《solution manual for 《investment analysis and portfolio management》 ch09.doc》由会员分享，可在线阅读，更多相关《solution manual for 《investment analysis and portfolio management》 ch09.doc（13页珍藏版）》请在三一办公上搜索。
1、CHAPTER 9MULTIFACTOR MODELS OF RISK AND RETURNAnswers to Questions1. Both the Capital Asset Pricing Model and the Arbitrage Pricing Model rest on the assumption that investors are reward with non-zero return for undertaking two activities: (1) committing capital (non-zero investment); and (2) taking
2、 risk. If an investor could earn a positive return for no investment and no risk, then it should be possible for all investors to do the same. This would eliminate the source of the “something for nothing” return.In either model, superior performance relative to a benchmark would be found by positiv
3、e excess returns as measured by a statistically significant positive constant term, or alpha. This would be the return not explained by the variables in the model.2. CFA Examination III (1989)2a.The Capital Asset pricing Model (CAPM) is an equilibrium asset pricing theory showing that equilibrium ra
4、tes of expected return on all risky assets are a function of their covariance with the market portfolio. The CAPM is a single-index model that defines systematic risk in relation to a broad-based market portfolio (i.e., the market index). This single factor (“beta”) is unchanging:Rj = Rf + Bj(Rm Rf)
5、whereRj = expected return on an asset or portfolioRf = risk-free rate of returnRm = expected return on the marketBj = volatility of the asset or portfolio to that of the market m.Arbitrage Pricing Theory (APT) is an equilibrium asset pricing theory derived from a factor model by using diversificatio
6、n and arbitrage. The APT shows that the expected return on any risky asset is a linear combination of various factors. That is, the APT asserts that an assets riskiness and, hence, its average long-term return, is directly related to its sensitivities to certain factors. Thus, the APT is a multi-fac
7、tor model which allows for as many factors as are important in the pricing of assets. However, the model itself does not define these variables. Unlike the CAPM, which recognizes only one unchanging factor, the key factors in APT can change over time. Rj = Rf + Bj1(RF1 Rf) + + Bjk(RFk Rf)whereRj = r
8、eturn on an assetRf = risk-free rate of returnBj= sensitivity of an asset to a particular factorRFk= expected return on a portfolio with an average (1.0) sensitivity to a factor kj= an assetk= a factorResearch suggests that several macroeconomic factors may be significant in explaining expected stoc
9、k returns (i.e., these factors are systematically priced):(1) Inflation;(2) Industrial production;(3) Risk premia as measured by the spread between low and high grade bonds; (4) Yield curve, (i.e., slope of the term structure of interest rates.Other researchers have identified additional factors whi
10、ch may influence an assets return.(5) Real GNP growth;(6) Rate of growth of real oil prices (i.e., an energy factor);(7) Real defense spending;(8) Market index. 2b. Because of APTs more general formulation, it is more robust and intuitively appealing than the CAPM. Many factors, not just the market
11、portfolio, may explain asset returns. This permits the stock selection process to take into account as many economic variables as are believed to be significant in a valuation context not only as to individual issues, but also as to groups, sectors or even the market as a whole. For example, given a
12、 forecast of a sudden spurt in the inflation rate, and of the resulting effect on interest rates, the analyst or portfolio manager can, via APT, arrive at an estimate of valuation changes across his/her selection universe and adjust portfolio exposures accordingly. Alternatively, stocks could be sel
13、ected and portfolios formed based on specific factor-sensitivity criteria set up in advance.3. The small firm effect refers to the tendency of small capitalization stocks to outperform large capitalization stocks. In and of itself, such evidence would not necessarily constitute evidence of market in
14、efficiency, because most tests of such “anomalies” are in fact joint tests of two elements: (1) an asset pricing model (e.g., the CAPM or APT) which reflects the risk-return tradeoff; and (2) market efficiency, in the sense of prices reflecting some set of information. If a test fails to account for
15、 such anomalies, it could be due to either (1) a mis-specified asset pricing model; or (2) market inefficiency, or both. 4. Studies of the efficient markets hypothesis suggest that additional factors affecting estimates of expected returns include firm size, the price-earnings ratio, and financial l
16、everage. These variables have been shown to have predictive ability with respect to security returns.5. CFA Examination II (1998)5(a).APT vs. the CAPMArbitrage pricing theory does not include any of the following three assumptions incorporated in the capital asset pricing model (CAPM): noted as part
