Investment Appraisal and Portfolio - Assignment Example

Part I: Portfolio Theory Given that the four projects available for Top Choice Investments to choose from are all indivisible, then the £2,000,000-fund can be invested in the following portfolios: Portfolio Initial Costs of Projects Total   A B C D Cost           1 1,200,000 800,000     2,000,000           2   800,000 1,200,000   2,000,000           3   800,000   1,200,000 2,000,000 The minimum return rate of 25% required by the investors will have to be satisfied. The return rates of the three portfolios are computed as follows: Port- First Project Second Project Total Expected Return folio Investment Expected Return Investment Expected Return on £2M-investment     Rate (in %) Amt (in £)   Rate (in %) Amt (in £) Rate (in %) Amt (in £)                   1 800,000 28% 224,000 1,200,000 22% 264,000 24.40% 488,000                   2 800,000 28% 224,000 1,200,000 30% 360,000 29.20% 584,000                   3 800,000 28% 224,000 1,200,000 34% 408,000 31.60% 632,000 Based on the foregoing computations, there are only two alternative combinations for the £2M-investment: namely, Portfolio 2 (Projects B & C) and Portfolio 3 (Projects B & D). Portfolio 1 (Projects A & B) does not meet the required minimum rate of return. In terms of return on investment, Portfolio 3 would be the better choice; it is expected to deliver a 31.60%-return rate, while Portfolio 2 is expected to deliver 29.20%. Meanwhile, the following computations serve to arrive at the risk rates (standard deviation) of the portfolios: Port-folio Weights of Projects   w₁ w₂ σ₁ (%) σ₂ (%) Cor. Coeff. Cov ₁,₂ σ²port σport                   1 0.40 0.60 10.00 8.00 0.70 56.00 65.92 8.12 2 0.40 0.60 10.00 15.00 0.65 97.50 143.80 11.99                   3 0.40 0.60 10.00 17.00 0.30 51.00 144.52 12.02 Thus, the three alternative portfolios for the £2M-investment of Top Choice Investments are summarized as follows: Portfolio Expected Risk Covariance Correlation   Return (%) (%) (%) Coefficients           1 24.40 8.12 56.00 0.70 2 29.20 11.99 97.50 0.65           3 31.60 12.02 51.00 0.30 While it has already been established that Portfolio 2 gives the higher expected return rate, the risk involved would also have to be considered. Portfolio 3 has the higher standard deviation. This means that the projects that make up Portfolio 3 are riskier by nature, or that they involve more uncertainties as compared to those in Portfolio 2. This, however, is not to be counted as a disadvantage for Portfolio 3 since it has turned out that the investors are known to be high risk-takers. They do not mind taking in more risk in exchange for higher return. Based on these given facts, Portfolio 3 is the better choice to recommend to the Top Choice Investments group. As for the combination of the two projects making up Portfolio 2, it has a positive covariance figure. Computed at 97.50%, this means that the two projects generally tend to move in the same direction in terms of positive and negative developments. The factors that are favorable for one project in Portfolio 2 are equally beneficial for the other project. Accordingly, the factors that are detrimental to one project have high chances of also negatively affecting the other project in Portfolio 2. As a portfolio, this does not present a good combination, since bad indications for one would mean similarly bad things for the other. With a correlation coefficient computed at 0.65, Portfolio 2 would be expected to increase in value during the good days of both projects and to decrease in value during the bad days. With such positive correlation coefficient, Portfolio 2 would suffer badly during days when either project in it would be adversely affected by prevailing situations. Such a scenario occurs when two projects in a portfolio involve the same industry, like the real estate industry. Therefore, if a portfolio is composed of a project in a building and another in an apartment, it would mean big damages to the valuation of the portfolio if the real estate industry is confronted by a credit crisis, by looming high bank interest rates, and the like. Meanwhile, Portfolio 3 has the lower covariance at 51%, and the lower correlation coefficient at 0.30. Being also positive like that of Portfolio 2, it also means that Portfolio 3 is not as diversified as would have been desired. However, its lower covariance figure denotes that compared to Portfolio 2, it has a better position in terms of resistance to erratic market trends. Similarly, the lower correlation coefficient of Portfolio 3 means that the two projects that compose it are not expected to be closely identical in terms of generation of revenues and returns. Between Portfolios 2 and 3, then, Portfolio 3 would again present the better combination of projects. Part II: Modern Portfolio Theory Modern Portfolio Theory is a combination of theories that provides a framework for analyzing investment decisions. It features theories that were developed to value risky assets, such as those of Markowitz, Sharpe and Ross. These theories all set out to measure risk in relation to projected returns on portfolios that are composed of different securities. They similarly recommend risk reduction through portfolio diversification. The