In calculating the Sortino ratio, I took the average monthly return for the hedge fund and annualized it by compounding to get 7.98%, but the return given in the solution is 7.36%. I don’t see how they are calculating the annualized return. I get that they are annualizing by multiplying by 12, but I do not see where the 0.6133% comes from. Does anyone see where that comes from? (It’s probably so obvious I’ll be embarrassed for asking.)
Do you take the average monthly return and annualize it? I thought you did the geometric mean where you multiple all the (1+r)'s and then take the (1/12) root? just a guess
I agree with you eisman4. The way they calculate late this is ridiculous. The chain linked return is actually 7.61%=1.006133^12. This is the return that should be used to calculate Sortino. What CFAI does instead is use 0.6133%X12=7.360%. Nonsensical!!! 0.6133% is the 12th root of 1.0761.
This return calc is shown in exhibit 30 on page 90, but I agree it is ridiculous. Besides, will we even need to calculate this or just know how to interpret results? There is no mention of calculate in the LOS for these, and no blue numbers next to these equations in the text. I keep calculating things like this for the EOC’s but see very few that show definitively that we need to know how to calculate for the test. Does anyone know for sure?
I don’t know where does the 0.6133% come from. But shall the “annualized return” be the ARITHMETIC average (mean return) in the denominator of Sortino Ratio instead of GEOMETRIC average ? Please refer to 6.3 of R39.
Please refer to P.89~90 in this reading.
If you do the compounding of the monthly return (1+r1)(1+r2)…(1+r12)= 1.0761 instead of doing the what the solution does, you are, in CFA speak, ‘gaming the Sortino ratio’, albeit unintentionally. I quote from gaming the Sharpe ratio: “Compounding the monthly returns but calculating the standard deviation from the (not compounded) monthly returns”, so - either you have the exact annual standard dev or - or you annualize it the way solution suggests (take geometric mean then multiply with 12) to avoid exaggerating the Sortino ratio. As I mentioned earlier several times, the CFAI text, in particular the EOC questions, have been ‘vetted’ by thousands of candidates from previous years, so obvious mistakes are rare (though not impossible), so if you think you find any of them in plain daylight, chances are more likely that ‘the joke is on you’.
Thank you very much for your guidances. So, the “correct way” to calculate the ARR (annualized rate of return) shall be : {[(1+r month1)* (1+r Month 2) * …(1+r month 12)]^1/12 -1} x12 when monthly rate of retun is given ? Can you advise where I can locate the “correct way” in the curriculum ?
AMA Wrote: ------------------------------------------------------- > Can you advise where I can locate the “correct > way” in the curriculum ? I don’t believe there is a direct reference to a formula. However, the EOC exercises are used to demonstrate/show in concrete calculation the concepts explained shortly in the text and I believe this is one of the cases. Here are some confirming pointers, if you will. 1. Annualizing implies to convert the mean and stddev from another time period (days, months) to annual time period. To do that, you multiple the mean/stddev with some constant. For montly to annual, you multiply the monthly mean with 12. I show the calculation as explained from the old man himself http://www.stanford.edu/~wfsharpe/art/sr/sr.htm 2. The next question is what (monthly) mean to be used: Sharpe used arithmetic (monthly) mean, but the CFAI means it is more correct to use geometric mean for historic calculation, as you see throughout the level III textbook, e.g., in the capital market expectations chapter “section: sample estimators” It is also consistent with the annualized return calculation over several years, which use geometric mean. Further on, I quote from level I textbook section “Using Geometric and arithmetic means” “For reporting historical returns, the geometric mean has considerable appeal because it is the rate of growth we would have had to earn each year to match the actual, cumulative investment performance… The geometric mean is an excellent measure of past performance.” For further reference, CFAI’s opinion is that arithmetic mean is good in FORWARD LOOKING context.
AMA Wrote: ------------------------------------------------------- > So, the “correct way” to calculate the ARR > (annualized rate of return) shall be : > {[(1+r month1)* (1+r Month 2) * …(1+r month > 12)]^1/12 -1} x12 when monthly rate of retun is > given ? > > Can you advise where I can locate the “correct > way” in the curriculum ? This seems to be a combination of ARITHMETIC average and GEOMETRIC average.
AMA Wrote: ------------------------------------------------------- > Thank you very much for your guidances. > > So, the “correct way” to calculate the ARR > (annualized rate of return) shall be : > {[(1+r month1)* (1+r Month 2) * …(1+r month > 12)]^1/12 -1} x12 when monthly rate of retun is > given ? > > Can you advise where I can locate the “correct > way” in the curriculum ? It’s on page 90, at the top. It gives the geometric mean of the monthly returns first, then an example of how to convert that to annualize that rate by taking the 12th root and multiplying by 12. Page 90 was referenced about 3 times in this thread - I feel like I’m taking crazy pills!
We take a geometric multiplied number ( e.g. and raise it to ( 12/count(months)) i.e. (1+r1)*(1+r2)*(1+r3)…(1+n)^(12/n)-1 This annualizes a set of monthly returns
FinNinja Wrote: ------------------------------------------------------- > AMA Wrote: > -------------------------------------------------- > ----- > > Thank you very much for your guidances. > > > > So, the “correct way” to calculate the ARR > > (annualized rate of return) shall be : > > {[(1+r month1)* (1+r Month 2) * …(1+r month > > 12)]^1/12 -1} x12 when monthly rate of retun is > > given ? > > > > Can you advise where I can locate the “correct > > way” in the curriculum ? > > > It’s on page 90, at the top. It gives the > geometric mean of the monthly returns first, then > an example of how to convert that to annualize > that rate by taking the 12th root and multiplying > by 12. > > Page 90 was referenced about 3 times in this > thread - I feel like I’m taking crazy pills! Yes, I noted that and I found the way in their calculations (also in EOC Q12B) as mentioned above. What I meant was no statement about such a calculation when Sharpe Ratio and Sortino Ratio were introduced elsewhere in the curriculum. Thank !