You can trade (long short) two assets, asset f is risk-free with expected return

Question

You can trade (long short) two assets, asset f is risk-free with expected return rf = 2%, and standard deviation of return equals to , = 0. Asset m is risky with expected return of E (rm) = 85 and standard deviation of return equals 6%. Since risk free return is pre-determined, throughout this question, you can assume pm. 0. You plan to invest in a portfolio of asset f and asset m. The portfolio weights on each assets adds up to 1, Denote the return on the portfolio as rp, and denote expected value and standard deviation of the portfolio return as p and 'p, respectively. Extra credit, 2 points! Provide an algebraic expression for Mp and Op as a function of rf, af, - Om, Ws and W. 1 2. Colnpute p and Op, if you pick W, = Wm-0.5 If you are seeking an expected portfolio return that equals and 11 respectively? In this case, what is the associated portfolio standard deviation ? Explain your trading strategy in layman's terms. 3 12%, what values do you assign to Wf

Explanation / Answer

a)

Return on portfolio=wf*return on f + wm*return on m=wf*return on f+(1-wf)*return on m=wf*(return on f-return on m)+return on m

Standard deviaiton of portfolio=wm*standard deviaiotn of m=(1-wf)*standard devation of m

b)

Return=0.5*(2%-8%)+8%=5%
Standard deviaiotn=0.5*6%=3%

c)

12%=wf*(2%-8%)+8%
=>wf=-4/6=-2/3
wm=5/3

Standard devation=(1-wf)*standard devation of m=(1-(-2/3))*6%=10%

We will inest in risk free and additionally short the asset m and invest those proceeds in risk free or asset f

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