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Mean-Variance Approach

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Analytical Corporate Valuation

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Abstract

The mean-variance approach is the most widely used in the portfolio selections. The portfolio selection is based on two variables: (i) expected value of the portfolio return; (ii) variance of the expected portfolio return measuring the portfolio risk. An efficient portfolio must satisfy the Pareto optimal condition. Therefore, the investor prefers the portfolio that is capable of maximising its expected return to an equal variance or the portfolio capable of minimizing its variance to an equal expected return. This approach simplifies the problem of portfolio selection. There are two main advantages: first, it does not require specification about probability distribution; second, it is simple and intuitive because it is only based on the mean and variance. However, it is also true that this approach neglects a lot of relevant information about distribution probability. The entire portfolio selection process can be simplified on the basis of two main phases of the portfolio selection process:

  1. (1)

    optimization phase: the aim is to define the diversified portfolio and the efficient frontier. The definition of the diversified portfolio is based on the statistical characteristics of the assets. Specifically, the expected return of the portfolio is equal to the weighted average of the expected returns of the assets, while the portfolio variance is the function of the covariance between the assets’ expected returns. The assumption refers to the investors’ homogeneous expectations about the statistical characteristics of the assets implying that all investors define the same efficient frontier.

  2. (2)

    maximization phase: the aim is to choose the optimal portfolio among the efficient portfolios defined on the efficient frontier. None of the efficient portfolios on the efficient frontiers can be preferred over the others by definition. The choice of the optimal portfolio among the efficient portfolios requires a clear definition of the investor’s preferences about risk.

While the optimization phase is characterized by objectivity because it is valid for the entire market and not for the single investor, the maximization phase is characterized by subjectivity because it is the function of the investor’s risk preferences. An analysis of the entire portfolio selection process based on the optimization and maximization phases can be carried out according to four main steps:

  • (step 1) construction of the diversified portfolio;

  • (step 2) construction of the efficient frontier;

  • (step 3) definition of the efficient portfolios;

  • (step 4) choice of the optimal portfolio.

The first three steps (1, 2, 3) define the optimization phase while the last step (4) defines the maximization phase.

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References

  • Alexander G (1976) The derivation of efficient sets. J Financ Quant Anal XI(5):817–830

    Article  Google Scholar 

  • Alexander G (1977) Mixed security testing of alternative portfolio selection models. J Financ Quant Anal XII(4):817–832

    Article  Google Scholar 

  • Alexander G (1978) A reevaluation of alternative portfolio selection models applied to common stock. J Financ Quant Anal XIII(1):71–78

    Article  Google Scholar 

  • Bawa VS, Brown SJ, Klein RW (1979) Estimation risk and optimal portfolio choice. North Holland, Amsterdam

    Google Scholar 

  • Bertsekas D (1974) Necessary and sufficient conditions for existence of an optimal portfolio. J Econ Theory 8(2):235–247

    Article  Google Scholar 

  • Blume M (1970) Portfolio theory: a step toward its practical application. J Bus 43(2):152–173

    Article  Google Scholar 

  • Brennan MJ, Kraus A (1976) The geometry of separation and myopia. J Financ Quant Anal XI(2):171–193

    Article  Google Scholar 

  • Brown S, Barry C (1985) Differential information and security market equilibrium. J Financ Quant Anal 20:407–422

    Article  Google Scholar 

  • Brumelle S (1974) When does diversification between two investments pay? J Financ Quant Anal IX(3):473–483

    Article  Google Scholar 

  • Buser S (1977) Mean-variance portfolio selection with either a singular or non-singular variance-covariance matrix. J Financ Quant Anal XII(3):436–461

    Google Scholar 

  • Canner N (1997) An asset allocation puzzle. Am Econ Rev 87(1):181–193

    Google Scholar 

  • Carhart M (1997) On persistence in mutual fund performance. J Financ 52:661–692

    Article  Google Scholar 

  • Cass D, Stiglitz J (1970) The structure of investor preferences and asset returns, and separability in portfolio allocation: a contribution to the pure theory of mutual funds. J Econ Theory 2(2):122–160

    Article  Google Scholar 

  • Castellani G, De Felice M, Moriconi F (2005) Manuale di Finanza 2. Teoria del portafoglio e mercato azionario, Il Mulino

    Google Scholar 

  • Cesari R (2012a) Introduzione alla finanza matematica. Concetti di base, tassi e obbligazioni, 2nd edn. McGraw-Hill, New York

    Google Scholar 

  • Cesari R (2012b) Introduzione alla finanza matematica. Mercati azionari, rischi, e portafogli, 2nd edn. McGraw-Hill, New York

