How Does a Rational Investor Build the Optimal Portfolio - Term Paper Example

Introduction to Modern Portfolio Theory Modern Portfolio theory was introduced by Harry Markowitz in 1952. Prior to the Modern Theory of Portfolio, investors focused on assessing the individual risk and return of individual securities to construct their portfolio. The basic idea was to construct a portfolio by identifying the securities having least risk. All the investment advices were therefore based on this principal of portfolio selection. The basic problem with this approach was the fact that if an investor assesses that any particular stock has a good risk return characteristics than investor can build up entire portfolio of assets from that particular stock. This was however considered as illogical as it supposed linear relationship between the risk and return profile of the stocks. Markowitz, by using the mathematics of Diversification, however proposed that investors focus on selecting portfolios based on their overall risk-reward characteristics instead of merely compiling portfolios from securities that each individually have attractive risk-reward characteristics. In a nutshell, inventors should select portfolios not individual securities. The basic assumptions behind this portfolio selection theory was that if we take single period returns of various securities and treat them as random variables than we can assign expected values, standard deviation and correlations to them. Once it is done, based on the expected returns, an investor can come up with the volatility of stock returns and can construct any portfolio. The expected returns and volatility of the stocks were approximated as the return and risks of the portfolio. Thus out of the whole universe of portfolios, certain portfolios will optimally balance the risk and rewards. This, in return, will create an efficient frontier for the investor and any portfolio lying on the efficient frontier will be optimal for the investor. The whole idea therefore was based on the assumption that the any risk averse investor will go for diversification in order to find an optimal balance between the risks and return profile of the individual securities to find out the optimal portfolio. It was proposed that the diversification will reduce the risks of the portfolio however it will not generally eliminate it. (Rubinstein). Theory put forward by Markowitz was the first effort to formalize the mathematics of diversification into the investment theory. Through diversification, an investor should maximize expected portfolio returns while minimizing the portfolio variance of the return. The major theoretical claim put forward through this theory was the fact that it is not the risk of the individual security that can bother the investor as the risks associated with it can be reduced through diversification but rather the contribution of the security to the overall variance of the portfolio which in turn depends upon the covariance of the securities with each other in the portfolio. Thus the risk of a portfolio depends upon the proportions of the individual stocks, their variances and covariance with each other. A change in any one of the above variables will virtually change the risk of the portfolio. (Statman). There often arises the question regarding the number of stocks in a portfolio which can minimize the risks of the portfolio and construct an efficient portfolio. It is largely believed that the diversification of portfolio creates reduction is risk as the number of stocks in portfolio increase. However this risk reduction is diminishing in nature i.e. as the number of stocks in the portfolio increases, the portfolio risk decreases at decreasing rate i.e. after some point in time, the risk can not be further reduced. This optimal number of stocks in portfolio thus describes the best optimal mix of the portfolio. Earlier studies on this issue suggest that 10 or more stocks in a portfolio can virtually exhaust the risk and thus the economic benefits of diversification thus minimize. Critique of the Markowitz theory One of the strongest observations made against the Modern Portfolio theory was based on the core assumption of theoretical framework that the volatility is the best measure of the risk of the portfolio. MPT was based on the assumption that any portfolio falling on the efficient frontier will be optimal for the investors who are risk adverse in nature. However how to actually define risk is debatable. (Morien). Thus the assumption that volatility hence standard deviation of the portfolio returns is the best measure of the portfolio risk is debatable. It has been empirically proven that high volatility do not necessarily give higher returns and neither the low risk provide low returns as other more compelling and uncontrollable factors push the risk profile of the portfolio in entirely different direction than anyone can perceive of. The modern portfolio theory brought a shift from analyzing the fundamentals to more risk based measures to analyze the securities thus effectively putting up higher bets on the high risk high return assumption. During 1977, J.Michael Murphy, in his paper on the Efficient Markets, Index Funds, Illusion, and Reality", Journal of Portfolio Management (Fall 1977), pp. 5-20.) Outlined four major studies in which it was empirically proven that there is a far weaker relationship between the risk and returns of the assets and that there may often be virtually no relationship between the risk and rewards related with the assets. (Morien). Apart from the weaker relationship between the risk and return, it is also argued that the volatility, over the period of time, do not remain same and it continue to change. Thus if stocks do not have a constant volatility and hence risk it therefore become difficult to use it as a factor to derive the meaningful changes in the portfolio risk and return. James Tobin’s theory James Tobin’s theory was one of the earliest attempts to modify the modern portfolio theory given by Henry Markowitz. James Tobin (1958) expanded on Markowitzs work by adding a risk-free asset to the analysis. This made it possible to leverage or deleverage portfolios on the efficient frontier. This lead to the notions of a super-efficient portfolio and the capital market line. Through leverage, portfolios on the capital market line are able to outperform portfolio on the efficient frontier. Thus through the creation of leverage, an investor can create an optimal portfolio by creating