mean-variance efficient frontier is a crucial tool in asset allocation that was introduced by the Nobel Prize winning Harry Markowitz of the University of Chicago in 1951. The optimization process has, thus, been simplified through such tool, which is illustrated by a graph that portrays the set of portfolios that maximizes the expected return for each level of risk or portfolio standard deviation. By means of it, the individual risks of asset components can be measured and the overall risks of portfolios can then be managed. As a rule, all portfolios that lie on the minimum-variance frontier represent the best risk-return combinations (Bodie, Kane & Marcus, 2009). Not one of them is better than the rest; it is simply a question of the investor’s attitude towards risk and his utility function. The latter determines the specific level of risk that the investor is willing for the equivalent level of return. The efficient frontier theory argues that portfolios made up of just one asset are generally inefficient – the better performing portfolios would always turn out to be the ones that are efficiently diversified – except when no other asset or portfolio of assets can deliver a higher expected return with equal or lower risk, or a lower risk with equal or higher return. Based on the Markowitz portfolio theory, the existence of the risk-free asset has been assumed. A risk-free asset is one with zero variance. The expected rate of return on it is always produced or delivered, so the risk or the standard deviation on the returns thereof is always equal to zero. Even the covariance and the correlation coefficient of portfolios that include a risk-free asset would then be computed as zero. (p. 280) Based on Markowitz’s portfolio theory, two major theories were proposed as models for valuing risky assets: namely, the Capital Asset Pricing Model (CAPM) and the Arbitrage Pricing Theory (APT). CAPM is the model that specifies what should be the expected or the required rate of returns on a risky asset, based on the risks it is exposed to (Reilly & Brown, 1997, p. 287). It is seen to continue to be a reliable model for pricing capital assets. Thus, it is useful in finding out whether assets at their given market prices are overpriced, underpriced or priced just right. Tests have shown that CAPM is helpful in learning more about the manners and ways by which the investment world moves and makes decisions. There are prevailing arguments against it, though, due to its underlying assumption that investors have quadratic utility functions and that the market prices of securities can reasonably be projected. In the real world, the market prices of securities follow no pattern or trend that can ever be successfully pre-determined. In the light of these arguments, Stephen Ross came up with the Arbitrage Pricing Theory (APT). APT is based on the assumptions that “capital markets are perfectly competitive,” and that investors will always choose to earn more than to earn less from their investments. APT cites many factors that affect the returns generated from a portfolio – such as GNP, political situation, or any others. In this respect, APT is unlike CAPM, which holds that the computed beta coefficient of an asset is the only influencing factor. (Reilly & Brown, 1997, p. 298) APT is far simpler than CAPM because it completely does away with most of the assumptions that go with CAPM, such as the utility function applicability, the proportional and formulated returns generated by the assets in a portfolio, the accuracy of the mean-variance efficiency frontier and the risks that all of the assets in the portfolio are supposed to inherently represent. While CAPM uses just a single factor – that is, beta – to compare the performance of a portfolio with that of the entire market, a three-factor model developed by Eugene Fama and Kenneth French names two additional tools, namely the size effect and book-to-market effect, to more efficiently measure market returns and value stocks (Reilly & Brown, 1997, p. 224). The size of a specific asset is noted to have an effect on the rate of return thereon. Asset sizes are measured in terms of their total market values. Then the ratio of the book value of a company’s share of stock to its market value (BV/MV) is also concluded by Fama and French to significantly have a positive relationship with future returns generated by such stock (p. 226). For all the theories formulated and models structured to attempt to explain the movement of market prices, there is no consistently accurate formula for it. Similarly, no rational observation would constantly apply to the way investors’ behave in the course of the daily activities in the financial markets. Thus, behavioral finance holds that investors are by nature irrational and that such irrationality influences the daily movements of the market prices. This theory differs from the psychologist’s view of the investors’ behavior. References Brigham, E. & Houston, J. (1998). Fundamentals of Financial Management. New York: The Dryden Press. Reilly, F. & Brown, K. (1997). Investment Analysis and Portfolio Management. New York: The Dryden Press. Bodie, Kane & Marcus. (2009). Investments 8th Edition. London: The McGraw-Hill Companies, Inc. Read More