Abstract
This chapter presents the key principles of modern portfolio theory (MPT). After a brief review of regression analysis it introduces the capital asset pricing model (CAPM) and its extension, the Fama–French three-factor-model, together with the basic assumptions of the two models and empirical tests. The limitations of the CAPM are pointed out and critical views are presented concerning both models which are based on the fundamental concept of rational investors.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
- 1.
Eugene F. Fama, born in 1939, is an American economist. He is known for his work on portfolio theory and asset pricing, both theoretical and empirical. He won the Nobel Prize in Economics in 2013 together with Robert J. Shiller and Lars Peter Hansen, see Reinganum (2013). His Ph.D. thesis (one of his supervisors was Nobel Prize winner Merton Miller) concluded that stock price movements are unpredictable and follow a random walk. Fama (1970) proposes the ground-breaking concept of efficient-markets (see Sects. 3.1 and 5.1) such that Fama is most often thought of as the father of the efficient-market hypothesis. Currently, he is a professor of finance at the University of Chicago, Booth School of Business.
- 2.
Kenneth R. French, born in 1954, is an American economist and professor of finance at Dartmouth College, Tuck School of Business. He has previously been a faculty member at MIT, the Yale School of Management, and the University of Chicago Booth School of Business. He obtained his Ph.D. in Finance in 1983 from the University of Rochester. French is an expert on the behavior of security prices and investment strategies and is most famous for his work on asset pricing with Eugene Fama and the Fama–French three-factor model (1992) as an extension of the CAPM (see Sect. 2.4).
- 3.
This paragraph is based on Lhabitant (2004, pp. 147–175).
- 4.
For an introduction to linear regression, see also DeFusco, McLeavey, Pinto, and Runkle (2004, pp. 395–420).
- 5.
The terms are from DeFusco et al. (2004, p. 395).
- 6.
For example, the term explanatory variable is used in Fama and MacBeth (1973, p. 618).
- 7.
DeFusco et al. (2004, p. 403): For simple linear regression, R 2 is the square of the correlation between X and Y.
- 8.
For an introduction to multi-linear regression, see also DeFusco et al. (2004, pp. 441–494).
- 9.
The terms are from DeFusco et al. (2004, p. 443).
- 10.
DeFusco et al. (2004, p. 457).
- 11.
Harry M. Markowitz, born August 24, 1927, in Chicago, Illinois, is an American economist who become famous for his pioneering work in modern portfolio theory . He earned his Bachelor of Philosophy from the University of Chicago in 1947 and received his Master and Doctor of Economics at the same university in 1950 and 1954, respectively. He held various positions with RAND corporation (1952–1963), Consolidated Analysis Centers, Inc. (1963–1968), the University of California, Los Angeles (1968–1969), Arbitrage Management Company, (1969–1972), and IBM’s T.J. Watson Research Center (1974–1983) before becoming a professor of finance at Baruch College of the City University of New York. He joined the University of California, San Diego in 1994 as a research professor of economics where he became a finance professor at the Rady School of Management in 2006. He received the John von Neumann Theory Prize in 1989 and the Nobel Memorial Prize in Economic Sciences in 1990.
- 12.
Although he is known as the father of MPT, Markowitz credits Andrew D. Roy with half of the honor in Markowitz (1999).
- 13.
An extension of these articles on MPT including different risk measures can be found in Schulmerich (2012b), Extending Modern Portfolio Theory: Efficient Frontiers for Different Risk Measures (white paper). A third white paper in this MPT trilogy is Can the Black–Litterman Framework Improve Asset Management Outcomes?, see Schulmerich (2013a).
- 14.
Reilly and Brown (1997, p. 279). This work offers a good introduction and is used as a standard reference work in the CFA curriculum. The sections in this book about the CAPM and its assumptions are based on this reference.
- 15.
Reilly and Brown (1997, p. 279).
- 16.
Reilly and Brown (1997, p. 279).
- 17.
