Acct 5210 Problem Set 1

FINA 5210 Problem Set 1 (Group 305)

Problem 1
(a)

WpC=[E(rp)-rf] ÷Aσp2 =6%÷2.5×(20%)2 =60%

WfC=100% - 60% = 40%

(b)
Expected return of Complete portfolio is: rCEc= WpC×E(rp)+ WfC×rf =60%×10% + 40%×4% =7.6%
The standard deviation of Complete portfolio is: σc = WpC × σp = 60% × 20% = 12%

Certainty-equivalent rate of return for investing in C: rc CE= Uc = rCEc- 1/2Aσc2 = 7.6% - 0.5×2.5×12%2 = 5.8%

Certainty-equivalent rate of return for investing in P: rp CE= Up= rCEp- 1/2Aσp2 = 10% - 0.5×2.5×20%2 = 5%

After we determine the optimal risky portfolio, the right mix between the risk-free asset and the optimal risky portfolio will be determined by investors. In this step, utility plays a role and investors can achieve
It means that the return on every unit risk taken, portfolio P generates higher return than the other two assets. This makes sense because P includes both of VW and 30-year bond, by better allocation between these two assets, it is possible to generate higher return with lower risks due to diversification.

(c)
Standard deviation of your client’s portfolio p̂: σp̂ = WVWσvw = 80% ×(0.001902)0.5 = 0.0349

Giving the standard deviation of p̂ is constant, which means σp̂ = σC*, which new portfolio C* represents portfolio including P and risk-free assets with same standard deviation as portfolio