Question

Answer questions 10-14 following this information. Mean -variance investor risk aversion (RA) level is 2. The expected return and standard deviation of three assets classes are as bellow,

Assets Class Expected Return Standard deviation of return

A 10% 25%

B 8% 15%

C 6% 12%

risk- free rate of return is 3% and the short fall level is 5% select the investors.

(12) Risk adjusted rate of return (Expected utility) is,

A. 7.98%, 5.97% and 9.94% B. 5.97%, 9.94% and 7.98% C. 9.94%, 7.98% and 5.97% D. none of the above

(13) Sharp (Reward volatility) Ratio is, A. 0.33, 0.22 and 0.28 B. 0.28, 0.33 and0.25 C. 0.22,0.28 and 0.33 D. none of the above

(14) Safety-First Ratio is, A. 0.083,0.20 and 0.20 B. 0.20, 0.20 and 0.083 C. 0.20, 0.083 and 0.20 D. none of the above

(15) the best asset class is A. A B. B C. C D. none of the above

Answer 1

The following informations are given the data:

Risk aversion level = 2

Risk free rate return = 3% = 0.03

Short fall level = 5% = 0.05

13. Answer

Risk adjusted rate of return (Expected utility) means that investor is taking some crucial decision without knowing the outcome. This decision can depend on risk aversion of the investors.

The formula for Expected utility = E(RA) – 0.005 X RB X A

Where, E(RA) = Expected return of the asset class

              RB = Risk aversion level

               A = Variance of return of the asset class

Asset Class  A

Expected utility = 0.1 - 0.005 x 2 x (0.25)2 ( here, it is given the standarad deviation ,so variance = square of standarad deviation)

  = 0.1 - 0.005 x 2 x 0.0625

= 0.09937

= 9.937 = approx 9.94 %

Asset Class B

Expected utility = 0.08 - 0.005 x 2 x (0.15)2

= 0.07977

= approx 7.98%

Asset Class C

Expected utility = 0.06 - 0.005 x 2 x ( 0.12)2

= 0.0598

= approx 5.98%

Therefore the option C is correct.

13. Answer

The formula for Sharp's Ratio = (RA - Rf) / A

where, RA = Expected return of the asset class

  Rf = Risk free return

A = Standarad deviation of asset class

Asset Class  A

Sharp's Ratio = (0.1 - 0.03) / 0.25

= 0.28

Asset Class B

Sharp's Ratio =( 0.08 -0.03) / 0.15

= 0.33

Asset Class C

Sharp's Ratio = ( 0.06 -0.03) / 0.12

= 0.25

Therefore the option B is correct.

14.Answer

The formula for Safety-First Ratio = (E(RA) – Shortfall level) / A

where, E(RA) = Expected return of the asset class

A = Standarad deviation of asset class

Here, shortfall level = 0.05 or 5%   

Asset Class  A

Safety-First Ratio = (0.1- 0.05) / 0.25

= 0.2

Asset Class B

Safety-First Ratio = (0.08 - 0.05) / 0.15

= 0.2

Asset Class C

Safety-First Ratio = ( 0.06 - 0.05) / 0.12

= 0.083

Therefore the option B is correct.

15. Answer

Best class asset can be identified based on its return. For asset class A the expected return is 10%..Comparing with other asset class B & C , the asset class A has more return.  Better return can get only through taking high risk. Therefore, the best asset class is A.

Therefore the option A is correct.