Niels H.D. Bohr (October 7, 1885–November 18, 1962) was a Danish physicist who made foundational contributions to understanding atomic structure and quantum theory, for which he received the Nobel Prize in Physics in 1922.
- 18.
- 19.
Robert C. Merton (born July 31, 1944), an American economist and professor at the MIT Sloan School of Management, is known for his significant contributions to continuous-time finance, especially the first continuous-time option pricing model, the Black–Scholes–Merton formula. Together with Myron Scholes, Merton received the Alfred Nobel Memorial Prize in Economic Sciences in 1997 for expanding the Black–Scholes–Merton formula. He earned his Doctor of Economics from the MIT in 1970 under the guidance of Paul Samuelson. He then joined the faculty of the MIT Sloan School of Management where he taught until 1988 before moving to Harvard Business School, where he stayed until 2010. In 2010 he rejoined the MIT Sloan School of Management as the School of Management Distinguished Professor of Finance. He is the past President of the American Finance Association.
- 20.
Merton (1972, p. 1856).
- 21.
Bodie, Kane, and Marcus (2009, p. 211).
- 22.
Risk-free assets are discussed below on page 118.
- 23.
Fischer S. Black (January 11, 1938–August 30, 1995), an American economist, is one of the authors of the famous Black–Scholes equation. He graduated from Harvard College in 1959 and received a Ph.D. in Applied Mathematics from Harvard University in 1964. He was initially expelled from the Ph.D. program due to his inability to settle on a thesis topic, having switched from physics to mathematics, then to computers and artificial intelligence. In 1971, he began to work at the University of Chicago but later left to work at the MIT Sloan School of Management. In 1984, he joined Goldman Sachs where he worked until his death in August 1995 from throat cancer.
- 24.
Michael C. Jensen (born November 30, 1939 in Rochester, Minnesota, U.S.) is an American economist working in the area of financial economics. He is currently the managing director in charge of organizational strategy at Monitor Group, a strategy consulting firm, and the Jesse Isidor Straus Professor of Business Administration, Emeritus, at Harvard University. He received his B.A. in Economics from Macalester College in 1962 and both his M.B.A. (1964) and Ph.D. (1968) degrees from the University of Chicago Booth School of Business, notably working with Professor Merton Miller, the 1990 co-winner of the Nobel Prize in Economics. Jensen is also the founder and editor of the Journal of Financial Economics. The Jensen Prize in corporate finance and organizations research is named in his honor.
- 25.
Myron S. Scholes (born July 1, 1941), a Canadian-born American financial economist, is one of the authors of the Black–Scholes equation. In 1968, after finishing his dissertation under the supervision of Eugene Fama and Merton Miller, Scholes took an academic position at the MIT Sloan School of Management where he met Fischer Black and Robert C. Merton, who joined MIT in 1970. For the following years Scholes, Black and Merton undertook groundbreaking research in asset pricing, including the work on their famous option pricing model. In 1997 he shared the Nobel Prize in Economics with Robert C. Merton “for a new method to determine the value of derivatives”. Fischer Black, who co-authored with them the work that was awarded, had died in 1995 and thus was not eligible for the prize. In 1981 Scholes moved to Stanford University, where he remained until he retired from teaching in 1996. Since then he holds the position of Frank E. Buck Professor of Finance Emeritus at Stanford.
- 26.
Black, Jensen, and Scholes (1972, p. 444).
- 27.
Reilly and Brown (1997, p. 284).
- 28.
This list of examples is mentioned in Reilly and Brown (1997, p. 284).
- 29.
Richard Roll mentioned human capital as part of the market portfolio in Roll (1977, p. 131 and p. 155).
- 30.
This reasoning is from Bodie, Kane, and Marcus (1999, p. 253).
- 31.
Bodie et al. (1999, p. 181).
- 32.
Fabozzi, Mann, and Choudhry (2002, p. 1).
- 33.