    Google Scholar 

  • Chan LKC, Karceski J, Lakonishok J (1999) On portfolio optimization: forecasting covariances and choosing the risk model. Rev Financ Stud 12:263–278

    Article  Google Scholar 

  • Chen A (1977) Portfolio selection with stochastic cash demand. J Financ Quant Anal XII(2):197–213

    Article  Google Scholar 

  • Chen A, Jen F, Zionts S (1971) The optimal portfolio revision policy. J Bus 44(1):51–61

    Article  Google Scholar 

  • Chen A, Kim H, Kon S (1975) Cash demands, liquidation costs and capital market equilibrium under uncertainty. J Financ Econ 2(3):293–308

    Article  Google Scholar 

  • Cohen K, Pogue J (1967) An empirical evaluation of alternative portfolio selection models. J Bus 46:166–193

    Article  Google Scholar 

  • Connor G, Korajczyk R (1993) A test for the number of factors in an approximate factor model. J Financ 48:1263–1291

    Article  Google Scholar 

  • Dalal AJ (1983) On the use of a covariance function in a portfolio model. J Financ Quant Anal XVIII(2):223–228

    Article  Google Scholar 

  • Dybving PH (1984) Short sales restrictions and kinks of the mean variance frontier. J Financ 39(1):239–244

    Article  Google Scholar 

  • Edwards F, Goetzmann W (1994) Short horizon inputs and long horizon portfolio choice. J Portfolio Manage 20(4):76–81

    Article  Google Scholar 

  • Elton EJ, Gruber MJ (1971) Dynamic programming applications in finance. J Financ XXVI(2):473–505

    Article  Google Scholar 

  • Elton EJ, Gruber MJ (1974) Portfolio theory when investment relatives are lognormally distributed. J Financ XXIX(4):1265–1273

    Article  Google Scholar 

  • Elton EJ, Gruber MJ (1977) Risk reduction and portfolio size: an analytical solution. J Bus 50(4):415–496

    Article  Google Scholar 

  • Elton EJ, Gruber MJ, Spitzer J (2006) Improved estimates of correlation coefficients and their impact on the optimum portfolios. Eur Financ Manage 12(3):303–318

    Article  Google Scholar 

  • Elton EJ, Gruber MJ, Brown SJ, Goetzmann WN (2013) Modern portfolio theory and investment analysis, 9th edn. Wiley

    Google Scholar 

  • Epps TW (1981) Necessary and sufficient conditions for the mean-variance portfolio model with constant risk aversion. J Financ Quant Anal XVI(2):169–176

    Article  Google Scholar 

  • Fama E (1968) Risk, return, and equilibrium: some clarifying comments. J Financ 23:29–40

    Article  Google Scholar 

  • Fama E (1981) Stock return, real activity, inflation and money. Am Econ Rev 71:545–565

    Google Scholar 

  • Fama E, MacBeth J (1973) Risk, return, and equilibrium: empirical tests. J Polit Econ 38:607–636

    Article  Google Scholar 

  • Farrell J (1974) The multi-index model and practical portfolio analysis. In: The financial analysts research foundation occasional paper, vol 4

    Google Scholar 

  • Francis JC (1975) Intertemporal differences in systemic stock price movements. J Financ Quant Anal 10(2):205–219

    Article  Google Scholar 

  • Hakansson N (1970) An induced theory of the firm under risk: the pure mutual fund. J Financ Quant Anal V(2):155–178

    Article  Google Scholar 

  • Hill R (1976) An algorithm for counting the number of possible portfolios given linear restrictions on the weights. J Financ Econ XI(3):479–487

    Google Scholar 

  • Jacob N (1974) A limited-divesification portfolio selection model for the small investor. J Financ XXIX(3):847–856

    Article  Google Scholar 

  • Jennings E (1971) An empirical analysis of some aspects of common stock diversification. JFinanc Quant Anal VI(2):797–813

    Article  Google Scholar 

  • Johnson K, Shannon D (1974) A note of diversification and the reduction of dispersion. J Financ Econ 1(4):365–372

    Article  Google Scholar 

  • Jones-Lee MW (1971) Some portfolio adjustment theorems for the case of non-negativity conditions on security holdings. J Financ XXVI(3):763–775

    Article  Google Scholar 

  • Kryzanowski L, To MC (1983) General factor models and structure of security returns. J Financ Quant Anal 18:31–52

    Article  Google Scholar 

  • Latane H, Tuttle D, Young A (1971) How to choose a market index. Financ Anal J 27(4):75–85

    Article  Google Scholar 

  • Ledoit O, Wolf M (2003) Improved estimation of the covariance matrix of stock returns with an application to portfolio selection. J Empir Financ 10(5):603–624

