## Wednesday, April 14, 2010

### Expert Level: Calculating the Sterling Ratio One of the questions asked during yesterday’s webinar has to do with the calculation of the Sterling Ratio:

Hello,

Attached are the screenshots to the Example and Solution in the courseware that I was referring to, which seems to be using a different methodology than what the reading material (and John) described. I’m just wondering which methodology we should be using for the exam, since the two methodologies will yield vastly different results.

Thanks.

The Sterling Ratio is covered in the "Risk" study session at the Expert Level of the CIPM curriculum. The question raised is Exercise LOS 2I from the CFA Institute's interactive courseware. I am not at liberty to include the screen shots here, but I will describe how I arrive at the solution.

The formula for the Sterling Ratio is: CompoundAnnualizedRoR / abs(AverageYearlyMaximumDrawdown – 10%)

The Sterling Ratio may be calculated as follows:

1. Geometric linking of the first year’s monthly returns results in an annual return of
-18.00%.

2. Geometric linking of the second year’s monthly returns results in an annual return of 15.99%.

3. Geometric linking of the third year’s monthly returns results in an annual return of 12.00%.

4. Geometric linking of the three annual returns results in a cumulative return of 6.53%.

5. Annualizing the cumulative return over the 3 year period results in a return of 2.13%.

6. The maximum drawdown in year 1 occurs from the start of the year through month 8. Geometrically linking the returns over this timeframe gives a drawdown (D1) of 22.24% (note that the negative is implied).

7. The maximum drawdown in year 2 occurs in month 17, which is a drawdown (D2) of 2.56%.

8. The maximum drawdown in year 3 occurs over months 29 and 30; geometric linking of the returns over those months indicates a drawdown (D3) of 3.98.

9. By adding D1, D2 and D3 and dividing the sum by 3, we get an average annual drawdown of 9.59% (again, note that the negative is implied).

It is at this point that the exercise solution seems to be in conflict with the reading entitled “Measuring the Volatility of Hedge Fund Returns” by Douglas S. Rogers and Christopher J. Van Dyke. I quote the authors:

“The challenge with the Sterling ratio is that if the average yearly maximum drawdown for any of the managers analyzed is less than the arbitrary 10%, then the denominator becomes negative and comparison with other managers with positive denominators is meaningless.”

Keep in mind that we are dealing with drawdowns, which are, by nature, negative numbers. Any negative number would be less than the “arbitrary 10%.” Thus, the statement the authors make would be pointless, unless they are referring to the absolute value of the drawdown being less than 10%.

Given my interpretation, the next steps to take to obtain the Sterling Ratio would be:

10. The numerator of the Sterling ratio is the annualized return of 2.1323%, and the denominator is abs[abs(-9.59) minus 10.00] which is equal to 0.41%. Thus the Sterling Ratio is 2.1323 / 0.41 = 5.20.

The solution to the exercise, however, shows the answer the last steps as follows:

11. The numerator of the Sterling ratio is the annualized return of 2.1323%, and the denominator is abs[-9.59 minus 10.00] which is equal to 19.59%. Thus the Sterling Ratio is 2.1323 / 19.59 = 0.11.

Quite a bit of difference in the answers! I believe this is the discrepancy in methodology that the candidate is referring to.

I believe the correct approach is to do step 10 rather than step 11. But, having said that, I will check with a couple of sources and let everyone know what I find out!