Spremann (2008, pp. 227–228), initially discussed in Tobin (1958, p. 66). In Markowitz (1999, p. 10), Harry Markowitz refers to the Tobin (1958) article as the first CAPM, and summarizes Tobin’s work. In Sect. 3.6. of Tobin’s article, the author presented his seminal result, today known as the Tobin separation theorem. Tobin assumed a portfolio selection model with M risky assets and one riskless asset: cash. Because these assets were monetary, i.e., “marketable, fixed in money value, free of default risk” (see Tobin 1958, p. 66), the risk was market risk , not default risk . Holdings had to be nonnegative. Borrowing was not permitted. Implicitly, Tobin assumed that the covariance matrix for risky assets is nonsingular. The result was that “the proportionate composition of the non-cash assets is independent of their aggregate share of the investment balance. This fact makes it possible to describe the investor’s decisions as if there were a single non-cash asset, a composite formed by combining the multitude of actual non-cash assets in fixed proportions.” (see Tobin 1958, p. 84).
- 34.
In the studies Kendrick (1974, 1976, 1994) and Eisner (1985, 1989) which used the cost-based approach, the size of human capital was about the size of non-human capital. In the study Jorgenson and Fraumeni (1989, 1992) which used the income-based approach, the share of human capital in total wealth was over 90 %.
- 35.
A good summary about the market portfolio is provided in Le, Gibson, and Oxley (2003).
- 36.
Reilly and Brown (1997, p. 279).
- 37.
Reilly and Brown (1997, p. 310).
- 38.
Reilly and Brown (1997, p. 310).
- 39.
- 40.
Literally, the beta premium is the premium per unit of beta. The CAPM implies that the beta premium is the excess market return, i.e., the difference between the expected return on the market portfolio and the risk-free rate. But this equality is equivalent to the fourth hypothesis, that zero-beta assets expect to earn the risk-free rate. The positive beta premium does not test the equality with the excess market return, only the positivity.
- 41.
Jensen (1967, p. 8).
- 42.
This terminology is from Roenfeldt, Griepentrog, and Pflaum (1978).
- 43.
Blume (1971, p. 4).
- 44.
Blume (1971, p. 7).
- 45.
Levy (1971, p. 57).
- 46.
Blume (1971, p. 6).
- 47.
Quote from Porter and Ezzell (1975, p. 369). See p. 370, Table 2, which compares Blume’s to Porter’s & Ezzell’s correlation numbers.
- 48.
Tole (1981, p. 47, Exhibit 1).
- 49.
This is pointed out in Reilly and Brown (1997, p. 310).
- 50.
Conclusion in Baesel (1974, p. 1493). Compare Table 1 on p. 1492 with Table 2 on p. 1493.
- 51.
Conclusion in Roenfeldt et al. (1978, p. 120 and Table 1 on p. 119).
- 52.
Reilly and Brown (1997, p. 311)
- 53.
Fama and French (2004, p. 32).
- 54.
Black et al. (1972, p. 10).
- 55.
Black et al. (1972, p. 8).
- 56.
Black et al. (1972, p. 11).
- 57.
Black et al. (1972, p. 9).
- 58.
Black et al. (1972, p. 8): An equal investment is indicated by using the average return and average risk (beta) of all securities in a portfolio.
- 59.
The excess return of a portfolio is the difference between the return of a portfolio and the return on a risk-free asset.
- 60.
In the general cross-sectional regression (2.38) that we described earlier, the average return, not the average excess return , is regressed on beta . The only difference is that we have to shift the graph from Fig. 2.16 down by the average risk-free rate r rf . So the second hypothesis stated on page 124, i.e., risk-free return on zero-beta assets, translates into: “The intercept a is zero.”
- 61.
Black et al. (1972, p. 25).
- 62.
Fama and MacBeth (1973, p. 614).
- 63.
Fama and MacBeth (1973, p. 610 and p. 613).
- 64.
Fama and MacBeth (1973, p. 614).
- 65.
Fama and MacBeth (1973, p. 616).
- 66.
Fama and MacBeth (1973, p. 614).
- 67.
Fama and MacBeth (1973, p. 614).
- 68.
