Covariance, Correlation, and Portfolio Risk and Capital Asset Pricing Model - Essay Example

Risk and Return a. Indifference curves in the context of risk and return The selection of the best portfolio for an investor can be done in a number of ways, but perhaps the commonest way is the use of preference curves. In this context, Damodaran (2010) states that a preference curve is a representation of an investor’s selection for risk and return, meaning the attitudes that the investor has towards risk and the associated return on an investment. The horizontal axis on an indifference curve represents the risk of an investment, while the vertical axis represents the earning or return that an investor would expect to earn from the investment. According to Campbell (1996), the indifference curve is a plot of the trade-off between an investor’s risk aversion and affinity against the return of an investment. The indifference curve can be used to reflect investor attitude or risk by refloating an investor’s preference. The plot of many indifference curves shows the different options that an investor would take. However, from the indifference map, the best option is to take the option that is highest that any other indifference curve. b. Selection of a suitable portfolio Indifference curves are not just used to display the risk aversion factors of an investor; in fact, the indifference curve can be used to select a suitable portfolio in terms of risk and return (Yin and Zhou, 2004). As already stated, the indifference curve is a plot of the risk and return preferences of an investor, therefore, to select the most suitable portfolio, an investor can utilize the mean-variance theory. The mean-variance theory of portfolio selection is derived from the indifference curve, where the map of the different indifference curves for an investor is plotted together (Maharakkhaka, 2011). From the plot of the indifference curves, the transitive preferences of an investor can be determined, which refers to the selection of the best preference curve as chosen by an investor. From an analysis of the transitive preferences, it is evident that the highest preference curve is the one that should be selected by the investor. From the indifference curve, the investor can determine the highest possible indifference curve, which, combined with the other indifference curves, gives the mean-variance portfolio or the most efficient portfolio in an investment. 2. Correlation and Co-variance a. Correlation and Co-variance The relationship between two variables can be measured or determined in different ways, but the commonest way is the determination of the correlation and covariance of the two variables. A number of variables are sometimes related in some way or another, either the occurrence of one variable affects the occurrence of the other variable, or the does not affect the working of the other variable. The covariance refers to the type of relationship that two variables have, meaning that it shows whether two variables have a positive or negative relationship. In this case, a positive relationship refers to the fact that one variable moves in the same direction as the other variable. Conversely, the correlation between two variables incorporates another dimension, the extent to which two variables are related. In addition to the covariance angle of determining whether variables are positively or inversely related, the correlation also shows the extent to which the variables are inversely or positively related. b. Covariance, Correlation, and Portfolio risk As already stated, the correlation between two variables is determined by the movement of one variable in relation to the movement of the other variable. In the investment market, diversification is a good practice, since it ensures that an investor does not lose an investment in case of a catastrophe or loss in market value. A positive correlation between assets means that one asset will move in the exact same way as another asset. In investment, stocks with low or negative correlation are used to reduce portfolio risk since when one asset falls; the other asset is bound to rise. This means that the best correlation between assets is a low or negative correlation, since the loss in one asset is not accompanied by a loss in the other asset. Therefore, these assets will reduce portfolio risk by reducing the risk of losing both assets at the same time, or the risk of having low-performing assets at the same time. c. Diversification and Portfolio Risk The relation between two assets can be either positive, negative, or zero correlation. Either way, there is the risk of loss if assets are lost in one location or portfolio. Utilizing the principle discussed above, the principle of correlation and reducing portfolio risk, it is possible for an investor to reduce the risk of loss in an investment. This is done through diversification, which refers to the spreading out of investments through different geographical locations, different risk portfolios, or different asset portfolios. The diversification of investments refers to the spreading out of investments to usually unrelated sectors, which will be useful in case one of the sectors is affected or losses. Diversification is important for portfolio risk since it helps to balance out the risk in a portfolio, which ultimately helps in the determination of the optimal portfolio. The diversification of investment reduces the risk of loss in case one investment is affected by market conditions, which means that the unrelated portfolio is not affected. 3. Capital Asset Pricing Model a. Market Portfolio in the CAPM The Capital Asset Pricing Model is a set of assumptions about the investment market and the behavior of investors, assumptions that are used to determine the return of assets in the market (Fama and French, 2004). The CAPM is usually focused on the systematic risk in the market, and one of the assumptions is the existence of the market portfolio. In the CAPM, the market portfolio refers to a portfolio where all the investments made in the assets correspond to the market value of each investment (Fama and French, 2004). This implies that all investors are rational, the market portfolio is measurable, and exists on the MVE frontier. The market portfolio is particularly important for the CAPM since it helps in the determination of the optimal investment portfolio, with the use of the assumptions of the market portfolio. The market portfolio is usually created from the assumption that the diversification costs in the market are minimal, or that diversification costs nothing, which implies that all assets in the market are traded. Therefore, diversification would only be limited by the holding of a portfolio consisting of all the assets in the economy, which is the market portfolio. b. Capital Asset Pricing Beta The risk of a portfolio is measured by the risk that an individual asset adds to the total portfolio (Fama and French, 2004). The total risk that is added by each asset is measured in terms of how each asset moves with the market (Fama and French, 2004). As already stated, the movement of one variable in relation to another variable can be defined as the covariance of the two assets. The standardized measure of this covariance, which is a measure if the risk of an investment, is called the beta. Therefore, beta can be defined as the measure of the non-diversifiable or systematic risk in a portfolio. The covariance of an asset in the CAPM measured by the risk of an asset in relation to the market index (Fama and French, 2004). c. Limitations of the CAPM Despite the positive factors of the CAPM discussed above, the CAPM has a myriad of limitations, key among them being the fact that the model makes many assumptions (Shapiro, 2010). Some of the assumptions of the CAPM are discussed above, and it is evident that some of them are not completely justifiable. The CAPM might also be considered unsatisfactory because of the difficulty in estimation of most of its parameters, for example, the market index is usually hard to determine, and the firm’s condition might have changed during the estimation period (Shapiro, 2010). The model does not always give consistent results, since if it did, there would always be a linear relationship between the two main variables in the model; the returns and the betas of the assets. Bibiliography Campbell, Y.A. (1996). Undrestanding Risk and Return, The Journal of Political Economy, 104(2), 298-345. Damodaran, A. (2010). Applied Corporate Finance. New York: Wiley Publishers. Damodaran, A. (2010). Estimating Risk Parameters, Stern School of Business. Fama, F. E., French, R.K. (2004). The Capital Asset Pricing Model: Theory and Evidence, Journal of Economic Perspectives, 18(3), 25-46. Maharakkhaka, B. (2011). The Performance of Mean-Variance Portfolio Selection and Its Opportunity Cost: The Case of Thai Securities, 2011 International Conference on Economics and Finance Research, 4, 149-153. Shapiro, A. (2010). Foundations of Multinational Financial Management, Wiley Publishers, Wiley. Yin, G., Zhou, X.Y. (2004). Mean-variance Portfolio Selection under Markov Regime: Discrete- Time Models and Continuous-time Limits, Automatic Control, IEEE Transactions, 49(3), 349-360. Read More