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Rate of Return if State Occurs State of Economy Probability of State of Economy

ID: 2781465 • Letter: R

Question

Rate of Return if State Occurs

  State of Economy

Probability of State of Economy

Stock A

Stock B

  Recession

0.20

0.06

-0.19

  Normal

0.50

0.08

0.16

  Boom

0.30

0.16

0.34

a. What is the expected return on Stock A?

b. What is the standard deviation of return on Stock B?

c. Which is riskier?

d If investors become more risk averse, what will happen to the price of stocks in general? Why?

Rate of Return if State Occurs

  State of Economy

Probability of State of Economy

Stock A

Stock B

  Recession

0.20

0.06

-0.19

  Normal

0.50

0.08

0.16

  Boom

0.30

0.16

0.34

Explanation / Answer

a. EV of Stock A= 0.2*0.06+0.5*0.08+0.3*0.16 = 0.1 = 10%

EV of Stock B= -0.2*0.19+0.5*0.16+0.3*0.34 = 0.144 = 14.4%

B. Standard deviation is computed using the excel function as below

= SQRT( sumproduct(Stock returns- EV)^2, Probabilities)

Hence Standard deviation is calculated as below

Standard deviation can also be computed as below

c. Project B is riskier.

d. Risk averse investors will opt for Stock A. Since the demand for stock A will be higher, the demand for Stock B will go down. Accordingly, the price of Stock A will be higher and the price of stock B will decline.

A B Recession 0.2 0.06 -0.19 Normal 0.5 0.08 0.16 Boom 0.3 0.16 0.34 Expected value 0.1 0.144 Standard deviation 0.04 0.184293