Fama and MacBeth (1973, p. 626).
- 69.
Fama and MacBeth (1973, p. 615).
- 70.
Fama and French (2004, p. 31).
- 71.
Fama and MacBeth (1973, p. 624).
- 72.
The beta premium turned negative during a short subperiod (1956–1960), but this does not invalidate the long-term result.
- 73.
Fama and MacBeth (1973, p. 618).
- 74.
This summary is from Fama and French (2004, p. 35).
- 75.
- 76.
Fama and French (1992, p. 429). Financial stocks were excluded because the high leverage that is normal for these firms probably does not have the same meaning for non-financial firms, where high leverage more likely indicates distress.
- 77.
Fama and French (1992, p. 431).
- 78.
Fama and French (1992, p. 431 and p. 433).
- 79.
The betas are calculated based on the monthly returns which were realized by the portfolios after they were set up. They have nothing to do with the beta used for the pre-ranking.
- 80.
The beta is calculated based on the monthly returns which were realized by the portfolios after they were set up. They have nothing to do with the beta used for the pre-ranking.
- 81.
Fama and French (1992, p. 433).
- 82.
Fama and French (1992, p. 440).
- 83.
Fama and French (1992, p. 439).
- 84.
Fama and French (1992, Table IV, p. 442).
- 85.
Fama and French (1992, p. 438).
- 86.
Fama and French (1992, p. 438).
- 87.
Fama and French (1992, pp. 441–442).
- 88.
Fama and French (1992, p. 441).
- 89.
Fama and French (1992, pp. 441–442).
- 90.
Fama and French (1992, pp. 442–443).
- 91.
Fama and French (1992, p. 440).
- 92.
Pettengill et al. (1995, pp. 102–104) for the argument.
- 93.
Pettengill et al. (1995, p. 110).
- 94.
Pettengill et al. (1995, p. 109).
- 95.
Richard Roll (born October 31, 1939) is an American economist, best known for his work on portfolio theory and asset pricing, both theoretical and empirical. In 1968, he received his Ph.D. from the Graduate School of Business at the University of Chicago in economics, finance, and statistics. In 1976, Roll joined the faculty at UCLA, where he remains as Japan Alumni Chair Professor of Finance. In 1987, Roll was elected President of the American Finance Association.
- 96.
This list of examples is mentioned in Reilly and Brown (1997, p. 284).
- 97.
Richard Roll mentions human capital as part of the market portfolio in Roll (1977, p. 131 and p. 155).
- 98.
Roll (1977, p. 136).
- 99.
β Pf is the portfolio beta measured relative to the portfolio m. The zero-beta asset Z has zero beta relative to m.
- 100.
Roll (1977, p. 130 and p. 136).
- 101.
Fama and French (2004, p. 43).
- 102.
Fama and French (2004, pp. 43–44).
- 103.
Fama and French (2004, p. 44).
- 104.
- 105.
- 106.
- 107.
The time-series regression was introduced on page 124 for one independent variable, but can easily be extended to multiple variables.
- 108.
Fama and French (1993, pp. 7–8).
- 109.
These explanations can be found in Davis, Fama, and French (2000, pp. 389–390).
- 110.
Lakonishok et al. (1994, p. 1542).
- 111.
Davis et al. (2000, p. 390).
- 112.
Daniel and Titman (1997, pp. 3–4).
- 113.
Stoll and Whaley (1983, p. 58).
- 114.
Stoll and Whaley (1983, p. 58).
- 115.
Amihud (2002, p. 31).
- 116.
Pástor and Stambaugh (2003)
- 117.
Pástor and Stambaugh (2003, p. 677).
- 118.
Pástor and Stambaugh (2003, p. 677).
- 119.
Chan and Chen (1991, pp. 1467–1468).
- 120.
van Dijk (2011, p. 16).
- 121.
Gompers and Metrick (2001, p. 17).
- 122.
Hou and Moskowitz (2005, p. 981).
- 123.
- 124.
