标题: R36 : means to game the Sharpe ratio [打印本页] 作者: DoubleDip 时间: 2011-7-11 15:22 标题: R36 : means to game the Sharpe ratio
V5, p87, the two statements in the last paragraph :
1. Does it mean ?
Yearly SD < monthly SD x 12^1/2 < weekly x 12^1/2 < daily SD < 250^1/2 ?
SD : Standard Deviation, ^1/2 : Square Root
2. Does it mean ?
The mean return used in the numerator of the calculated Sharpe ration is resulted from
compounding 12 months returns while the Standard Deviation from a single month's
return (or the mean of 12 month returns) is used in the denominator ?
Anyone can advise ?作者: dyga 时间: 2011-7-11 15:22
1. By lengthening the measurement interval - std deviation increases.
Usually annual std dev > weekly std dev.
But what is a way this number can be gamed?
if you calculated a weekly std deviation and converted it into a annual std deviation using
annual std dev calculated = weekly std dev * sqrt(52) (since there are 52 weeks in a year) the annual calculated std dev will be a smaller number.
but numerator likewise would not be affected. It would be more or less the same number (r weekly * 52 would be approximately equal to r-annual.)
but now since a lower annual std dev calculated is used - the sharpe ratio now would be a HIGHER number (since the denom. is lower).
2:
Returns are compounded. So numerator = (1+rweek1)*(1+rweek2)*...(1+rweek52) - 1
std dev = monthly std dev*sqrt(12). (not compounded).
return would most likely be equivalent to the annual return (or off by a very little bit).
but std deviation calculated as above would be lower - so end result Sharpe Ratio would be higher.
CP作者: bodhisattva 时间: 2011-7-11 15:22
CP, thank you very much for your response !
1. What you meant are :
Acutually (usually) : Yearly SD > monthly SD > weekly SD > daily SD
if the Yearly SD is calculated as : monthly SD x 12^1/2 or weekly SD x 52^1/2 or
daily SD x 250^1/2, the calculated Yearly SD will be lower than the actual yearly SD,
i.e., the calculated yearly SD is an under-estimated one and the calculated Sharpe ratio
will be HIGHER than the actual/real one.
Am I right ?
2. In your example, I think the return in the numerator shall be : (1+r month1)*
(1+r Month 2) * ...(1+r month 12) -1 , since you use "monthly" SD in the denomintor.
What is the monthly SD here ? The SD of a specific single month's return ?
And this will lead to higher Sharpe ratio (than real one) ?
Since sqrt(12) = 3.464 and the annualized yearly return (compounded from monthly
returns) is not necessarily 3.464x greater than the annualized yearly return, therefore,
I think it is not necessarily that the calculated Sharpe ratio will be HIGHER than the
actual/real one. i.e., there is a likelyhood that the the calculated Sharpe ratio will be
LOWER than the actual/real one. But in any case, the calculated Sharpe ratio will be a
distorted one.
Am I correct ?作者: pennyless 时间: 2011-7-11 15:22
I come back to this issue because I still can't get it. Anyone can help ?作者: ll11 时间: 2011-7-11 15:22
AMA technical you may be but darn it you overthink everything .............................returns are linked geometically while standard deviation is a function of sqrt(T)
"Simplify as much as possible, but no further."
my boi Bert作者: Unforseen 时间: 2011-7-11 15:22
1) It may simply mean that SD(based on annual return) < SD(based on monthly return) and etc.
It's the "smoothing", I think.
2) I also have a difficulty in understanding it. It is more a general problem than specific to Sharpe ratio.
SD(based on monthly return) = SD_M x sqrt(12)
R > Sum(12 monthly return)=Avg(monthly return)*12. It could be "<" in a bear market due to compounding.
But we usually use avg(monthly return) in SD calculation....kind of inconsistent.
PS. R and SD here are annualized.
Edited 1 time(s). Last edit at Monday, April 4, 2011 at 10:43AM by deriv108.作者: NakedPuts00 时间: 2011-7-11 15:22
1) is a gaming.
2) is more like a problem of Sharpe Ratio itself. If not calculating that way, what else can we do?作者: former 时间: 2011-7-11 15:22
pimpineasy Wrote:
-------------------------------------------------------
> AMA technical you may be but darn it you overthink everything .............................returns
> are linked geometically while standard deviation is a function of sqrt(T)
>
> "Simplify as much as possible, but no further."
>
> my boi Bert
This forum is open for discussions of any issue in the curriculum !作者: Roflnadal 时间: 2011-7-11 15:22
alta
since you dont understand me i think u stand under me .......................
never meant it as a dis or a dont discuss this topic ................all i was pointing out is that AMA has a tendency to overthink things when a much simpler approach would be more elegant
Edited 1 time(s). Last edit at Monday, April 4, 2011 at 11:28AM by pimpineasy.作者: bboo 时间: 2011-7-11 15:22
pimpineasy Wrote:
-------------------------------------------------------
> alta
> since you dont understand me i think u stand under me .......................
>
> never meant it as a dis or a dont discuss this topic ................all i was pointing out is
> that AMA has a tendency to overthink things when a much simpler approach would be more > elegant
I don't think he is overthinking, you can see here other candidates have same questions (including me). It good to raise question here and get clarification through discussions.作者: strikethree 时间: 2011-7-11 15:22
whether you do annual return as a geometric mean of monthly returns or as an arithmetic mean of returns - you are not going to have returns going too far off from each other.
however std dev of returns (denominator) would change.
I think that is the point of this entire statement.
-- need to be consistent in the period used.
-- do not try to forecast a bigger period's std. dev from a smaller period's. (once you did that - you would have a lower std. deviation on the bigger period).
-- and then use that new lower std. deviation in the sharpe ratio - your sharpe ratio would be overstated.
CP作者: IAmNeil 时间: 2011-7-11 15:22
Correction to my previous message.
I think statement 1 shall mean that ASD from DAILY (rather than ASD from weekly return or monthly return) which shall be HIGHEST and shall be used in calculation of Sharpe Ratio (especially, for hedge funds, since monthly returns are reported).作者: PalacioHill 时间: 2011-7-11 15:22
Following are fundamental issues : In calculation of Sharpe Ratio,
1. Statement 1
Why ASD (Annualized Standard Deviation) of daily returns is generally higher than the weeky, which is, in turn, higher than the monthly ?
I don't have answer but I think statement 1 shall mean that ASD from monthly return (rather than ASD from weely return or daily return) which shall be lowest and shall be used in calculation of Sharpe Ratio (especially, for hedge funds, since monthly returns are reported).
2. Statement 2
What is the correct way to calculate the ARR (Annualized Rate of Return), given monthly
or weekly or daily rate of retun ?
I am sorry it seems I missed something because I don't remember where this is stated formally in the curriculum. But it seems the "correct way" shall be : {[(1+r month1)* (1+r Month 2) * ...(1+r month 12)]^1/12 -1} x12 when monthly rate of retun is given.
Please refer to P.89~90 in this reading and EOC Q12B. In these 2 cases, the ARR calculated from : (1+r month1)* (1+r Month 2) * ...1+r month 12) -1 are higher than those calculated by the "correct way" and this shall be a means to gaming.
As for SD, I think basically no way to compound the SD from the monthly return and ASD = MSD x ^12 shall be used when monthly rate of retun is given. (MSD : Monthly SD)
