22.1. Markowitz Portfolio Theory

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1 NPTEL Course Course Title: Security Analysis and Portfolio Management Course Coordinator: Dr. Jitendra Mahakud Module-11 Session-22 Markowitz Portfolio Theory Markowitz Portfolio Theory The pioneering work of Prof. Harry Markowitz is known as the Portfolio Theory or Modern Portfolio Theory (MPT) was first introduced in his paper entitled as Portfolio Selection published in the Journal of Finance in In the early 1960s, although the investment community talked about risk, but there was no specific measure for the quantification of the risk. As the first basic premises to interpret a portfolio model, investors had to quantify their risk variable. The basic portfolio model was developed by Harry Markowitz, who derived the expected rate of return for a portfolio of assets and an expected risk measure. In 1990, he along with Merton Miller and William Sharpe won the Nobel Prize in Economic Sciences for the theory. In a more general interpretation the theory emphasizes on the importance of diversifying to reduce risk in the sense that, investor will prefer to choose various securities cautiously taking mainly into consideration the way in which the price of each security changes in comparison to that of every other security in the portfolio, rather than choosing securities individually. The main outcome of the Portfolio Theory is that with optimum diversification, the risk weight of a portfolio shall be less than the average risk weights of the securities it contains. Similar to any other theory of financial economics portfolio theory also based upon the following key assumptions: Investors consider each investment alternative as being presented by a probability distribution of expected returns over some holding period. Investors minimize one-period expected utility, and their utility curves demonstrate diminishing marginal utility of wealth. Investors estimate the risk of the portfolio on the basis of the variability of expected returns. 1 Harry Markowitz (1952), Portfolio Selection, Journal of Finance Vol. 7, No. 1, pp

2 Investors base decisions solely on expected return and risk, so their utility curves are a function of expected return and the expected variance (or standard deviation) of returns only. For a given risk level, investors prefer higher returns to lower returns. Similarly, for a given level of expected returns, investors prefer less risk to more risk. Using these five assumptions, Markowitz mean-variance portfolio theory suggest that, a single asset or portfolio of assets is considered to be efficient if no other asset or portfolio of assets offers higher expected return with the same (or lower) risk, or lower risk with the same (or higher) expected return. As per this theory Markowitz shows that the expected rate of return of a portfolio is the weighted average of the expected return for the individual investments in the portfolio. The Markowitz theory has four basic premises: (i) Portfolio diversification. The purpose of diversification is to reduce the standard deviation of the total portfolio and assumes that imperfect correlations exist among securities (ii). Inclusion of various assets with negative correlation, (iii) Minimization of unsystematic risk i.e., It is specific to the company or industry. It is also known as "specific risk", this risk is specific to individual stocks. (e.g., business risk, financial risk). (iv) The only systematic risk remains in the market portfolio and variability in all risky assets caused by macroeconomic variables. In this regard systematic risk can be measured by the standard deviation of returns of the market portfolio and can change over time Markowitz portfolio theory strives to maximize return for a given risk or, minimize risk for a given return. This becomes possible by quantifying the notions of return and risk, and identifying a class of idealized portfolios for which an analysis is tractable. The theory states that when two portfolios have the same volatility but different means then the one with the greater mean is said to be more efficient because it promises greater return for the same risk. Every frontier portfolio with mean return μ > μmv is more efficient than every other portfolio with the same volatility. This segment of the frontier is called the efficient frontier. Every frontier portfolio with mean μ < μmv is less efficient (inefficient frontier) than every other portfolio with the same volatility. In other words any portfolio that lies on the upper part of the curve is efficient: it gives the maximum expected return for a given level of risk. The efficient frontier quantifies the relationship between risk and return and a rational investor will only ever hold a portfolio 2

3 that lies somewhere on the efficient frontier. The maximum level of risk that the investor will take on determines the position of the portfolio on the line. A portfolio management theory typically assumes that investors prefer efficient frontier portfolios and will therefore select an efficient frontier portfolio that is optimal given some measure of the risk aversion of an investor. The theory suggests a hypothesis on the basis of which, expected return on a portfolio for a given amount of portfolio risk is attempted to be maximized or alternately the risk on a given level of expected return is attempted to be minimized. An individual investor s utility curve specifies the trade-offs he is willing to make between expected return and risk The slope of the efficient frontier curve decreases steadily as you move upward These two interactions will determine the particular portfolio selected by an individual investor With respect to the efficient frontier, these utility curves determine which particular portfolio on the efficient frontier best suits an 3