Financial stocks were excluded because the high leverage that is normal for these firms probably does not have the same meaning for non-financial firms, where high leverage more likely indicates distress.
- 125.
Fama and French (1992, p. 431).
- 126.
Fama and French (1993, p. 10).
- 127.
Methodology from Fama and French (1993, pp. 8–9).
- 128.
Fama and French (1993, p. 8).
- 129.
Fama and French (1993, p. 19).
- 130.
See Sect. 2.3.3 about empirical tests.
- 131.
Fama and French (1993, p. 21).
- 132.
Fama and French (1993, p. 35).
- 133.
Fama and French (1993, p. 38).
- 134.
Fama and French (1993, p. 38).
- 135.
Fama and French (1993, p. 40).
- 136.
Fama and French (1993, p. 39).
- 137.
Fama and French (1993, pp. 40–41).
- 138.
Fama and French (1993, p. 41).
- 139.
Fama and French (1993, p. 41).
References
Altman, E. I., Jacquillat, B., & Levasseur, M. (1974, December). Comparative analysis of risk measures: France and the United States. Journal of Finance, 29(5), 1495–1511.
Amihud, Y. (2002). Illiquidity and stock returns: Cross-section and time-series effects. Journal of Financial Markets, 5(1), 31–56.
Artmann, S., Finter, P., Kempf, A., Koch, S., & Theissen, E. (2012, January). The cross-section of German stock returns: New data and new evidence. Schmalenbach Business Review (SBR), 64, 20–43.
Baesel, J. B. (1974, December). On the assessment of risk: Some further considerations. Journal of Finance, 29(5), 1491–1494.
Bahl, B. (2006, September). Testing the Fama and French three-factor model and its variants for the Indian stock returns. U.K.: Department of Economics, University of Warwick.
Ball, R. (1978). Anomalies in relationship between securities’ yields and yield-surrogates. Journal of Financial Economics, 6, 103–126.
Banz, R. (1981). The relationship between returns and market value of common stock. Journal of Financial Economics, 9, 3–18.
Basu, S. (1977). Investment performance of common stocks in relation to their price-earnings ratios: A test of the efficient market hypothesis. Journal of Finance, 32(3), 663–682.
Bauer, R., Cosemans, M., & Schotman. P. C. (2010). Conditional asset pricing and stock market anomalies in Europe. European Financial Management, 16(2), 165–190.
Bhandari, L. C. (1988). Debt/equity ratio and expected common stock returns: Empirical evidence. Journal of Finance, 43(2), 507–528.
Black, F. S. (1972). Capital market equilibrium with restricted borrowing. Journal of Business, 45(3), 444–455.
Black, F. S., Jensen, M. C., & Scholes, M. S. (1972). The capital asset pricing model: Some empirical tests. In Studies in the theory of capital markets (pp. 79–121). New York: Praeger Publishers.
Black, F. S., & Scholes, M. S. (1974, May). The effect of dividend yield and dividend policy on common stock prices and returns. Journal of Financial Economics, 1(1), 1–22.
Blume, M. E. (1971, March). On the assessment of risk. Journal of Finance, 26(1), 1–10.
Blume, M. E., & Friend, I. (1973). A new look at the capital asset pricing model. Journal of Finance, 28(1), 19–33.
Bodie, Z., Kane, A., & Marcus, A. J. (1999). Investments (4th ed.). New York: Irwin/McGraw-Hill.
Bodie, Z., Kane, A., & Marcus, A. J. (2009). Investments (8th ed.). Boston: Irwin/McGraw-Hill.
Chan, K. C., & Chen, N.-F. (1991, September). Structural and return characteristics of small and large firms. Journal of Finance, 46(4), 1467–1484.
Chan, L. K. C., Hamao, Y., & Lakonishok, J. (1991, December). Fundamentals and stock returns in Japan. Journal of Finance, 46(5), 1739–1764.
Chen, A., & Fang, S. (2009). Uniform testing and portfolio strategies for single and multifactor asset pricing models in the Pacific Basin markets. Applied Economics, 41(15), 1951–1963.
