This paper is concerned with how an investor can select a portfolio based on Markowitz principles. Markowitz’s selection theory (1952) gives essential guidelines to investors when selecting portfolios that best meet their objectives. A good portfolio is one which is one that can offer an investor a chance to make an informed capital decision. Markowitz’s approach enables investors to know that there is a risk-return trade-off.
According to him, investors should begin analyzing their portfolios by gathering information related to individual risks and concludes with information related to a portfolio as a whole. According to Markowitz, the aim is to enable investors to find portfolios that meet their specific objectives. Portfolio selection is a process that can guide any investor in committing his or her resources to investment. The approach is particularly essential as it is based on the efficient frontier concept which assumes that for a specified standard deviation, a rational investor would choose a portfolio with the highest return.
This paper discusses a number of principles advocated by Markowitz that guide investors to make investment decisions. The first principle depicts investors as being risk-averse and in need to maximize expected returns. The second guides investors on how the expected returns and risks of individual securities contribute to the expected return and risk of a portfolio. The third assists the investor to analyze the effectiveness of diversification for different degrees of covariance among securities in a portfolio. Finally, the last principle helps the investor to select the optimal portfolio along the efficient frontier curve. Based on these principles, I will certainly accept the investment offer.
Markowitz Portfolio Theory (1952) is based on the assumption that investors are risk-averse and in need to maximize expected returns. Expected returns theory attempts to quantify the risk of a portfolio and its expected return. The business environment is always unpredictable. Thus investors face the challenge of making their investments based on what they expect in the future. Markowitz’s principle of expected return helps investors to predict the future and make appropriate business decisions.
However, the theory of the expected return cannot fully guarantee the investor the actual outcome. This is because the principle does not put into consideration the possible risks of return. It is important to note that expected returns and the risk of individual securities contribute to the expected returns and risks of a portfolio.
According to Markowitz (1952), a portfolio’s expected return is the discounted average of the expected returns of securities constituting it. Therefore investors should know that portfolio risks depend on other factors apart from variances of component securities. For instance, the performance of a portfolio may directly be affected by unanticipated stiff competition, labor disputes, or an economy facing a recession. Investors are therefore advised to factor in variability to cater for deviations from the expected outcomes. Variance principles help investors with a reasonable gauge of security risk.
Analytically, variance is computed as follows:
Var (S) = Sum i (Si – E(S))2 / N
Where Sum i means to sum over all elements of set S,
N is the number of elements in S,
Si is the ith element of the set S,
and E(S) is the mean over the values of a set
The formula shows variance as a measure of the dispersion of returns calculated by squaring the difference between each return in a series and the mean return for the series, then averaging these squared differences. When dealing with samples the exact mean and variance cannot be computed but estimated. Given a sample U with M elements Ui, i=1,2, M, we obtain an unbiased estimate of the mean as follows:
Mu = Sum i Ui / M,
While an unbiased estimate s2 of the variance is obtained from the formula
s2 = Sum i (Ui – mu) 2/ (M-1)
Although variance is a reasonable risk gauge, the average of two securities will not necessarily give a good indication of the risk of a portfolio comprising two securities. Risks on portfolios also depend on the extent to which the two securities move together. Markowitz also explores the important element of diversification which enables to invest in multiple securities.
An important way an investor can reduce the risks of investment is through diversification. According to Markowitz, diversification is keen to” not putting all your eggs in one basket”. Investors can diversify their portfolios whose holdings are concentrated in one area in different ways. For instance, instead of investing in stocks belonging to a single company, an investor may invest in other industries. This helps investors to avoid losses in case an event happens to the only company they have invested in. The principle of diversification also helps an investor to invest in securities whose investment returns move together.
Diversification enables investors to combine investments within a portfolio. These then aid them to predict how a portfolio of a different kind of investment can on average lead to higher returns and pose lower risks than individual investments found within a portfolio. Therefore through diversification, an investor is able to reduce market risks by investing in multiple securities. However, for diversification to work, it is not enough to add risk to a portfolio. Standard deviation gives an important relationship between risk and return. It is a measure of the risk of return. When the standard deviation is high it indicates that there is a large disparity in the return series. Through it, investors are able to determine the ratio to invest in each asset while minimizing the risks of the entire portfolio.
Covariance between two securities is calculated by multiplying the standard deviation of the first, the second, and the correlation coefficient between the two. The correlation coefficient is a measure of the relationship that exists between the return of the two securitiesCorrelation coefficient value ranges from 1 to -1. The correlation coefficient will be positive if one security return is lower than its average return. When another security return is lower than its average return then the correlation coefficient will be negative. The coefficient is not a reliable measure of covariance because it measures the direction and level of association between security returns only. It does not put into consideration variability in each security’s returns.
Covariance can therefore be computed as follows:
Given two sets, Si and Sj, the covariance is
Cov (i,j) = sumk (Sik – E(Si)) (Sjk – E(Sj)) / N,
Where Sik is the kth element of set Si and N is the number of elements in each set.
According to Markowitz (1952), an investor would be willing to take a certain level of risk to earn a return. Investors tend to become less and less willing to risk more as the total goes up. This is well illustrated in Markowitzs’ efficient frontier theory where all efficient portfolios are placed together to form an efficient frontier. Through efficient frontier, theory investors are able to carry out asset allocation. Asset allocation helps the investor to achieve the objective of creating a diversified portfolio with a level of risk that is acceptable and with the highest expected return given that level of risk. Modern portfolio theory explains how investors tend to select portfolios based on higher returns and lower standard deviations.
The objective of this paper has been to discuss Markowitz’s portfolio selection principles. His portfolio theory lays a basic concept needed to understand the modern portfolio theory. Markowitz portfolio assumes that investor behavior is indicated by risk aversion and return maximization. Today’s investors should consider Markowitz’s principles because they acknowledge the fact that the future is uncertain. These principles explicitly explain the importance of discounting anticipated returns.
He pioneered an important idea in the theory of portfolio selection. He goes further to illustrate how expected returns and risks of individual securities contribute to the expected returns and risk of a portfolio. His theory provides information critical when choosing the best portfolio for any given level of risk. This is explained by three simple statistics, that is, the mean, standard deviation, and correlation. This process aids investors in their final choice of the optimal portfolio along an efficient frontier curve. Markowitz’s portfolio theory has revolutionized financial management to date.
References
Markowitz, H. M. (1952) Portfolio Selection. Journal of Finance, 7(1), 77-91.
Markowitz, H. M. (1959) Portfolio Selection: Efficient Diversification. John Willey & Sons., Inc. New York.