4 individual investor. In the above figure the two different types of investors will chose different portfolios as per the best suitable utility curve hypothesis. While the risk averse investor selects the portfolio X the risk lover investor selects portfolio Y with higher level of portfolio risk. Although the portfolio X and Y are on the same efficient frontier the choice of the selected one i.e., X and Y by the two different types of investor depends up on the matching of the desired utility curve with the available alternatives in the efficient frontier. The rule to choose the required portfolio for generating the expected return is to pick up those portfolios which are at that point of tangency between the utility curve and efficient frontier. Put it differently, as the optimal portfolio has the highest utility for a given investor, it lies at the point of tangency between the efficient frontier and the utility curve with the highest possible utility. Additional Readings: Alexander, Gordon, J., Sharpe, William, F. and Bailey, Jeffery, V., Fundamentals of Investment, 3 rd Edition, Pearson Education. Bodie, Z., Kane, A, Marcus,A.J., and Mohanty, P. Investments, 6 th Edition, Tata McGraw-Hill. Bhole, L.M., and Mahakud, J. (2009), Financial institutions and markets.5th Edition, Tata McGraw Hill (India). Fisher D.E. and Jordan R.J., Security Analysis and Portfolio Management, 4th Edition., Prentice-Hall. Jones, Charles, P., Investment Analysis and Management, 9 th Edition, John Wiley and Sons. Prasanna, C., Investment Analysis and Portfolio Management, 3rd Edition, Tata McGraw-Hill. Reilly, Frank. and Brown, Keith, Investment Analysis & Portfolio Management, 7th Edition, Thomson Soth-Western. Additional Questions with Answers Session 22: Markowitz Portfolio Theory 1. Explain Markowitz Portfolio Theory? Ans. Markowitz showed that the variance of the rate of return was a meaningful measure of portfolio risk under a reasonable set of assumptions. He also derived a formula for computing the variance of a portfolio. These formulas for the variance of a portfolio not only indicate the importance of diversifying your investments to reduce the total risk of a portfolio, but also showed how to effectively diversify. Markowitz theory achieved the following: Markowitz demonstrated that the variance of the rate of return is a meaningful measure of portfolio risk under reasonable assumptions. 4

5 Derives the expected rate of return for a portfolio of assets and an expected risk measure Shows that the variance of the rate of return is a meaningful measure of portfolio risk Derives the formula for computing the variance of a portfolio, showing how to effectively diversify a portfolio 2. What is the meaning of Efficient Frontier? Ans. The efficient frontier represents that set of portfolios with the maximum rate of return for every given level of risk, or the minimum risk for every level of return Frontier will be portfolios of investments rather than individual securities: Exceptions being the asset with the highest return and the asset with the lowest risk Any portfolio that lies on the upper part of the curve is efficient: it gives the maximum expected return for a given level of risk. A rational investor will only ever hold a portfolio that lies somewhere on the efficient frontier. The maximum level of risk that the investor will take on determines the position of the portfolio on the line. 3. What is the implication of Macroeconomic Factors towards Systematic Risk? Ans. Systematic risk is the variability in all risky assets caused by macroeconomic variables Examples of Macroeconomic Factors Affecting Systematic Risk: Variability in growth of money supply, Interest rate volatility, Variability in industrial production, corporate earnings, cash flow 4. Differentiate between Systematic and Unsystematic risk. Ans. Systematic Risk: Only systematic risk remains in the market portfolio and is the variability in all risky assets caused by macroeconomic variables Systematic risk can be measured by the standard deviation of returns of the market portfolio and can change over time Beta measures an asset s systematic risk Unsystematic Risk: It is specific to the company or industry. It is also known as "specific risk", this risk is specific to individual stocks. Like business risk and financial risk. Unsystematic risk is uncorrelated with systematic risk. The part of an asset s risk that is not correlated with the market portfolio 5

6 5. How diversification can reduce Unsystematic Risk of a given portfolio? Ans. Diversification and the Elimination of Unsystematic Risk: The purpose of diversification is to reduce the standard deviation of the total portfolio This assumes that imperfect correlations exist among securities As the number of securities added to a portfolio increases, the average covariance for the portfolio declines 6