Based on the following information calculate the expected return and standard de

Question

Based on the following information calculate the expected return and standard deviation for the two stocks (show the calculation):

State of Economy

Probability of State occurring

Stock Y Return

Stock Z Return

Recession

0.15

-0.1

-0.02

Normal

0.70

0.15

0.1

Boom

0.15

0.28

0.15

a. E(R) Stock Y (13.20% is the answer)

b. Standard deviation of Stock Y return (10.76% is the answer)               

c. E(R) Stock Z (8.95% is the answer)

d. Standard deviation of Stock Z return (4.92% is the answer)              

State of Economy

Probability of State occurring

Stock Y Return

Stock Z Return

Recession

0.15

-0.1

-0.02

Normal

0.70

0.15

0.1

Boom

0.15

0.28

0.15

a. E(R) Stock Y (13.20% is the answer)

b. Standard deviation of Stock Y return (10.76% is the answer)               

c. E(R) Stock Z (8.95% is the answer)

d. Standard deviation of Stock Z return (4.92% is the answer)              

Explanation / Answer

Answer:a The expected return of an asset is the sum of the probability of each return occurring times the probability of that return occurring.

So, the expected return of each stock asset is:

E(RY) = .15(-.1) + .70(.15) + .15(.28)

E(RY)=0.132 or 13.20%

Answer:b To calculate the standard deviation, we first need to calculate the variance. To find the variance, we find the squared deviations from the expected return. We then multiply each possible squared deviation by its probability, and then sum. The result is the variance.

So, the variance and standard deviation of each stock is:

sY2 =.15(-.1 – 0.132)2 + .70(.15 – 0.132)2 + .15(.28 – 0.132)2

sY2 = .011586

sY = (.011586)1/2

sY = .1076 or 10.76%

Answer:c The expected return of an asset is the sum of the probability of each return occurring times the probability of that return occurring.

So, the expected return of each stock asset is:

E(RZ) = .15(-.02) + .70(.1) + .15(.15)

E(RZ)=0.0895 or 8.95%

Answer:d To calculate the standard deviation, we first need to calculate the variance. To find the variance, we find the squared deviations from the expected return. We then multiply each possible squared deviation by its probability, and then sum. The result is the variance.

So, the variance and standard deviation of each stock is:

sZ2 =.15(-.02 – 0.0895)2 + .70(.1 –0.0895)2 + .15(.15 –0.0895)2

sZ2= .00242475

sZ = ( .00242475)1/2

sY = .0492 or 4.92%

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