Chui, A. C. W., & Wei, K. C. J. (1998, August). Book-to-market, firm size, and the turn-of-the-year effect: Evidence from Pacific-Basin emerging markets. Pacific-Basin Finance Journal, 6(3–4), 275–293.
Daniel, K., & Titman, S. (1997). Evidence on the characteristics of cross-sectional variation in stock returns. Journal of Finance, 52(1), 1–33.
Davis, J. L., Fama, E. F., & French, K. R. (2000). Characteristics, covariances, and average returns: 1929 to 1997. Journal of Finance, 55(1), 389–406.
De Bondt, W. F. M., & Thaler, R. H. (1985). Does the stock market overreact? Journal of Finance, 40(3), 793–805.
DeFusco, R. A., McLeavey, D. W., Pinto, J. E., & Runkle, D. E. (2004). Quantitative methods for investment analysis (2nd ed.). Charlottesville: CFA Institute.
Douglas, G. W. (1969). Risk in the equity markets: An empirical appraisal of market efficiency. Yale Economic Essays, 9, 3–45.
Eisner, R. (1985). The total incomes system of accounts. Survey of Current Business, 65(1), 24–48.
Eisner, R. (1989). The total incomes system of accounts. Chicago: University of Chicago Press.
Elsas, R., El-Shaer, M., & Theissen, E. (2003, February). Beta and returns revisited: Evidence from the German stock market. Journal of International Financial Markets, Institutions and Money, 13(1), 1–18.
Fabozzi, F. J., Mann, S. V., & Choudhry, M. (2002). The global money markets. Hoboken: Wiley.
Faff, R. (2001). A multivariate test of a dual-beta CAPM: Australian evidence. Financial Review, 36(4), 157–174.
Faff, R. (2004). A simple test of the Fama and French model using daily data: Australian evidence. Applied Financial Economics, 14(2), 83–92.
Fama, E. F. (1970). Efficient capital markets: A review of theory and empirical work. Journal of Finance, 25(2), 383–417.
Fama, E. F., & French, K. R. (1992). The cross-section of expected stock returns. Journal of Finance, 47(2), 427–465.
Fama, E. F., & French, K. R. (1993). Common risk factors in the returns on stocks and bonds. Journal of Financial Economics, 33, 3–56.
Fama, E. F., & French, K. R. (2004, Summer). The capital asset pricing model: Theory and evidence. Journal of Economic Perspectives, 18(3), 25–46.
Fama, E. F., & MacBeth, J. D. (1973). Risk, return, and equilibrium: Empirical tests. Journal of Political Economy, 81(3), 607–636.
Fletcher, J. (1997, May–June). An examination of the cross-sectional relationship of beta and return: U.K. evidence. Journal of Economics and Business, 49(3), 211–221.
Fletcher, J. (2000, Autumn). On the conditional relationship between beta and return in international stock returns. International Review of Financial Analysis, 9(3), 235–245.
French, C. W. (2002). Jack Treynor’s ‘Toward a theory of market value of risky assets’. Available at SSRN: papers.ssrn.com/sol3/papers.cfm?abstract_id=628187.
Friend, I., & Blume, M. E. (1970). Measurement of portfolio performance under uncertainty. American Economic Review, 60(4), 561–575.
Gibbons, M. R., Ross, S. A., & Shanken, J. (1989, September). A test of the efficiency of a given portfolio. Econometrica, 57(5), 1121–1152.
Gompers, P. A., & Metrick, A. (2001, February). Institutional investors and equity prices. Quarterly Journal of Economics, 116, 229–259.
Griffin, J. M. (2002, Summer). Are the Fama and French factors global or country specific? Review of Financial Studies, 15(3), 783–803.
Herrera, M. J., & Lockwood, L. J. (1994, September) The size effect in the Mexican stock market. Journal of Banking and Finance, 18(4), 621–632.
