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WorksheetsIndex model
Total questions: 15
Worksheet time: 8mins
As diversification increases, the total variance of a portfolio approaches
0
1
the variance of the market portfolio
infinity
As diversification increases, the firm-specific risk of a portfolio approaches
0
1
infinity
(n – 1) × n
The index model was first suggested by
Markowitz
Sharpe
Miller
Graham
A single-index model uses __________ as a proxy for the systematic risk factor.
the current account deficit
a market index, such as the S&P 500
the growth rate in GNP
the unemployment rate
The index model has been estimated for stocks A and B with the following results:
RA = 0.03 + 0.7RM + eA.
RB = 0.01 + 0.9RM + eB.
σM = 0.35; σ(eA) = 0.20; σ(eB) = 0.10.
The covariance between the returns on stocks A and B is
0.0384
0.0406
0.1920
0.0772
Analysts may use regression analysis to estimate the index model for a stock. When doing so, the slope of the regression line is an estimate of
the α of the asset
the β of the asset
the σ of the asset
the δ of the asset
Analysts may use regression analysis to estimate the index model for a stock. When doing so, the intercept of the regression line is an estimate of
the α of the asset
the β of the asset.
the σ of the asset.
the δ of the asset
In a factor model, the return on a stock in a particular period will be related to
firm-specific events.
macroeconomic events
the error term
both firm-specific events and macroeconomic events
Assume that stock market returns do not resemble a single-index structure. An investment fund analyzes 150 stocks in order to construct a mean-variance efficient portfolio constrained by 150 investments. They will need to calculate _____________ expected returns and ___________ variances of returns
150; 150
150; 22500
22500; 150
22500; 22500
Assume that stock market returns do not resemble a single-index structure. An investment fund analyzes 150 stocks in order to construct a mean-variance efficient portfolio constrained by 150 investments. They will need to calculate ____________ covariances
12
150
22,500
11,175
Consider the single-index model. The alpha of a stock is 0%. The return on the market index is 16%. The risk-free rate of return is 5%. The stock earns a return that exceeds the risk-free rate by 11%, and there are no firm-specific events affecting the stock performance. The β of the stock is
0.67
0.75
1.0
1.33
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 0.18 and σM was 0.24, the β of the portfolio would be approximately
0.75
0.56
0.07
1.03
The index model has been estimated for stocks A and B with the following results:
RA = 0.01 + 0.5RM + eA.
RB = 0.02 + 1.3RM + eB.
σM = 0.25; σ(eA) = 0.20; σ(eB) = 0.10.
The covariance between the returns on stocks A and B is
0.0384
0.0406
0.1920
0.0050
The index model has been estimated for stocks A and B with the following results:
RA = 0.01 + 0.8RM + eA.
RB = 0.02 + 1.2RM + eB.
σM = 0.20; σ(eA) = 0.20; σ(eB) = 0.10.
The standard deviation for stock A is
0.0656
0.0676
0.2561
0.2600
The single-index model (choose the best)
greatly reduces the number of required calculations relative to those required by the Markowitz model
greatly reduces the number of required calculations relative to those required by the Markowitz model and enhances the understanding of systematic versus nonsystematic risk
greatly increases the number of required calculations relative to those required by the Markowitz model
enhances the understanding of systematic versus nonsystematic risk
