T-Mobile Wi-Fi 9:04 PM RiskCAPMProblems2017.docx Risk and CAPM Problems . Assume
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T-Mobile Wi-Fi 9:04 PM RiskCAPMProblems2017.docx Risk and CAPM Problems . Assume the following return and volatility information for two assets A and B Return Deviation Standard 6% Asset A 10% Asset B 20% 12% Assuming you build an equally weighted portfolio of these two assets, calculate the portfolio for the following three cases a. A and B are independent assets b. A and B are perfectly correlated assets c. A and B are completely negatively correlated assets What is the maximum standard deviation for this portfolio? 2. Give an example of an unsystematic risk 3. Give an example of a systematic r 4. Which of the above two risks can be isk eliminated through diversification? 5. Which of these portfolios is not on the efficient frontier? a. 4% return, 10% risk b, 6% return, 14% risk c, 5% return, 14% risk d, 7% return, 20% riskExplanation / Answer
Since we have constructed equaly weighted portfolio of these 2 assets,
Return of the portfolio = 50%*Ra + 50%*Rb (where Ra is the return of the first asset and Rb is the return of the second asset.
Return of the portfolio = 50%* 10% + 50%*20% = 5% + 10% = 15%
Now, for standard deviation, the formula is as follows
Std deviation of portfolio = (Wa*Wa*std dev A*std dev A + Wb*Wb*std dev b*std dev b + 2*Wa*Wb*std dev A*std dev B * corelation)^0.5
Now 1) if correlation is 0 i.e. they are independent, then
Std deviaion of the portfolio = (0.5*0.5*6%*6% + 0.5*0.5*12%*12% + 0)^0.5 = 6.7%
b) if perfectly correlated, correlation = 1, so putting these values,
Std deviaion of the portfolio = (0.5*0.5*6%*6% + 0.5*0.5*12%*12% + 0.5*0.5*6%*12%*1 )^0.5 = 7.93%
c) if completely negative correlated, correlation = -1, so putting these values,
Std deviation of the portfolio = (0.5*0.5*6%*6% + 0.5*0.5*12%*12% - 0.5*0.5*6%*12%*1 )^0.5 = 5.19%
As can be seen, the maximum standard deviation of the portfolio is when corelation is 1 and that is 7.93%
2. Unsystematic risk are risks that are company specific and that can be removed with diversification for eg labor problems,
3. Systematic risk are the risks that are country wide and cannot be diversified. eg the great recessions.
4. As said above, unsystematic risk can be eliminated through diversification.
5. Returns increase with risk in efficient frontier. so b. 6% return, 14% risk is NOT on efficient frontier
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