Portfolio Theory and Investment Analysis - Term Paper Example

Portfolio Theory and Investment Analysis The objective of the trustee is to give advice on investment strategy and management given that the investment portfolio has the following characteristics: (1) 40% of the funds invested are in one large UK company; (2) 10% each are in the stocks of six other large companies; (3) Average monthly correlation between the stocks is 0.65; and, (4) Beta of the portfolio against the FTSE All-Share Index is 1.03. The charity uses the dividend income from this investment portfolio to provide funds for supporting its operations. Therefore, the objective of the investment strategy is to maximise the value of the investment as to give the highest possible annual return. More specifically, the trustees want to know the following: (1) The impacts of having a small number of stocks in the portfolio and concentrating the investment in large stocks. (2) The benefits of moving some of the investment to international securities. (3) How derivatives may be used to enhance returns and manage risk. Does Size Matter The answer to the first concern depends on the answer to the following basic question in the minds of the charity's trustees: what is the highest possible and most realistic annual return that the investment portfolio could earn It is not easy to predict the return of a portfolio because many things could happen to funds once these are invested. To find out the realistic historical returns for various investments, investors consult the Equity and Gilt Study of Barclays (2006), which has studied this for over half a century. Figures 1 (68) and 2 (69) show how equities performed better compared to gilts and T-bills over the last century since a 100 investment in equities at end-1899 was worth 1,340,324 by end-2005. The same investment in gilts was worth 20,159 and in T-bills 17,021. When adjusted for inflation, the investment in equities would be worth 22,426; gilts 337; and T-bills 284 (Barclays, 2006, p. 62-63). This proves that the strategy of investing in equities would give the highest and most realistic return. In the year 2005, for example, equities returned 18.8% for the year, much higher than gilts (6%) and T-bills (2.7%), all figures having been adjusted for inflation. The Barclays Equity Income Index is derived from the yield of the FTSE All-Share Index because in their view, this is "the most representative method of evaluating equity performance over the period" (Barclays, 2006, p. 59). Given these pieces of information, what would be the best return that the UK charity could expect from its investments The attractiveness of any investment, whether bonds, securities, real estate, or a corner street business, depends on two variables: (1) Expected return: how much the investment would earn over a period of time; and, (2) Risk: the uncertainty that the investment would earn the expected return. One finance model used to assess an investment's attractiveness based on these two factors is the Capital Asset Pricing Model or CAPM,1 which equates expected return with the market return, the risk free rate, and the relative behaviour - defined as beta () - of the price of a security relative to the behaviour of the market. The basic criterion of CAPM is straightforward: an investment is attractive if its risk premium (the additional return over the risk-free rate) is equal to or higher than the risk of the market. Given the charity's investment portfolio = 1.03, the investment gave a return that was 3% higher than the All-Share Index return. If the All-Share Index had an 18.8% return, meaning a 1 million investment was worth 1,018,800 by year-end, the charity's investment would earn an extra 3% and would be worth 1,019,364 instead. The , however, has a downside: if the All-Share Index dropped, the value of the charity's investments would drop by an additional 3%. Why this happens is explained by risk, which affects the return of any investment. Every investment is exposed to two types of risk: the risk affected by the factors to which the business is exposed, and the risk to which the whole stock market is exposed. The first risk, called security risk, becomes realised when the company CEO has an accident or the industry competition intensifies. The second risk, called market risk, is the probability the economy enters into a recession, which would bring down the prices of most stocks in the market. Security risk is specific to each company and could be balanced through portfolio diversification (Markowitz, 1952), a strategy based on the observation that stock prices move differently in relation to the general movement of the stock market. Therefore, investors could reduce the unpredictability of returns (or risk) by investing in a mixture or portfolio of stocks whose prices do not move exactly in the same way. When stock market prices are rising, some stock prices rise with it whilst some go the opposite way, and not at the same rates. This aspect of stock price behaviour is measured by the correlation coefficient, which in turn depends on the standard deviation, a measure of how far a stock price moves from its average or mean value. As an example, a stock whose price moves from 2 to 10 promises a higher return (400%) than a stock whose price goes from 4 to 8 (giving a return of 100%), even