R36 : means to game the Sharpe ratio returns, monthly, statements, single

DoubleDip

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 ?

IAmNeil

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).

PalacioHill

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)

Any further response is appreciated !

strikethree

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

bboo

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.

Roflnadal

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.

former

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 !

NakedPuts00

1) is a gaming.
2) is more like a problem of Sharpe Ratio itself. If not calculating that way, what else can we do?

ll11

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

Unforseen

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.