Question 1

What is the standard deviation of the returns on a stock given the following information?

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Question 2

The rate of return on the common stock of Lancaster Woolens is expected to be 21 percent in a boom economy, 11 percent in a normal economy, and only 3 percent in a recessionary economy.The probabilities of these economic states are 10 percent for a boom, 70 percent for a normal economy, and 20 percent for a recession.What is the variance of the returns on this common stock?

Accepted Answer

The variance can be calculated using the formula:
Variance = (probability of boom economy x return in boom economy)^2 +
            (probability of normal economy x return in normal economy)^2 +
            (probability of recessionary economy x return in recessionary economy)^2 
            - (expected rate of return)^2

Plugging in the given values, we get:
Variance = (0.10 x 0.21)^2 + (0.70 x 0.11)^2 + (0.20 x 0.03)^2 - (0.10 x 0.21 + 0.70 x 0.11 + 0.20 x 0.03)^2
         = 0.002244
Therefore, the answer is C.

Question 3

What is the standard deviation of the returns on a $30,000 portfolio which consists of stocks S and T? Stock S is valued at $21,000.

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Question 4

You own the following portfolio of stocks.What is the portfolio weight of stock C?

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Question 5

If the economy is normal, Charleston Freight stock is expected to return 16.5 percent.If the economy falls into a recession, the stock's return is projected at a negative 11.6 percent.The probability of a normal economy is 80 percent while the probability of a recession is 20 percent.What is the variance of the returns on this stock?

Accepted Answer

E(r) = (0.80 × 0.165) + (0.20 × -0.116) = 0.1088Var = 0.80 (0.165 - 0.1088)² + 0.20 (-0.116 - 0.1088)² = 0.012634

Question 6

The risk-free rate of return is 3.9 percent and the market risk premium is 6.2 percent.What is the expected rate of return on a stock with a beta of 1.21?

Accepted Answer

E(r) = 0.039 + (1.21 × 0.062) = 11.40 percent

Question 7

What is the variance of the returns on a portfolio comprised of $5,400 of stock G and $6,600 of stock H?

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Question 8

What is the expected return on a portfolio that is equally weighted between stocks K and L given the following information?

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Question 9

The market has an expected rate of return of 11.2 percent.The long-term government bond is expected to yield 5.8 percent and the U.S.Treasury bill is expected to yield 3.9 percent.The inflation rate is 3.6 percent.What is the market risk premium?

Accepted Answer

Market risk premium = Expected market return - Risk-free rate
= 11.2% - 3.9%
= 7.3%

Question 10

What is the expected return on a portfolio comprised of $6,200 of stock M and $4,500 of stock N if the economy enjoys a boom period?

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Question 11

What is the expected return on this portfolio?

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Question 12

What is the standard deviation of the returns on a portfolio that is invested 52 percent in stock Q and 48 percent in stock R?

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Question 13

You would like to combine a risky stock with a beta of 1.68 with U.S.Treasury bills in such a way that the risk level of the portfolio is equivalent to the risk level of the overall market.What percentage of the portfolio should be invested in the risky stock?

Accepted Answer

Beta_Portfolio = 1.0 = [(x) × 1.68] + [(1 - x) × 0]; x = 60 percent

Question 14

What is the variance of the returns on a portfolio that is invested 60 percent in stock S and 40 percent in stock T?

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Question 15

The common stock of Jensen Shipping has an expected return of 14.7 percent.The return on the market is 10.8 percent and the risk-free rate of return is 3.8 percent.What is the beta of this stock?

Accepted Answer

E(r) = 0.147 = 0.038 + β (0.108 - 0.038); β = 1.56

Question 16

Your portfolio is comprised of 40 percent of stock X, 15 percent of stock Y, and 45 percent of stock Z.Stock X has a beta of 1.16, stock Y has a beta of 1.47, and stock Z has a beta of 0.42.What is the beta of your portfolio?

Accepted Answer

Beta_Portfolio = (0.40 × 1.16) + (0.15 × 1.47) + (0.45 × 0.42) = 0.87

Question 17

You own a portfolio with the following expected returns given the various states of the economy.What is the overall portfolio expected return?

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Question 18

What is the expected return on a portfolio which is invested 25 percent in stock A, 55 percent in stock B, and the remainder in stock C?

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Question 19

What is the beta of the following portfolio?

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Question 20

The returns on the common stock of New Image Products are quite cyclical.In a boom economy, the stock is expected to return 32 percent in comparison to 14 percent in a normal economy and a negative 28 percent in a recessionary period.The probability of a recession is 25 percent while the probability of a boom is 20 percent.What is the standard deviation of the returns on this stock?

Accepted Answer

E(r) = (0.20 × 0.32) + (0.55 × 0.14) + (0.25 × -0.28) = 0.071Var = 0.20 (0.32 - 0.071)² + 0.55 (0.14 - 0.071)² + 0.25 (-0.28 - 0.071)² = 0.045819Std dev = √0.045819 = 21.41 percent

Quiz 13: Cost of Capital

What is the standard deviation of the returns on a stock given the following information?

What is the standard deviation of the returns on a $30,000 portfolio which consists of stocks S and T? Stock S is valued at $21,000.

You own the following portfolio of stocks.What is the portfolio weight of stock C?

The risk-free rate of return is 3.9 percent and the market risk premium is 6.2 percent.What is the expected rate of return on a stock with a beta of 1.21?

What is the variance of the returns on a portfolio comprised of $5,400 of stock G and $6,600 of stock H?

What is the expected return on a portfolio that is equally weighted between stocks K and L given the following information?

The market has an expected rate of return of 11.2 percent.The long-term government bond is expected to yield 5.8 percent and the U.S.Treasury bill is expected to yield 3.9 percent.The inflation rate is 3.6 percent.What is the market risk premium?

What is the expected return on a portfolio comprised of $6,200 of stock M and $4,500 of stock N if the economy enjoys a boom period?

What is the expected return on this portfolio?

What is the standard deviation of the returns on a portfolio that is invested 52 percent in stock Q and 48 percent in stock R?

You would like to combine a risky stock with a beta of 1.68 with U.S.Treasury bills in such a way that the risk level of the portfolio is equivalent to the risk level of the overall market.What percentage of the portfolio should be invested in the risky stock?

What is the variance of the returns on a portfolio that is invested 60 percent in stock S and 40 percent in stock T?

The common stock of Jensen Shipping has an expected return of 14.7 percent.The return on the market is 10.8 percent and the risk-free rate of return is 3.8 percent.What is the beta of this stock?

Your portfolio is comprised of 40 percent of stock X, 15 percent of stock Y, and 45 percent of stock Z.Stock X has a beta of 1.16, stock Y has a beta of 1.47, and stock Z has a beta of 0.42.What is the beta of your portfolio?

You own a portfolio with the following expected returns given the various states of the economy.What is the overall portfolio expected return?

What is the expected return on a portfolio which is invested 25 percent in stock A, 55 percent in stock B, and the remainder in stock C?

What is the beta of the following portfolio?