a super efficient portfolio. However, James Tobin’s theory was also not sufficient to fulfill the gap between actually outlining what practically an investor can do in order to maximize the return on his portfolio. In order to fulfill that gap, another model of risk and return was proposed by William Sharpe which is called Capital Asset Pricing Model. Capital Asset Pricing Model Capital Asset Pricing Model is another model through which can be used to find the optimal mix of portfolio. Developed after the Markowitz theory of Modern Portfolio Theory. What was considered as an extension of MPT, CAPM is now considered as one of the most important innovations in the field of finance which provided investors the necessary tool to assess the risk and return in better way so that an optimal portfolio can be developed. According to CAPM, every investment carries two risks. One is called systematic risk which is the risk of being in the market. This risk was later dubbed as beta. (Burton) Which according to CAPM cannot be eliminated or minimized therefore what investor need to look into is the individual risk profile of the securities in the portfolio to build an optimal mix. The other—unsystematic risk—is specific to a companys fortunes. Since this uncertainty can be mitigated through appropriate diversification, Sharpe figured that a portfolios expected return hinges solely on its beta—its relationship to the overall market. The CAPM helps measure portfolio risk and the return an investor can expect for taking that risk. Criticism of Theory The model which has been used to evaluate the risk and return profile of this stock is Capital Asset pricing Model or CAPM. Theoretically, CAPM model works under certain special conditions. The first condition outlined under this model suggest that the individuals are risk averse in nature therefore they will maximize their end period wealth. It is because of these theoretical limitations, the CAPM model is often termed as One Period model. The second very critical weakness of this model is the fact that CAPM outlines that all the investors have uniform information and thus every information is available to the investors which often not the case. This assumption is especially in contrast to the Efficient Market Hypothesis Theory which clearly indicates the degrees of information available and the market’s cumulative response to it. There is also growing evidence which suggest that the equilibrium prices under perfect market conditions do not reward diversification. (Khan) It is therefore largely argued that the non-inclusion of diversification in the pricing of the assets effectively nullify the impacts which diversification can have on the risk profile of the asset. International Securities and Portfolio Optimization It is believed that international diversification reduces the risk of holding the international securities therefore it is very important that in order to build an optimal portfolio, international securities may be considered as a viable option to take on. As the crux of the modern portfolio theory suggest that the market risk cannot be eliminated therefore what is required is the diversification of the individual securities. When the number of securities increase within the portfolio whether the international or local securities, the risk of the portfolio declines thus leaving the market risk only to be covered and since the international securities possess different dynamics than the local securities therefore there are some unique risks associated with investing in the international securities to bring in the optimal portfolio. Since portfolios having the international orientation have unique risks like foreign exchange risk therefore inclusion of the international securities in the optimal portfolio reduces that risk thus investors can achieve an optimal portfolio by investing into international securities. However it is also the fact that investing into international securities distorts the correlation between the individual securities of the portfolio thus making it somewhat challenging to build an optimal portfolio however it is believed that building up of optimal portfolio with the international securities can reduce the risk as compared to the local portfolio. The combination of local as well international securities will offset some of the unique risks associated with both of the portfolios. International diversification benefits induce investors to demand foreign securities. If addition of a foreign security to the portfolio risks reduction for a given level of return, or if it increases the expected return for a given level of risk, the security adds value to the portfolio. A security that adds value will be demanded, bidding up the price of the security, resulting in a lower cost of capital for the issuing firm. Conclusion Diversification is considered as key to the successful development of the optimal portfolios. In order to minimize the risk and maximize the returns, investors have found various combinations of assets with differing degrees of risk and return so that an optimal portfolio can be build up. While building the optimal portfolios with Risky assets, investors often find themselves at cross roads as to whether go for the international diversification or remain in the local markets. However studies suggest that international portfolios provide superior performance over the locally developed portfolios and in order to build an optimal portfolio investors may consider investing into international securities so that the unique risks associated with individual markets can be lessen to take advantage of the diversification. The earlier theories of Portfolio selection suggest that investors need to find out the optimal combinations of the based on expected returns, standard deviations and correlations of the assets and based on this criterion the investor chooses the optimal portfolio based on his risk and return profile. References Burton, Jonathan. "Revisiting The Capital Asset Pricing Model." May 1998. University of Stanford. 17 March 2008 . Khan, M.A.Ali. "The capital-asset-pricing model and arbitrage pricing." Economic Science (1997). Morien, Travis. "Modern Portfolio Theory Criticism." 17 March 2008 . Rubinstein, Mark. "Markowitzs "Portfolio Selection": A Fifty-Year Retrospective." The Journal of Finance 57.3 (2002): 1041-1045. Statman, Meir. "How Many Stocks Make a Diversified Portfolio?,." The Journal of Financial and Quantitative Analysis 22.3 (1987): 353-363. Read More