Probability Future Return - X Future Return - Y .1 -10% -35% .2 2% 0% .4...

Probability

Future Return - X

Future Return - Y

.1

-10%

-35%

.2

2%

0%

.4

12%

20%

.2

20%

25%

.1

38%

45%
A. Given R_X = 12%, find R_Y
B. Given σ_y = 20.35%, find σ_X
Calculate CV_X and CV_Y
Compare their σ and CV to decide which one is more risky per dollar of return

Expert Solution

(A) Computation of RY

Yi (A)	Probability (p) (B)	RY (A)*(B)
(35)	0.1	(3.5)
-	0.2	-
20	0.4	8.0
25	0.2	5.0
45	0.1	4.5
Total RY	14.0

Hence, RY = 14%

(B) Computation of standard deviation of X

Xi	RX	(Xi - RX)	(Xi - RX)^2 (A)	Probability (p) (B)	(Xi - RX)^2 * p (A) *(B)
(10)	12	(22)	484	0.1	48.4
2	12	(10)	100	0.2	20
12	12	-	0	0.4	0
20	12	8	64	0.2	12.8
38	12	26	676	0.1	67.6
					148.8

Standard deviation (S.D.) of X = Square root of 148.8

= 12.20%

Coefficent variation of X = (S.D. of X / RX)

= (12.2 / 12)

= 1.016

Coefficent variation of Y = (S.D. of Y / RY)

= (20.35 / 14)

= 1.453

Lower the Standard deviation and Coefficent of variation, better the risk-return trade-off. Since the standard deviation and coefficient variation of Y is higher as compared to X, hence Y is more risky per dollar of return.

jeff jeffy answered 2 years ago

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