Heston, S. L., Rouwenhorst, K.G., & Wessels, R. E. (1999). The role of beta and size in the cross-section of European stock returns. European Financial Management, 5(1), 9–27.
Hodoshima, J., Garza-Gómez, X., & Kunimura, M. (2000, November–December) Cross-sectional regression analysis of return and beta in Japan. Journal of Economics and Business, 52(6), 515–533.
Hou, K., & Moskowitz, T. J. (2005, Autumn) Market frictions, price delay, and the cross-section of expected returns. Review of Financial Studies, 18(3), 981–1020.
Jensen, M. C. (1967). The performance of mutual funds in the period 1945–1964. Journal of Finance, 23(2), 389–416.
Jorgenson, D., & Fraumeni, B. M. (1989). The accumulation of human and nonhuman capital, 1948–84. In R. E. Lipsey & H. S. Tice (Eds.), The measurement of saving, investment, and wealth. Chicago: University of Chicago Press. http://www.nber.org/chapters/c8121.pdf?new_window=1. Accessed 8 Feb 2014.
Jorgenson, D., & Fraumeni, B. M. (1992). The output of the education sector. In Z. Griliches (Ed.), Output measurement in the service sectors. Chicago: University of Chicago Press. http://www.nber.org/chapters/c7238.pdf?new_window=1. Accessed 8 Feb 2014.
Kendrick, J. W. (1974) The accounting treatment of human investment and capital. Review of Income and Wealth, 20(4), 439–468.
Kendrick, J. W. (1976). Conceptual foundations of the study. In The formation and stocks of total capital (pp. 1–21). New York: National Bureau of Economic Research (NBER).
Kendrick, J. W. (1994) Total capital and economic growth. Atlantic Economic Journal, 22(1), 1–18.
Lakonishok, J., & Shapiro, A. C. (1986, December). Systematic risk, total risk and size as determinants of stock market returns. Journal of Banking and Finance, 10(1), 115–132.
Lakonishok, J., Shleifer, A., & Vishny, R. W. (1994, December) Contrarian investment, extrapolation, and risk. Journal of Finance, 49(5), 1541–1578.
Le, T., Gibson, J., & Oxley, L. (2003). Cost- and income-based measure of human capital. Journal of Economic Surveys, 17(3), 271–307.
Levy, R. A. (1971, November–December) On the short-term stationarity of beta coefficients. Finance Analysts Journal, 27(6), 55–62.
Lhabitant, F. S. (2004). Hedge funds quantitative insights. Hoboken: Wiley.
Lintner, J. (1965a). The valuation of risk assets and selection of risky investments in stock portfolios and capital budgets. Review of Economics and Statistics, 47(1), 13–37.
Lintner, J. (1965b, December). Security prices, risk, and maximal gains from diversification. Journal of Finance, 20(4), 587–615.
Litzenberger, R., & Ramaswamy, K. (1979, June). The effect of personal taxes and dividends on capital asset prices: Theory and empirical evidence. Journal of Financial Economics, 7(2), 163–195.
MacKinlay, A. C., & Richardson, M. P. (1991, June). Using generalised method of moments to test mean-variance efficiency. Journal of Finance, 46(2), 511–527.
Markowitz, H. M. (1952). Portfolio selection. Journal of Finance, 7(1), 77–91.
Markowitz, H. M. (1999, July/August) The early history of portfolio theory: 1600–1960. Financial Analysts Journal, 55(4), 5–16.
Merton, R. C. (1972, September). An analytic derivation of the efficient portfolio frontier. Journal of Financial and Quantitative Analysis, 7(4), 1851–1872.
Miller, M. H., & Scholes, M. S. (1972). Rates of return in relation to risk: A re-examination of some recent findings. In M. C. Jensen (Ed.), Studies in the theory of capital markets (pp. 47–78). New York: Praeger Publishers.
Mossin, J. (1966, October). Equilibrium in a capital asset market. Econometrica, 34(4), 768–783.
Pástor, L., & Stambaugh, R. F. (2003). Liquidity risk and expected stock returns. Journal of Political Economy, 111(3), 642–685.