17、s i, ii, and iii:i.Investor utility function or quadratic utility function. Capital market theory assumes investors want to maximize utility in terms of risk and return preferences; maximum return per unit of risk or minimum risk per unit of return. From the Markowitz model forward, relevant risk ha
18、s been measured by variance of returns or standard deviation. APT makes no assumptions regarding investor preferences; the multifactor model commonly used in APT does not include any exponents higher than 1. ii.Normally distributed returns. The probability distribution of expected returns of an inve
19、stment and the associated dispersion or variability of those returns form the basis of Markowitz portfolio theory and the CAPM. Normal or symmetrically distributed security returns enable estimation of a variance term. In the CAPM, all investors have identical estimates for the probability distribut
20、ions of future returns (homogeneous expectations).APT does not describe or specify or require an assumption about security return distributions of any kind.iii.The market portfolio. The CAPM assumes that pricing, valuation, risk, and return are solely functions of an assets relationship to a market
21、portfolio of all risky assets. In practice, the market portfolio is difficult to specify, so a mistakenly specified market portfolio might result. Roll called this misspecification “benchmark error.”APT does not consider or include an assumption of a market portfolio. APT is predicated on a common s
22、et of several (macroeconomic) factors.5(b).Conceptual Difference between APT and the CAPMConceptually, in APT, return is a function of a set of common factors. In the CAPM, return is a function of a market portfolio of all risky assets. Thus, one difference between APT and the CAPM can be described
23、by the fact that APT is a multifactor model that attempts to capture several non-market influences that cause securities or assets to change in price whereas the CAPM is a single-index model that assumes securities or assets change in price because of a common co-movement with one market portfolio o
24、f all risky assets.Another conceptual difference between APT and the CAPM is that, in application of the theory, the market portfolio (or “factor”) required by the CAPM is specified. In APT, the common factors are not identified, but the common factors in APT are often described or accepted as inclu
25、ding inflation or unanticipated deflation; default risk, government corporate security spread, risk premiums or interest rate spreads; changes in the term structure of interest rates; changes in real final sales, GDP growth or a similar proxy for long-run profits on an economy-wide basis; major poli
26、tical upheavals; and exchange rates.A third difference between APT and the CAPM lies in the incorporation of sensitivity coefficients to measure or describe the risk of assets or securities. APT incorporates a number of sensitivity coefficients. These coefficients determine how each independent vari
27、able or macroeconomic factor affects each asset. Different assets are affected to different degrees or extents by the common factors. In the CAPM, the only sensitivity factor is beta, an assets sensitivity to the changes in the market portfolio (often called an assets “systematic risk”).6. A market
28、factor of 1.2 means the mutual fund is 1.2 times as sensitive as the market portfolio, all other factors held equal. The SMB (“small minus big”) factor is the return of a portfolio of small capitalization stocks minus the return to a portfolio of large capitalization stocks. A value of 0.3 indicates
29、 the fund tends to react negatively to small cap factors; thus the fund is primarily invested in large cap stocks. The HML (“high minus low”) factor is the return to a portfolio of stocks with high ratios of book-to-market value less the return to a portfolio of low book-to-market returns. A value o
30、f 1.4 indicates the fund reacts positively to this factor; thus the fund is weighted toward high value stocks. 7. CFA Examination III (1990)The value of stock and bonds can be viewed as the present value of expected future cash flows discounted at some discount rate reflecting risk. Anticipated econ
31、omic conditions are already incorporated in returns. Unanticipated economic conditions affect returns. Industrial production. Industrial production is related to cash flows in the traditional discounted cash flow formula. The relative performance of a portfolio sensitive to unanticipated changes in
32、industrial production should move in the same direction as the change in this factor. When industrial production turns up or down, so too shares in the return on the portfolio. Portfolios sensitive to unanticipated changes in industrial production should be compensated for the exposure to this econo
