Mutual Fund (Separation) TheoremYour uncle asks for investment advice. Currently

Question

Mutual Fund (Separation) TheoremYour uncle asks for investment advice. Currently he has $10,000 invested in Portfolio P,which has an expected return of 10.5% and a volatility of 8%. Suppose the riskfree rate is5%, and the tangent portfolio has an expected return of 18.5% and a volatility of 13%.

(a) To maximize his expected return without increasing his volatility, which portfolio wouldyou recommend?

(b) If your uncle prefers to keep his expected return the same but minimize his risk, whichportfolio would you recommend?

(c) Draw a graph with volatility on the x-axis and expected return on the y-axis. Sketchthe frontier and include the capital market line. Label the following:• efficient frontier• inefficient frontier• minimum variance portfolio• tangent portfolio• riskfree rate• your uncle’s portfolio (Portfolio P)• portfolio in part (a)• portfolio in part (b)

(d) Explain the Mutual Fund (Separation) Theorem.

Explanation / Answer

1.Best portfolios are combinations of the risk free investement and the tangent portfolio.

If we invest an amount of X in the tangent portpolio , The expected return and volatality are

ER=Rf+x(Rm-Rf)

=5%+x(18.5-5%)

SD(Rx)=XSDR(t)=x13%

So, to maintain the volatality of 8% X =8%/13%=61.5%

In this cas your uncle shoud invest 61.5% of his money in

money ($ 61500) in the tangent portfolio

And remaining 38.5% in the risk free investment. then his expected return will be 5%+61.5%*13.5%=13.3%

Alternatively, to keep expected return at 10.5%   x must satisfy 5%+x(13.5%)=10.5%

So x=40.7%

Now your uncle should invest $ 40700 in the tangent portfolio and $ 59300 in the risk free investment, lowering his volatility level to (40.7%)*13%=5.29%

The lowest possible given his expected return

Related Questions

Navigate

• Browse (All)
• Browse M
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.