Question

Consider the following information:

Rate of Return If State Occurs | |||||||||||

State of | Probability of | ||||||||||

Economy | State of Economy | Stock A | Stock B | ||||||||

Recession | .25 | .04 | –.17 | ||||||||

Normal | .30 | .10 | .17 | ||||||||

Boom | .45 | .15 | .37 | ||||||||

a. |
Calculate the expected return for the two stocks. |

Expected return for A | % |

Expected return for B | % |

b. |
Calculate the standard deviation for the two stocks. |

Standard deviation for A | % |

Standard deviation for B | % |

Answer #1

**(A) EXPECTED
RETURN**

**Expected Returns -
Stock A**

= [0.04 x 0.25] + [0.10 x 0.30] + [0.15 x 0.45]

= 0.01 + 0.03 + 0.0675

= 0.1075

= 10.75%

**Expected Returns -
Stock B**

= [-0.17 x 0.25] + [0.17 x 0.30] + [0.37 x 0.45]

= -0.0425 + 0.051 + 0.1665

= 0.175

= 17.50%

**(B) STANDARD
DEVIATION**

**Stock A**

Variance

= [(4 – 10.75)^{2} x 0.25] + [(10 – 10.75)^{2} x
0.30] + [(15 – 10.75)^{2} x 0.45]

= 11.3906 + 0.1688 + 8.1281

= 19.6875

**Therefore, Standard Deviation = Square Root of (19.6875)
= 4.44%**

**Stock B**

Variance

= [(-17 – 17.50)^{2} x 0.25] + [(17 – 17.50)^{2}
x 0.30] + [(37 – 17.50)^{2} x 0.45]

= 297.56 + 0.08 + 171.11

= 468.75

**Therefore, Standard Deviation = Square Root of (468.75)
= 21.65%**

Consider the following information:
Rate of Return if State Occurs
State of
Probability of
Economy
State of Economy
Stock A
Stock B
Recession
.10
.04
−
.17
Normal
.60
.09
.12
Boom
.30
.17
.27
a.
Calculate the expected return for Stocks A and B. (Do
not round intermediate calculations and enter your answers as a
percent rounded to 2 decimal places, e.g., 32.16.)
b.
Calculate the standard deviation for Stocks A and B.
(Do not round intermediate...

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Rate of Return if State Occurs
State of
Probability of
Economy
State of Economy
Stock A
Stock B
Recession
.10
.04
−
.17
Normal
.60
.09
.12
Boom
.30
.17
.27
a.
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not round intermediate calculations and enter your answers as a
percent rounded to 2 decimal places, e.g., 32.16.)
b.
Calculate the standard deviation for Stocks A and B.
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Stock B
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