2: (46 POINTS) A pension fund manager is considering investing in 2 mutual funds: a stock fund(S), a long-term government and corporate bond fund (B). The following table presents the expected return and standard deviation of the stock fund and of the bond fund:

The correlation between the stock fund and the bond fund is = :25

	Expected return (ri)	Standard deviation ( i)
Stock fund (S)	:24	:40
Bond fund (B)	:12	:20

(a) Find the mininimum variance portfolio. That is, Ond the proportion invested in the stock fund,wMIN and the proportion invested in the bond fund, wMIN = 1 wMIN : Find the expected return of

SBSthe min variance portfolio, E rMIN and its standard deviation, MIN:

(b) Tabulate and draw the portfolio frontier of the 2 risky funds. That is, vary wS and wB = 1 wSin increments of .20. Complete the following table:

wS	wB	E(rP)	P
0	1
:20	:8
:40	:6
:60	:4
:8	:2
1:00	0

and draw the portfolio frontier on a graph with E (rP ) on the vertical axis and P on the horizontal axis. On that graph identify the minimum variance portfolio and the e cient portfolio frontier.

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(c) A Treasury Bill money market fund is now available with an 8% safe return (rf = :08): Draw the capital market line (CML). Identify the intercept with the vertical axis and the tangency point with the e cient portfolio frontier for risky assets. What is the e cient set in this case?

(d) Find the market portfolio. That is Ond the proportion invested in the stock fund, wMARKETS

and the proportion invested in the bond fund, wMARKET = 1 wMARKET of the market portfolioBS

Find the expected return of the market portfolio, E(rM) and its standard deviation, M: Find the Sharpe ratio.

(e) An investor requires a target expected return of 15%, that is E (rT ) = :15: Find the standard deviation of her portfolio, T . What proportion will she invest in the monetary market fund, wMONEY ?What proportion will she invest in the stock fund, wS? What proportion will she invest in the bond fund, wB?

(f) If the investor wanted to invest only in the stock fund and bond fund and achieve a target return of E (rT ) = :15; how much would she have to invest in the stock fund, wS and how much in the bond fund, wB?What would be the level of risk of this new portfolio?