Portfolio Concepts

Question 1

At a recent analyst meeting an Invest Forum, analysts Michelle White and Ted Jones discussed the use of the capital asset pricing model (CAPM) and the arbitrage pricing theory (APT). White states that the CAPM implies that investors hold a risky portfolio of all assets weighted according to their relative market value capitalisations. Jones states that the APT implies that investors will make investments decisions by allocating their money between a risk free asset and the market portfolio.

• only Jones is correct
• only White is correct
• both statments are correct
• neither statement is correct

Answer 1

The CAPM assumes all investors have identical expectations and all use mean-variance analysis, implying that they all identify the same risky tangency portfolio (the “market portfolio”) and combine that risky portfolio with the risk-free asset when creating their portfolios. Because all investors hold the same risky portfolio, the weight on each asset must be equal to the proportion of its market value to the market value of the entire portfolio. Therefore, White is correct. In contrast, the APT places no special emphasis on the market portfolio. In fact, the APT does not even require that the “market portfolio” exist. Therefore, Jones is incorrect.

Question 2

Analysts Linda Yarbrough and Pamela Burke recently discussed the application of the market model. Yarbrough comments that, assuming betas remains constant, the market model prediction of the covariance between any two assets rises during a period of rising market volatility. Burke states that the market model prediction of covariance will not be correct if the firm’s unique components of asset returns are correlated.

• only Burke is correct
• only Yarbrough is correct
• both statements are correct
• neither statement is correct

Answer 2

The market model makes a number of assumptions which lead to the prediction that the covariance between two assets equals the product of the asset betas times the market variance. Therefore, Yarbrough is correct. One of the assumptions of the market model is that firm-specific events are uncorrelated across firms. If the assumption is violated, then the market model predictions of the covariance will be wrong. Burke’s statement is correct.

Question 3

Which of the following statements is least likely a prediction of the single-factor market model:
All the investors hold the market portfolio, so the CML is defined as the capital allocation line with the market portfolio as the tangency portfolio.
There are two components to the variance of the returns on Asset i: a systematic component related to the asset’s beta and an unsystematic component related to firm-specific error terms.
The expected return as Asset i depends on the market’s expected return, the sensitivity of Asset i’s returns to the market, and the average return to Asset i not related to the market return.
The covariance between two assets is related to the betas of the two assets and the variance of the market portfolio.

Answer 3

The single-factor market model does not predict that all investors hold the market portfolio. The market model makes three predictions:
The expected return on Asset i depends on the market’s expected return, the sensitivity of Asset i’s returns to the market, and the average return to Asset i not related to the market return.
There are two components to the variance of the returns on Asset i: a systematic component related to the asset’s beta and an unsystematic component related to firm-specific surprises.
The covariance between two assets is related to the betas of the two assets and the variance of the market portfolio.

Question 4

A multifactor model uses factors that are stock or company characteristics, such as price-to-book and price-to-earnings ratios, that have been shown to affect asset returns. This type of multifactor model would be called a:

• statistical factor model
• systematic factor model
• fundamental factor model
• macroeconomic factor model

Answer 4

Fundamental factor models focus on microeconomic factors. Each factor, whether a ratio or a descriptor, has unique factor values.

Question 5

A portfolio that has the same factor sensitivities as the S&P 500, but does not hold all 500 stocks in the index, is called as:

• factor portfolio
• tracking portfolio
• market portfolio
• arbitrage portfolio

Answer 5

A tracking portfolio is a portfolio with a specific set of factor sensitivities. Tracking portfolios are often designed to replicate the factor exposures of a benchmark index like the S&P 500. In fact, a factor portfolio is just a special case of a tracking portfolio. One use of tracking portfolios is to attempt to outperform the S&P 500 by using the same exposures as the S&P 500, but with a different set of securities that the S&P 500.

Question 6

A portfolio with a factor sensitivity of one to the yield spread factor and a sensitivity of zero to all other macroeconomic factors is best described as a:

• factor portfolio
• tracking portfolio
• market portfolio
• arbitrage portfolio

Answer 6

A factor portfolio is a portfolio with a factor sensitivity of 1 to a particular factor and zero to all other factors. It represents a pure bet on that factor. For example, a portfolio manager who believes GDP growth will be greater than expected, but has no view of future interest rates and wants to hedge away the interest rate risk in his portfolio, could create a factor portfolio that is only exposed to the GDP factor and not the interest rate factor.

Question 7

Factor investments managers a tracking portfolio which claims to outperform the S&P 500. The active factor risk and active specific risk for the tracking portfolio are most likely to be:

• high active factor risk and high active specific risk
• high active factor risk and low active active specific risk
• low active factor risk and high active specific risk
• low active factor risk and low active specific risk

Answer 7

A tracking portfolio is deliberately constructed to have the same set of factor exposures to match (“track”) a predetermined benchmark. The strategy involved in constructing a tracking portfolio is usually an active bet on asset selection (the manager claims to beat the S&P 500). The manager constructs the portfolio to have the same factor exposures as the benchmark but then selects superior securities (subject to the factor sensitivities constraint), this outperforming the benchmark without taking on more systematic risk than the benchmark. Therefore, a tracking portfolio, with active asset selection but with factor sensitivities that match those of the benchmark, will have little or no active factor risk but will have high active specific risk.

Question 8

Which of the following is the most important assumption underlying the market model:
The expected value of the error term is correlated with the market return.
The firm-specific surprises are uncorrelated across assets.
The errors are uncorrelated to the probability distribution function.
The expected value of the error term is not 1.

Answer 8

The market model makes three assumptions:
The expected value of the error term is zero. (Choice A is tempting but not complete enough to be correct).
The errors are uncorrelated with the market returns.
The firm-specific surprises are uncorrelated across assets.