(1 point) If I have a strategy with a Sharpe ratio of 2, and you have a differen
ID: 2802968 • Letter: #
Question
(1 point) If I have a strategy with a Sharpe ratio of 2, and you have a different, uncorrelated strategy with a Sharpe ratio of 3, what would be the Sharpe ratio of a strategy that invests 50% into your strategy and 50% into my strategy? (Which of the following do we know for sure?)
a) The Sharpe ratio will be less than 2
b) The Sharpe ratio will be more than 2 and less than 3, but that’s all we know
c) The Sharpe ratio will be more than 2, and possibly even more than 3
d) The Sharpe ratio will be right around 2.5
e) Impossible to answer with the information given
CIRCLE ONE: A B C D E
Explanation / Answer
Answer: e) Impossible to answer with the information given.
Explanation:
Sharpe ratio for a portfolio = (Expected poartfolio return-Risk free return)/Standard deviation of the portfolio.
When two portfolios are combined, the standard deviation of the new portfolio, has to be recalculated using the standard deviations of the component portfolios using the formula:
Formula for SD of a portfolio combining two other portfolios =
[Wa^2*Sda^2+Wb^2*SDb^2+2*Waq*Wb*Sda*SDb*Cor(a,b)]^0.5
As no details as to the SD of the two existing portfolios is given, the SD and hence the Sharpe ratio of the new combined portfolio cannot be found out with the available details.
Formula for SD of a portfolio combining two other portfolios =
[Wa^2*Sda^2+Wb^2*SDb^2+2*Waq*Wb*Sda*SDb*Cor(a,b)]^0.5
where, Wa and Wb are the weights of the two portfolios, SDa,SDb their standard deviations and Cor(a,b), the correlation between them.As no details as to the SD of the two existing portfolios is given, the SD and hence the Sharpe ratio of the new combined portfolio cannot be found out with the available details.
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