Question 1

KMW Inc. has an estimated beta of 1.45. Given a forecasted market return of 12% and a T-bill rate 3%, using the index model and the adjusted beta, what is the forecasted return?

Accepted Answer

The correct answer is A because the forecasted return using the index model and the adjusted beta is 14.7%.

Question 2

Suppose you held a well-diversified portfolio with a very large number of securities, and that the single index model holds. If the σ of your portfolio was 0.14 and σ_M was 0.19, the β of the portfolio would be approximately

Accepted Answer

The beta (β) of the portfolio can be calculated using the formula: β = σP / σM, where σP is the standard deviation of the portfolio and σM is the standard deviation of the market. Given σP = 0.14 and σM = 0.19, β = 0.14 / 0.19 ≈ 0.74.

Question 3

Using the single index model, what is the alpha of a stock with beta of 1.2, a market return of 14%, risk free rate of 3% and the actual return of the stock is 18%?

Accepted Answer

The alpha ($\alpha$) of a stock in the single index model is calculated using the formula: $\alpha = R_i - [R_f + \beta_i(R_m - R_f)]$, where $R_i$ is the actual return of the stock, $R_f$ is the risk-free rate, $\beta_i$ is the beta of the stock, and $R_m$ is the market return. Plugging in the given values: $\alpha = 18\% - [3\% + 1.2(14\% - 3\%)] = 18\% - [3\% + 1.2(11\%)] = 18\% - [3\% + 13.2\%] = 18\% - 16.2\% = 1.8\%$.

Question 4

Suppose the following equation best describes the evolution of β over time:β_t = 0.30 + 0.70β_t− ₁If a stock had a β of 0.82 last year, you would forecast the β to be _______ in the coming year.

Accepted Answer

The forecast for β in the coming year is calculated as β_t = 0.30 + 0.70(0.82) = 0.87.

Question 5

VM Inc. has an estimated beta of 1.08. Given a forecasted market return of 10% and a T-bill rate 2%, using the index model and the adjusted beta, what is the forecasted return?

Accepted Answer

The forecasted return using the Capital Asset Pricing Model (CAPM) is calculated as: Risk-Free Rate + Beta * (Market Return - Risk-Free Rate). Plugging in the values: 2% + 1.08 * (10% - 2%) = 2% + 1.08 * 8% = 2% + 8.64% = 10.64%. Since the options are rounded, 10.4% is the closest to the calculated value.

Question 6

Using the single index model, what is the alpha of a stock with beta of 1.3, a market return of 14%, risk free rate of 4% and the actual return of the stock is 14%?

Accepted Answer

The alpha ($\alpha$) of a stock in the single index model can be calculated using the formula: $\alpha = R_i - [R_f + \beta_i(R_m - R_f)]$, where $R_i$ is the actual return of the stock, $R_f$ is the risk-free rate, $\beta_i$ is the beta of the stock, and $R_m$ is the market return. Plugging in the given values: $\alpha = 14\% - [4\% + 1.3(14\% - 4\%)] = 14\% - [4\% + 1.3(10\%)] = 14\% - [4\% + 13\%] = 14\% - 17\% = -3\%$.

Question 7

HAW Inc. has an estimated beta of 0.87. Given a forecasted market return of 9% and a T-bill rate 3%, using the index model and the adjusted beta, what is the forecasted return?

Accepted Answer

The forecasted return can be calculated using the Capital Asset Pricing Model (CAPM): Expected Return = Risk-Free Rate + Beta * (Market Return - Risk-Free Rate). Substituting the given values: 3% + 0.87 * (9% - 3%) = 8.22%, which rounds to 8.5%.

Quiz 8: Index Models