if both have an average price of 6. The higher the standard deviation ( 4 vs. 22), the higher would be the return (400% vs. 100%) Based on this insight, investors who want a higher expected return can invest their funds in a mixture of stocks with different values of returns, correlation coefficients, and standard deviations. By mixing stocks, the investor could get a higher average return for a lower average correlation. This practice of mixing stocks is called Portfolio Investment Theory. With correlation as a measure of risk, Markowitz (1952) concluded that diversification - or owning more than one stock - brings down the risk of a portfolio of stocks whilst earning relatively higher expected returns. Another important insight is that the expected return of a security eventually depends only on the price volatility of the stock, or its price fluctuations relative to the market, which is measured using historical data and captured by the variable defined as (Sharpe, 1964; Lintner, 1965). What this insight shows is that the two types of risk already mentioned - market and security risks that are characteristic of all stocks in a diversified portfolio - could be managed. If the and correlation coefficient are known, it is possible for investors to predict the return of a portfolio of stocks. The two sides of the CAPM equation reflect two aspects of risk, a non-diversifiable market risk and a diversifiable security risk that could be minimised by holding a portfolio of securities. Beta measures risk and provides the investor with a method to assess whether the investment conforms to his/her ability to manage risk; a > 1 indicates the investment is riskier than the market as defined by the behaviour of the All-Share Index. In the case of the UK charity's portfolio where = 1.03 and the average monthly correlation = 0.65, what could be the effect of having only a few stocks versus having many stocks Based on the insights of Markowitz, Sharpe, and Lintner, the effect would depend only on the . Each stock behaves differently vis--vis the market and each other. Would it be possible to earn a higher return Yes, but only if the charity is willing to increase its from 1.03 to, say 1.30, and also willing to decrease the correlation to a value between 0 and -1. Would it matter if the charity invests in big companies and limits its investments to a small number of stocks of large companies It would depend on the of each stock (the correlation is already part of the calculation of ) and the share of the fund invested in each stock, but investing in big companies is less risky because their is closer to 1. The reason is that because of their size and the number of years they have been in the market, their stock price behaviour is close to that of the market, unlike that of smaller companies which still have a long way to go in terms of experience in managing risk, which in turn is reflected in the stock price. How many stocks should be included Previous studies (Statman, 1987) showed that investing in too many stocks would not be worth it, and that the best results from diversification come from the first few stocks. The stock where the trustee puts in the highest share of its investment funds should be the stock with a that comes closest to the amount of risk that the charity is willing to carry. A conservative portfolio is where the total weighted average = 1 or as close as possible to it. Would International Investments Help Another possibility open to the charity is to invest part of its portfolio in stocks overseas. This is another strategy to diversify the portfolio by investing in the stock market of other countries. The advantage of this strategy is that the economies, and therefore the stock markets, of these countries behave differently from the UK economy. In fact, their correlations with the FTSE 100 index are less than 1, which means that they gain and lose less - or bring down the risk and also the expected returns - of a UK stock portfolio. Investing in these overseas markets also allow the fund to take advantage of opportunities that may not be available locally in the UK, such as higher profits from higher sales. Investing overseas also provides the charity with additional protection so that it does not suffer huge losses if the UK markets go down, which could happen for any of several reasons: a terrorist attack in London, a financial scandal linked to the sub-prime mortgage mess in the US, or if Prime Minister Gordon Brown loses popularity and his replacement, whoever s/he may be, fails to manage the economy. Placing an investment portfolio in several stocks in one country may be as risky as placing them in only one stock. Diversification gives benefits of increasing expected returns because it lowers the level of risk. By taking advantage of unique market characteristics in other countries, investors can enhance their returns. All these would depend, of course, on the of the stocks the investor chooses. Just putting the funds in an emerging, or even in a stable, market would not be enough. The task of the investor, with the help of the portfolio manager, is to select the right stock that meets the charity's criteria for balancing risk and return. If it decides to maintain a portfolio that is close to 1, then it should look for the stock or stocks that have values of close to 1 or the