    Article  Google Scholar 

  • Levy H (1984) Measuring risk and performance over alternative investment horizons. Financ Anal J 40(2):61–67

    Article  Google Scholar 

  • Levy RA (1971) On the short-term, stationary of beta coefficients Financ Anal J 27(5):55–62

    Google Scholar 

  • Lewis AL (1988) A simple algorithm for the portfolio selection problem. J Financ 43(1):71–82

    Article  Google Scholar 

  • Lintner J (1965) The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets. Rev Econ Stat XLVII:13–37

    Article  Google Scholar 

  • Markowitz H (1952) Portfolio selection. J Financ 7(1):77–91

    Google Scholar 

  • Markowitz H (1956) The optimization of a quadratic function subject to linear constraints. Naval Res Log 3(1–2):111–133

    Article  Google Scholar 

  • Markowitz H (1959) Portfolio selection: efficient diversification of investment. Wiley, New York

    Google Scholar 

  • Markowitz H (1976) Markowitz revisited. Financ Anal J 32(4):47–52

    Article  Google Scholar 

  • Markowitz H (2014) The theory and practice of rational investing. Risk-return analysis, vol I, McGraw-Hill

    Google Scholar 

  • Markowitz H (2016) The theory and practice of rational investing. risk-return analysis, vol. II, McGraw-Hill

    Google Scholar 

  • Martin J, Klemkosky R (1975) Evidence of heteroscedasticity in the market model. J Bus 48(1):81–86

    Article  Google Scholar 

  • Merton R (1972) An analytic derivation of the efficient portfolio frontier. J Financ Quant Anal VII(4):1851–1872

    Article  Google Scholar 

  • Meyers S (1973) A re-examination of market and industry factors in stock price behavior. J Financ VIII(3):695–705

    Article  Google Scholar 

  • Mossin J (1968) Optimal multiperiod portfolio policies. J Bus 41(2):215–229

    Article  Google Scholar 

  • Officer RR (1973) The variability of the market factor of the New York stock exchange. J Bus 46(3):434–453

    Article  Google Scholar 

  • Ohlson J (1975) Portfolio selection in a log-stable market. J Financ Quant Anal X(2):285–298

    Article  Google Scholar 

  • Pogue G, Solnik B (1974) The market model applied to European common stocks: some empirical results. J Financ Quant Anal IX(6):917–944

    Article  Google Scholar 

  • Pye G (1973) Lifetime portfolio selection in continuous time for a multiplicative class of utility functions. Am Econ Rev LXIII(5):1013–1020

    Google Scholar 

  • Robichek A, Cohn R (1974) The economic determinants of systemic risk. J Financ XXIX:439–447

    Article  Google Scholar 

  • Ross SA, Westerfield R, Jaffe J, Jordan BD (2015) Corporate finance, 11th edn, McGraw-Hill

    Google Scholar 

  • Rubinstein M (1973) The fundamental theorem of parameter-preference security valuation. J Financ Quant Anal VIII(1):61–69

    Article  Google Scholar 

  • Rudd A, Rosenberg B (1980) The market model in investment management. J Financ 35(2):597–606

    Google Scholar 

  • Saltari E (2011) Appunti di Economia Finanziaria, Esculapio

    Google Scholar 

  • Schafer S, Brealey R, Hodges S (1976) Alternative models of systematic risk. In: Elton EJ, Gruber MJ (eds) International capital markets. North-Holland, Amsterdam

    Google Scholar 

  • Sharpe W (1971) Mean-absolute-deviation characteristic lines for securities and portfolios. Manage Sci 18(2):1–13

    Article  Google Scholar 

  • Smith K (1968) Alternative procedures for revising investment portfolios. J Financ Quant Anal III(4):371–403

    Article  Google Scholar 

  • Statman M (1987) How many stocks make a diversified portfolio? J Financ Quant Anal 22(3):353–363

    Article  Google Scholar 

  • Sunder S (1980) Stationary of market risk: random coefficients tests for individual stocks. J Financ 35(4):883–896

    Article  Google Scholar 

  • Tobin J (1958) Liquidity preference as behaviour towards risk. Rev Econ Stud 25(2):65–86

    Article  Google Scholar 

  • Wagner W, Lau S (1971) The effect of Diversification on Risk. Financ Anal J 27(5):48–53

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Law and Economics of Productive Activities, Sapienza University of Rome, Rome, Italy

    Pasquale De Luca

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De Luca, P. (2018). Mean-Variance Approach. In: Analytical Corporate Valuation. Springer, Cham. https://doi.org/10.1007/978-3-319-93551-5_5

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