33、mic factor. Inflation. Inflation is reflected in the discount rate, which generally is as follows: K = real return + hedge for inflation + risk premium. Unexpected inflation will quickly be factored into k by the market as investors attempt to hedge the loss of purchasing power. Thus, the discount r
34、ate would move in the same direction as the change in inflation.High inflation could also affect cash flows in the DCF formula, but the effect will probably be more than offset by higher Ks nominal cash flow growth rates do not always match expected inflation rates. If the growth in nominal cash flo
35、ws lags the inflation rate, the relative performance of a portfolio sensitive to rising inflation should decline over time. Investments in bonds are subject to significant adverse inflation effects. Hence, higher unanticipated inflation will negative affect portfolio values. Risk premia or quality s
36、preads. Risk premia affect the magnitude of the DCF discount rate. The risk premium measure represents investor attitudes toward risk-bearing and perceptions about the general level of uncertainty. When the return in low versus high quality bonds widens, there is likely to be a negative impact on th
37、e values of stock and bonds, particularly for lower quality companies. Riskier cash flows require higher discount rates, and widening quality spreads often signal greater uncertainty about profit levels and debt service requirement. Yield curve shifts. Yield curve shifts affect the discount rate. If
38、 a parallel upward shift occurs, it would mean investors are requiring higher return to hold all assets. Hence, with high discount rates, portfolio values would fall. If the curve becomes steeper, longer duration assets, such as long-term bonds and growth stocks, would be negatively affected more th
39、an shorter-term assets. 8. The macroeconomic approach to identifying the factors in a multi-factor asset pricing model tries to find variables that explain, the underlying reasons for variations in the cash flows and investment returns over time. The microeconomic approach concentrates on the charac
40、teristics of the securities themselves.Conceptually, it is possible for the two approaches to lead to the same estimate for expected returns. Practically speaking, it is not likely that they will. The two sets of factors, while probably significantly correlated, are not likely to be perfectly correl
41、ated, leading to differences in estimates. 9. The three factors used by Fama and French in heir microeconomic model are the excess market return; SMB (“small minus big”) he difference between the returns to a portfolio of small capitalization stocks and a portfolio of large capitalization stocks; an
42、d HML (“high minus low”) - the difference in returns to a portfolio of high book-to-market value stocks and low book-to-market stocks. This type of approach focuses on the various characteristics of the underlying securities. The macroeconomic approach, as its name implies, concentrates on more gene
43、ral, economy-wide variables that cause variation in the cash flows and investment returns.10. Multifactor model typically include a market portfolio return as one of the factors. Thus the coefficients on the other factors in the model indicate the marginal sensitivity of returns to those specific fa
44、ctors. Higher values indicate greater sensitivity of returns to that factor. In a macroeconomic-based model such as the one developed by Chen, Roll, and Ross, returns on a particular security might be much more sensitive to the credit spread than to one of the other macro variables. The investor cou
45、ld then assess whether that security fit his particular investment profile.Likewise, a microeconomic-based model would identify sensitivity to certain characteristics, such as small vs. large firm, etc. Again, the investor could then select securities based on the sensitivities to the various charac
46、teristics. 11.11(a).One study that does not support the APT is that of Reinganum on the small-firm effect. Reinganum hypothesized that if the APT were a superior theory to CAPM, the APT would explain the small-firm effect where the CAPM could not. However, his results did not support that hypothesis
47、. The small-firm portfolio still had significant positive excess returns, while the large firm portfolio had significant negative excess returns. A study that supports the APT is that of Cho, Elton, and Gruber. Their study tended to support the basic contention of the APT that factors other than the
48、 market portfolio affect security returns. 11(b). Shankens contention that the APT is not testable is in essence that the APT is not falsifiable. If a test finds that returns are not explained by a particular set of factors, that is not taken as evidence that the APT is incorrect, but that the particular set of factors is wrong. On the other hand, if a study finds that some other set of factors does explain returns, that is taken as evidence if favor of the APT. The APT gives no guidance as to the proper set of factors, so in that sense it cannot be falsified. Dybvig and Ross counter this
