Question

Consider the following information about three stocks: State of Economy Probability of State Rate of Return if State Occurs Stock A Stock B 0.24 0.36 0.17 0.13 0.00 -0.28 Boom Normal Bust 0.35 0.50 0.15 Stock C 0.55 0.09 -0.45 a. What is the expected return of Stock A? The standard deviation? (6 points) b. If your portfolio is invested 40% each in A and B and 20% in C, what is the portfolio expected return? The standard deviation? (13 points) c. If the expected T-bill rate is 3.8% and the portfolio has a beta of 1.6, what is expected market risk premium? (4 points)

Answer 1

A В D E F G Н 21 22 a) 23 Expected Return of StockA 24 [A] [B State of Economy (ER-AR)2 [C] Probability of State -[A Rate of Return [B] [A]*IC] ER-AR 25 +F26* B26 +F27* B27 26 Boom 0.24 =+C26-D29 +E26 *E26 =+B26*C26 0.35 0.5 0.17 0 +E27*E27 27 Normal +B27*C27 +C27-D29 28 Bust +B28*C28 =+C28- D29 +E28*E28 +F28* B28 0.15 -SUM(D26:D28) Expected Return SUM(G26:G28) 29 -SQRT(G29) Standard Deviation 30 31 Expected Return of Stock B 32 [A] [B Rate of Return [B State of Economy (ER-AR)2 [C] A] IC] Probability of State -[A ER-AR 33 -+B34* C34 +E34*E34 +F34 * B34 +F35 *B35 34 Boom 0.35 0.36 +C34- D37 0.13 =+C35-D37 |-+с36-D37 +E35 *E35 35 Normal 0.5 +B35 * C35 -+B36*C36 36 Bust 0.15 -0.28 +E36*E36 +F36*B36 -SUM(G34: G36) Expected Return -SUM(D34:D36) 37 38 -SQRT(G37) Standard Deviation 39

А В C D E G Н 42 Expected Return of Stock C 43 Probability of State -[A [A] [B (ER-AR)2 [C] State of Economy Rate of Return [B] A] IC] ER-AR 44 0.55 +B45*C45 +C45-D48 +E45*E45 +F45*B45 0.35 45 Boom 0.09 +B46*C46 +C46-D48 +E46*E46 +F46* B46 46 Normal 0.5 0.15 +F47* B47 +B47*C47 =+C47-D48 +E47*E47 47 Bust -0.45 48 Expected Return SUM(D45:D47) SUM(G45:G47) 49 =SQRT(G48) Standard Deviation 50 51 52 53 54 b) Portfolio Expected Return 55 Percentage Expected Return Portfolio return Stock 56 0.4 57 A =+B57*C57 +D29 0.4 +B58*C58 58 B +D37 59 C 0.2 +D48 =+B59*C59 60 Portfolio Expected Return SUM(D57:D59)

fox F68 A C D E 63 Stock Standard Deviation Portfolio Standard Deviation Percentage 64 65 A +F30 +B65*C65 0.4 66 B 0.4 =+F39 =+B66*C66 0.2 =+B67*C67 67 C +F50 68 Portfolio Standard Deviation SUM(D65:D67) 69 70.

a)
Expected Return of Stock A
State of Economy	Probability of State -[A]	Rate of Return [B]	[A] * [B]	ER-AR	(ER-AR)2 [C]	[A]*[C]
Boom	0.35	0.24	0.084	0.071	0.005041	0.001764
Normal	0.5	0.17	0.085	0.001	0.000001	0.00
Bust	0.15	0	0	-0.169	0.028561	0.004284
	Expected Return		0.169			0.006049
			Standard Deviation		0.078
Expected Return of Stock B
State of Economy	Probability of State -[A]	Rate of Return [B]	[A] * [B]	ER-AR	(ER-AR)2 [C]	[A]*[C]
Boom	0.35	0.36	0.126	0.211	0.044521	0.015582
Normal	0.5	0.13	0.065	-0.019	0.000361	0.00
Bust	0.15	-0.28	-0.042	-0.429	0.184041	0.027606
	Expected Return		0.149			0.043369
			Standard Deviation		0.208
Expected Return of Stock C
State of Economy	Probability of State -[A]	Rate of Return [B]	[A] * [B]	ER-AR	(ER-AR)2 [C]	[A]*[C]
Boom	0.35	0.55	0.1925	0.38	0.1444	0.05054
Normal	0.5	0.09	0.045	-0.08	0.0064	0.00
Bust	0.15	-0.45	-0.0675	-0.62	0.3844	0.05766
	Expected Return		0.17			0.1114
			Standard Deviation		0.334
b)	Portfolio Expected Return
Stock	Percentage	Expected Return	Portfolio return
A	40%	0.169	0.0676
B	40%	0.149	0.0596
C	20%	0.17	0.034
Portfolio Expected Return			0.1612
Stock	Percentage	Standard Deviation	Portfolio Standard Deviation
A	40%	0.078	0.0311
B	40%	0.208	0.0833
C	20%	0.334	0.0668
Portfolio Standard Deviation			0.1812

c) Expected Return of Portfolio = 16.12% ( As calculated above)

R_f = 3.8%

B = 1.6

ER= R_f + B *( Market Risk Premium)

16.12% = 3.8% + (1.6*R_p)

12.32% = 1.6* R_p

R_p = 12.32%/ 1.6

= 7.7 %

Market Risk premium = 7.7 %