Lade

CHAPTER 11
FACTOR MODELS AND THE ARBITRAGE PRICING THEORY


1. An expected return is an ex-ante measure or prediction of what the return on an asset will be in the future. An observed return is an ex-post or historical measure of the return on an asset in the past. It is impossible to predict the surprise component in a return because it is a random innovation in the price change of anasset.

2. a. Real GNP was higher than anticipated. Since returns are positively related to the level of GNP, returns should rise based on this factor.
b. Inflation was exactly the amount anticipated. Since there was no surprise in this announcement, it will not affect Lewis-Striden returns.

c. Interest rates are lower than anticipated. Since returns are negatively relatedto interest rates, the lower than expected rate is good news. Returns should rise due to interest rates.

d. The chairman’s death is bad news. Although the chairman was expected to retire, his retirement would not be effective for six months. During that period he would still contribute to the firm. His untimely death means that those contributions will not be made. Since he was generallyconsidered an asset to the firm, his death will cause returns to fall. However, since his departure was expected soon, the drop might not be very large.

e. The poor research results are also bad news. Since Lewis-Striden must continue to test the drug, it will not go into production as early as expected. The delay will affect expected future earnings, and thus it will dampen returns now.f. The research breakthrough is positive news for Lewis Striden. Since it was unexpected, it will cause returns to rise.

g. The competitor’s announcement is also unexpected, but it is not a welcome surprise. This announcement will lower the returns on Lewis-Striden.

The systematic factors in the list are real GNP, inflation, and interest rates. The unsystematic riskfactors are the president’s ability to contribute to the firm, the research results, and the competitor.

3. Using a benchmark composed of Greek equities is wrong because the equities included are not of the same style as those in an Irish growth fund.

4. See Section 11.4 for a full discussion of this issue.

5. The market portfolio has to lie on the security market line bydefinition. If a security plots below the line it means that the security is overpriced. In this situation nobody would want to hold it, and its price would fall until the expected return was high enough to plot back on the Security Market Line.

6. Assuming the market portfolio is properly scaled, it can be shown that the one-factor model is identical to the CAPM.

7. Any return can beexplained with a large enough number of systematic risk factors. However, for a factor model to be useful as a practical matter, the number of factors that explain the returns on an asset must be relatively limited.

8. The market risk premium and inflation rates are probably good choices. The price of wheat, while a risk factor for Ultra Bread, is not a market risk factor and will not likely bepriced as a risk factor common to all equities. In this case, wheat would be a firm specific risk factor, not a market risk factor. A better model would employ macroeconomic risk factors such as interest rates, GDP, energy prices, and industrial production, among others.

9. The main difference is that the market model assumes that only one factor, usually a stock market aggregate, is enough toexplain stock returns, while the Carhart model assumes a 4-factor model relying on 4 factors (SML, HML, Momentum, market risk premium) to explain returns.

10. The fact that APT does not give any guidance about the factors that influence security returns is a commonly-cited criticism. However, in choosing factors, we should choose factors that have an economically valid reason for potentially...