Pettengill, G. N., Sundaram, S., & Mathur, I. (1995, March). The conditional relation between beta and returns. Journal of Financial and Quantitative Analysis, 30(1), 101–116.
Porter, R. B., & Ezzell, J. R. (1975, October) A note on the predictive ability of beta coefficients. Journal of Business Research, 3(4), 365–372.
Reilly, F. K., & Brown, K. C. (1997) Investment analysis and portfolio management. Chicago: Dryden Press.
Reinganum, M. R. (1981, December) A new empirical perspective on the CAPM. Journal of Financial and Quantitative Analysis, 16(4), 439–462.
Reinganum, M. R. (2013). 2013 Nobel Prize in economic sciences recognizes the important contributions of quant equity. State Street Global Advisors.
Roenfeldt, R. L., Griepentrog, G. L., & Pflaum, C. C. (1978, March). Further evidence on the stationarity of beta coefficients. Journal of Financial and Quantitative Analysis, 13(1), 117–121.
Rogers, P., & Securato, J.R. (2007, November). Comparative study of CAPM, Fama and French model and reward beta approach in the Brazilian market. University of Vicosa and University of Sao Paulo.
Roll, R. (1977). A critique of the asset pricing theory’s tests. Journal of Financial Economics, 4(2), 129–176.
Rosenberg, B., Reid, K., & Lanstein, R. (1985). Persuasive evidence of market inefficiency. Journal of Portfolio Management, 11(3), 9–16.
Schulmerich, M. (2012a). The efficient frontier in modern portfolio theory: Weaknesses and how to overcome them. State Street Global Advisors. SSgA Capital Insights.
Schulmerich, M. (2012b). Extending modern portfolio theory: Efficient frontiers for different risk measures. State Street Global Advisors. SSgA Capital Insights.
Schulmerich, M. (2013a). Can the Black-Litterman framework improve asset management outcomes? State Street Global Advisors. SSgA Capital Insights.
Schulmerich, M. (2013b, July/August). The efficient frontier in modern portfolio theory: Weaknesses and how to overcome them. In Investments & Wealth Monitor (pp. 27–32). Greenwood Village: IMCA - Investment Management and Consultants Association.
Sharpe, W. F. (1964). Capital asset prices: A theory of market equilibrium under conditions of risk. Journal of Finance, 19(3), 425–442.
Spremann, K. (2008). Portfoliomanagement (4th ed.). München: Oldenbourg Verlag.
Stambaugh, R. F. (1982). On the exclusion of assets from tests of the two-parameter model. Journal of Financial Economics, 10, 237–268.
Stoll, H. R., & Whaley, R. E. (1983). Transaction costs and the small firm effect. Journal of Financial Economics, 12(1), 57–79.
Strong, N., & Xu, X. G. (1997, March). Explaining the cross-section of U.K. expected stock returns. British Accounting Review, 29(1), 1–23.
Tobin, J. (1958, February). Liquidity preference as behavior towards risk. Review of Economic Studies, 25(2), 65–86.
Tole, T. M. (1981, Winter). How to maximize stationarity of beta. Journal of Portfolio Management, 7(2), 45–49.
van Dijk, M. A. (2011, September). Is size dead? A review of the size effect in equity returns. Journal of Banking and Finance, 1–40. http://papers.ssrn.com/sol3/papers.cfm?abstract_id=879282##. Accessed 3 Jan 2014.
Wang, F., & Xu, Y. (2004, November–December) What determines Chinese stock returns? Financial Analysts Journal, 60(6), 65–77.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Schulmerich, M., Leporcher, YM., Eu, CH. (2015). Modern Portfolio Theory and Its Problems. In: Applied Asset and Risk Management. Management for Professionals. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55444-5_2
Download citation
DOI: https://doi.org/10.1007/978-3-642-55444-5_2
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-55443-8
Online ISBN: 978-3-642-55444-5
eBook Packages: Business and EconomicsEconomics and Finance (R0)