Question

Probability of State of Economy	State of Economy	Return of Stock A	Return of Stock B
0.20	Bear	0.05	-0.05
0.40	Normal	0.07	0.10
0.40	Bull	0.10	0.20

A) Calculate the expected return for each stock.

B) What is the correlation between the returns of the two stocks?

C) Assume the market has an expected return of 10% and a standard deviation of 20%. Also, ρ_B,M = 0.8. Calculate Beta for Stock B.

Answer 1

@ Expected return of stock A (RA) RA - E probability * Sehung = 0.20 X 0.05 +0.40% 0.07 + 0.40.80.10. - 0.078) Supected schurn of stock 8 (Re] RB = { Probability & Sections 0.20.X-0.05 + 0.4080.10 + 0.40 X 0.20 OU o calculation of correlation behrew sations of the two stocks the

state of Returing RA B-5 All {PARAS Economy me Returns of som hel restoje dardlo 0.05 0.078 -0.028 0.000764 Bear -0.05 0.11 -0.16 0.0256 0.00448 normal 0.07 0.078 -0.008 0.000064 0.10 -0.01 0.0001 0.09 0.0081 0.00008 0.00198 Bull 0.10 0.078 0.022 0.000484 0.20 0.11 standard deviation of A = J z prob [Rawa? - Se prob (lig-Zgj ? -{[0.20% 0.0256)+ (0.40x0.000] A - J (0.20% 0.000274] + [0.40x8.c064) + (0.40X0.00484] ) +(0.408 0.0061] LOA DA - 0.01939071942 0.09165151389 î 0.000000 co variance of (4,8) - E probability (daxde] => [0.20 X 0.00448] + [6.40% ] +0.40%0.0998] >) 0003378. 0.00172. = cov (A,B) correlation r(A,B) JAKOB 0.00172 - Ef you take recimals = [0.01939021842x(0,091659389] 0.9678206444 € [0.97-

criver "mit = 10.7. AMOS correlatiow calculation of O mrt - 2011 r18, mkt ) = 0.8 Be Of Ple, mut) Omkt

sady we calculated OB = 0.09165 151389 OB = 9.174. Therelor Share on 9,14 * B = 9.17 x 0.8 20 -) 0.3668 to decinals =) (0:37 to decimall