Question

Assume security returns are generated by the single-index model. R 1 =a 1 + beta 2 R M +e 1 where R 1 is the excess return for security and R N market’s excess returnThe risk-free rate is 4% Suppose also that there are three securities A8and characterized by the following data!

Saved Assume that security returns are generated by the single-index model R; - ei + BiRM + ej where is the excess return for security i and Ry is the market's excess return. The risk-free rate is 4%. Suppose also that there are three securities A, B, and C characterized by the following data: Security Pi E(R) Die 0.8 151 245 B 1.1 18 15 1.4 21 18 a. If Ox=20%, calculate the variance of returns of securities A, B, and C Variance Security A Security B Security C b. Now assume that there are an infinite number of assets with retur characteristics identical to those of A B, and respectively. What will be the mean and variance of excess returns for securities A Band C? (Enter the variance answers as a percent squared and mean as a percentage. Do not round Intermediate calculations. Round your answers to the nearest whole number.) Mean Variance Security A Security B Security C

Answer 1

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Answer:

Solution - A:

A: 5

B: 3.63

C: 2.85

Solution - A:

A: 9% , 8.32

B: 14% , 7.09

C: 17% . 11.08

Working:

solution : Given data, * Assume that security returns are generated by the single - index model, R; = 2; +BRM tei. where, * R is the excess return for security and RM is the market's excess returns * the risk - free rate is ¢ opo Now we can write, . using single Index model, Expected return of an Individual security. Ro a ap + Bp RM R; z. Retum of securely return component represented - Specific

by the alpha of the Secuivity. Ra Ra = Market related return component represented by the term. E(79) - Of = 15% -4.%. = A B c R = = 90% = 14% = 17% = 68% -4% = 21.), -4% W 2 919 - of A = 9-4 = 50%, B 214-4210% c -14-4 =13% Now we have to calculate the variance of return of Secuivities A, B and c, R; = xy + Bi Roti

* using of this formula calculate market return = A = R = x +8 PM 9-5 + oifera) 0,8(km) – 9-5. 218CRA] =4, Pri e 5, А с Ru - ә = security. B = RM = Rp = 0&+Bo Romi =14 = 10+ 101 CRALD DotCRA) = 14-10. hol Cra) 24.

RM - - 3,63. . Security B = Rm = 3,63 & security c = RM = Re = Lot Bo Rai c. 1 7 = 13 + 104 CRM ) = 17-13 104CPM) = 44, RM €2186. i security c = RM = 2185. variance security a security B Security C 3.63 2.85

calculate of Now . we have to expected retursi security A = RP = R + Borre - 5 to 885 25+ 4 =90% Security A = 90% y Security B = Rp = 10 +11 (3.63) = 10+ 3.99 = 13.99 = 14% " Security B = 14%)

Ret 13t 104. = 1373199 = 16.99 -17% security c = 17% * The variance of individual Security (62). ola variance of individual security, o2 = 8 m to om P a variance of market index return. = Beta coefficient of individual security. Ivariance of residual returns of Individual security, od

<p security. A = to =0.8X0.8 X0,20 70.20 +0.24 X0:24. =066. * 004 +0.0576, =0.0256 of 0.0576 2010832 = 8.32% security A = 8132 %] BOR Flil XL1 X02x0,2 +0,15%0.15. 31:21X0.04 +0.0225. C0.0484 +0.0225. 0.0709. 7.09% = 7,09570). = si security B =

security.cc OSEBE O tome 1.4 X 1.4 X0.20 X0-20 +0.1870118 =1196X0.04 +010324. 0.0784 7016324, Ou1108 al1008% - 11.08%| is security cao Mean variance security A seturity 8 security c 14 l7 % %0 8.32 7109 1108