.56% as where Fund Manager B has a maximum drawdown of 5.23%.

 

Diagram 1

Sharpe vs Calmar vs Pain to Gain ratio

 

Sharpe Ratio shouldn’t be the only risk metric used to see if a fund manager is doing well.  There are other risk metrics that one can use to evaluate if a fund manager is taking excessive risk. Two risk metrics that can be used are the Calmar ratio and the Pain to Gain ratio.  The Calmar Ratio was developed by Terry W. Young in 1991, the Calmar Ratio is short for California Managed Account Reports.  The equation for the Calmar ratio is below:

 

Calmar Ratio = (Compounded Annual Rate of Return/ Maximum Drawdown)

 

The lower the Calmar Ratio, the worse the investment performed on a risk-adjusted basis over the specified time period; the higher the Calmar Ratio, the better it performed. The Calmar Ratios for Fund Manager A is .370426 while the Calmar Ratio for Fund Manager B is 4.876514.

The other ratio is the Pain to Gain ratio that has been popularized by Jack Schwager in his book Hedge Fund Wizards, an excellent read! The equation for the Pain to Gain Ratio is below:

 

Pain to Gain Ratio = (Total sum of all monthly returns/ABS (total of negative monthly returns)

ABS = absolute value

 

The higher the pain to gain ratio the better the fund manager has performed on a risk adjusted basis over the time period; as where the lower the pain to gain ratio the worse the fund manager has performed over the time period.  The pain gain ratios for both Fund Managers are extremely high.  The pain to gain ratio for Fund Manager A is 4.44 while the pain to gain ratio for Fund Manager B is 47.3.  These two fund managers both have excellent pain to gain ratios and any fund manager that has a pain to gain ratio over 3 has done really well!

Diagram 2

Sharpe vs Calmar vs Pain to Gain ratio (2)Chad Grant

 

 

 

 

 

Author: admin

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