Assume the following capital market expectations. Answer the three questions below:

	E(r)	Std. Deviation
Stocks	0.14	0.245
Bonds	0.09	0.148
Cash	0.06	0.000
Correlation (rs, rb)	-0.2378

1. Find:

1. The most efficient way (lowest risk way) to achieve an E(r) of 9% from a portfolio of cash, stocks and bonds.

First locate O* (the optimal risky portfolio) by solving for:

W_s^* = ________, W_b^* = ________, E(r_p)^* = ________, _p^* = ________

Cov(r_s, r_b) = _{bs * b * s}

₌ -0.2378 * 0.245 * 0.148

W_s* = [E(r_s) - r_rf] _b² -[E(r_b) - r_rf] Cov(rs, rb)

[E(r_s) - r_rf] _b² +[E(r_b) r_rf] _s² -[E(r_s) - r_rf + E(r_b) - r_rf] Cov(r_s, r_b)

W_b* = 1- W_s*

Portfolio Expected Return

E(r_p) = w_s r_s + w_b r_b

Portfolio Standard Deviation

_p = w_s² _s² + w_b² _b² + 2 (w_s w_b)Cov(r_s, r_b)

Now explore what proportion would need to be invested in O* as well as in risk-free assets.

E(r_c) = 9.00% = 6% + y (E(r_p)^* - 6%

y = proportion in O_p^*= ________

1-y = proportion in cash = ________

2. The standard deviation of the portfolio.

_c^* = ________

3. The proportion invested in the three assets of cash, stocks and bonds.

Cash (1-y) = ________

Stocks (W_s^* )(y) = ________

Bonds (W_b ^*)(y) = ________

(on excel)