4. Suppose you are an investment professional who is considering to invest in a
ID: 2808235 • Letter: 4
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4. Suppose you are an investment professional who is considering to invest in a portfolio of three risky assets, Si,S2 and S3. Suppose that the risk-free rate of return is 1%. It is known that the tangency portfolio contains 5% of Si, 30% of S2 and 65% of S3. It is also known that the expected return and the standard deviation of the return for the tangency portfolio are 10% and 5% respectively. (a) Ifyou want the volatility (standard deviation) of the return on a portfolio to be 3%, what proportions [6 marks] (b) If you want the expected return on your investment to be 13%, what proportions of your funds [6 marks] of your funds should be in the risk-free asset, asset S, asset S2 and asset S3? should be in the risk-free asset, asset Si, asset S2 and asset S3?Explanation / Answer
a) Let w1 be the weightage of Risk free asset in the portfolio so that SD becomes 3
present SD of the portfoliio = 5
SD of Risk free asset = 0
Therefore, we get following equation -
w1 x 0 + (1 - w1) x 5 = 3
Solving the above equation, -
5 - w1 x 5 = 3
w1 = 2/5 or 40%
Therefore, proportion of risk free asset in the portfolio will be 40%
and that S1 , S2 and S3 = 5 *0.6 , 30* 0.6 and 65*0.6 i.e 3%, 18% and 39% respectively
b) Let w1 be the weightage of Risk free asset in the portfolio so that expected return becomes 13%
present expected return of the portfolio = 10%
Return on Risk free asset = 1%
Therefore, we get following equation -
w1 x 1 + (1 - w1) x 10 = 13
Solving the above equation, -
w1 + 10 -10w1 = 13
-9 w1 = 3
w1 = -3/9 = -33.33%
that means, we have to short sell the risk free asset from our portfolio such that its weightage is -33%
Weightage of S1, S 2 and S3 will be = 5 x 1.3333 , 30 x 1.3333 and 65 x 1.3333
that is 6.67 %, 40% and 86.67% respectively
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