market return. Given different stock markets with different values of correlation with the FTSE 100 Index, which stock market would give the best return If the investor wants to follow the principles of diversification already discussed earlier, a country with the lowest correlation with and higher returns than the FTSE 100 should be selected. Based on the MSCI website (MSCI, 2007), the three regions that best fit these criteria are the Pacific ex Japan (+24.92%), Nordic countries (+15.98%), and Eurozone (15.38%). Investing in these regions would help reduce risk and enhance returns. How Derivatives Can Help Returns, or the earnings from a portfolio investment, can go up or become higher by maximising the difference between the price at which the stock was bought and the price at which it was bought. Since the stock price reflects the expected profits to be earned by the corporation which the stock represents, choosing a profitable company, or one that has the highest potential to be profitable, would be the most important decision a portfolio manager can make. Most companies share these profits by giving dividends, so these could be added to the earnings from a stock investment that would increase total returns to shareholders. Ideally, the earnings from an investment would be the sum of the capital gains (difference between buying and selling price) and the dividends. In real life, however, it is possible to enhance the earnings from stock investments by using financial innovations called derivatives, which would allow an investor to buy stocks at a lower price and sell them at a higher price, even if one does not own the stock (Eiteman, Stonehill and Moffett, 2004)! Derivatives are financial instruments that allow investors to trade stocks without the benefit of ownership (i.e., no dividends) by capitalising on the differences in stock prices. In fact, derivatives called options allow investors to trade not only on the basis of stock prices but also on the basis of the exchange index (like the FTSE 100), futures contracts, or even real estate. Options are linked to a stock and have a strike price (an expected price for the stock at which the option would be bought or sold), an expiration date (on which the option to buy or sell could be exercised), and a premium (the price paid for the option, which would always be much lower than the price of the stock). Options are of two types: Calls and Puts. A call option gives the owner the right, but not the obligation, to buy a stock at the strike price before the expiration date, after which the call option is worthless. A put option gives the owner the right (but not the obligation) to sell a stock at the strike price anytime before the option expires. Call and put options allow non-owners of the stock to earn from "guessing" the price behaviour of stocks. An investor who thinks the price would go up can buy a call option with a strike price lower than the expected price, earning a profit from the price difference. If the stock price does not go up, the option is worthless because the buyer of the call option would buy the stock at a lower price from the market, but the seller of the option earns from the premium. If the seller of the option does not own the stock, and the stock price goes up, then the seller could lose money if the price differential is lower than the premium (which is often the case). This is called a naked position, because the option seller could "lose" everything. However, if the seller owned stocks, a situation described as a covered call, it would sell the stocks at the strike price, earning the premium plus the difference between the buying and the strike price. A put option gives the buyer of the option the right to sell a stock at the strike price anytime before the option expires, whilst the seller of the put option has the obligation to buy shares at the strike price if the buyer of the put option decides to sell (or assign) the shares to the buyer. A put is "in the money" if the strike price is above the market price, and "out of the money" if the strike price is below the market price. Put option sellers can acquire a protective put position by selling (or shorting) the stocks at a price equal to the strike price so that it could earn the premium paid by the buyer of the put option. Otherwise, if the stock price collapses, it has to buy the stocks at the strike price and suffer the loss from the difference in market price. Bibliography Barclays. Equity Gilt Study 2006. London: Barclays, 2006. Eiteman, D.K., Stonehill, A.I., and Moffett, M.H. Multinational Business Finance, 10th ed. New York: Addison-Wesley, 2004. Lintner, J. "The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets." Review of Economics and Statistics 47 (1965): 13-37. Markowitz, H. "Portfolio Selection." Journal of Finance 7 (1952): 77-91. MSCI Barra. MSCI Barra Global Investable Market Indices as of 17 December 2007. Accessed 17 December 2007, from: http://www.mscibarra.com/products/indices/stdindex/performance.html Sharpe, W. "Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk." Journal of Finance 19 (1964): 425-442. Statman, M. "How Many Stocks Make a Diversified Portfolio" Journal of Financial and Quantitative Analysis, 22 (1987): 353-364. Figure 1: (Source: Barclays, 2006, p. 64) Figure 2: (Source: Barclays, 2006, p. 64) Read More