sharpe ratio of a combination of portfolios

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hala_madrid

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in some questions where you must get a combination of corner portfolios, return of the combination = weight of the first one x its return + weight of the second one x its return
ok
is the sharpe ratio of the combination also weight of the first one x its sharpe ratio + weight of the second one x its sharpe ratio, or is it non linear?
I think that, as sharpe ratio includes volatility in the denominator, this should not be linear, so above calculation would be wrong
what do you think?
thx
 
Within the readings, I think (don’t have the book in front of me) they did a linear calculation of the volatitlity of the new portfolio? The risk of the new portfolio will not be greater than the risk of the either corner portfolios anyway.
 
it is actually the answer to one of the questions in 2005 exam, available online:
“the combination of corner portfolios 4 and 5 has the highest sharpe ratio among the efficient portfolios that meet her requirements”
no way we can get the sharpe ratio of a combination of corner portfolios, and compare it to each corner portfolio´s sharpe ratio
I think this argument of CFA is wrong
 
Wait one quick second….
If we are talking about corner portfoilio here (SS7), you may have noticed how the material shows us how to calculate the resulting portfolio’s std (it was approximating with weighted average of each corner portfolio’s std.) So, I won’t say the calculation is completely wrong given the context, I would say the calcuation would be a good approixmation of the resulting sharp.
Somebody correct me if my reason is not reasonable at all.
Thanks.
 
The key word is ‘meet her requirement’. That is the only portfolio that matters. If a corner portfolio exactly met investor’s requirement, why bother combining it with another corner portfolio? Just pick that portfolio which is on EF anyway.
 
yes ws, that what schweser (I think) says
rand0m wrote a good post about this:
if st dev is just the average, you are assumming correlation is 1 (somebody correct me if I am wrong)
but it is impossible for corner portfolios to have a correlation of 1, conceptually, right?
 
^Yes! However, given the material…all I am saying is that such calcuation (maybe, and maybe) is not compeletly wrong, it is only an approximation of the resulting sharp ratio.
 
If the required return is say 8% and the two closest corner portfolios are with 7% returns and 9% returns. You would then take the weights of each corner portfolio and multiply 50% (I made it easy) times their asset weightings to get the asset Weightings for your 8% Expected Return portfolio. You now have the Weights, just say 60% S&P and 40% Lehman Agg. They will provide you with Expected Returns and Std. Deviations. If they gave you correlations you could calculate the portfolio std deviation, however, they probably won’t so you can approximate the std deviation of the 8% portfolio by taking 50% of the 7% portfolio’s std deviation and the 9% portfolios std deviation. This is only “approximate”…you can now calculate the Sharpe Ratio if they provided you with the T-Bill or Rf rate…If not back into it if they gave you sharpe ratios for the corner portfolios….Ok I have blabbed on about this enough…I lost what I was even talking about originally…
 
hala_madrid Wrote:
——————————————————-
> yes ws, that what schweser (I think) says
>
> rand0m wrote a good post about this:
>
> if st dev is just the average, you are assumming
> correlation is 1 (somebody correct me if I am
> wrong)
>
> but it is impossible for corner portfolios to have
> a correlation of 1, conceptually, right?
Right
 
Taking a weighted average of standard deviations of two portfolios gives the upper bound on the standard deviation of the combination because the correlation term, which is positive, is neglected. A corollary of this would be that the Sharpe ratio calculated using this value of standard deviation will represent a lower bound for the actual number.
 
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