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

How does a rational investor build the optimal portfolio Should international securities be added to that Introduction The modern portfolio theory was introduced by Harry Markowitz with the publication of his paper "Portfolio Selection" in the Journal of Finance in 1959 and is called Markowitz portfolio theory (MPT). It is now the major guidance for portfolio allocation decisions for mutual funds, pension funds, and nearly any entity seeking to maximize investment portfolio returns and minimize risks. By exploring how risk-averse investors can construct optimal portfolios through consideration of the trade-off between market risk and expected returns, Markowitz presents the benefits of diversification. Out of a variety of risky investments, an investor can compile an effective portfolio of investments, each of which will offer the maximum possible expected return for a given level of risk. Investors are therefore supposed keep one of the optimal portfolios on the effective level and the rest to adjust to the market risk. The latter is reached through the leverage or de-leverage of that portfolio with positions in a risk-free investment such as government bonds. The following paper presents the utility of the MPT for contemporary decision making. The objective of the investor is discussed to find an effective allocation of assets and liabilities which implies investor's balance and efficiency of an investment. Rational investor thinking Active portfolio managers constantly buy and sell a great number of common stocks. Their job is to try to keep their clients satisfied, and that means consistently outperforming the market so that on any given day, if a client applies the obvious measuring stick-"How is my portfolio doing compared to the market overall"-the answer is positive and the client leaves her money in the fund. To keep on top, active managers try to predict what will happen with stocks in the coming six months and continually churn the portfolio, hoping to take advantage of their predictions. On average, today's common stock mutual funds own more than one hundred stocks and generate turnover ratios of 80 percent (Lewis, Mizen 2000). Index investing, on the other hand, is a buy-and-hold passive approach. It involves assembling, and then holding, a broadly diversified portfolio of common stocks deliberately designed to mimic the behavior of a specific benchmark index, such as the Standard & Poor's 500 Price Index (S&P 500). Compared to active management, index investing is somewhat new and far less common. Since the 1980s, when index funds fully came into their own as a legitimate alternative strategy, proponents of both approaches have waged combat to determine which one will ultimately yield the higher investment return. Active portfolio managers argue that, by virtue of their superior stock-picking skills, they can do better than any index. Index strategists, for their part, have recent history on their side. In a study that tracked results in a twenty-year period, from 1977 through 1997, the percentage of equity mutual funds that have been able to beat the S&P 500 dropped dramatically, from 50 percent in the early years to barely 25 percent in the last four years. Since 1997, the news is even worse. As of November 1998, 90 percent of actively managed funds were underperforming the market (averaging 14 percent lower than the S&P 500), which means that only 10 percent were doing better. Active portfolio management, as commonly practiced today, stands a very small chance of outperforming the S&P 500. Because they frenetically buy and sell hundreds of stocks each year, institutional money managers have, in a sense, become the market. Their basic theory is: Buy today whatever we predict can be sold soon at a profit, regardless of what it is. The fatal flaw in that logic is that, given the complex nature of the financial universe, predictions are impossible. Further complicating this shaky theoretical foundation is the effect of the inherent costs that go with this high level of activity -costs that diminish the net returns to investors. When we factor in these costs, it becomes apparent that the active money management business has created its own downfall. Indexing, because it does not trigger equivalent expenses, is better than actively managed portfolios in many respects. But even the best index fund, operating at its peak, will only net exactly the returns of the overall market. Index investors can do no worse than the market-and no better (Lewis, Mizen 2000). From the investor's point of view, the underlying attraction of both strategies is the same: minimize risk through diversification. By holding a large number of stocks representing many industries and many sectors of the market, investors hope to create a warm blanket of protection against the horrific loss that could occur if they had all their money in one arena that suffered some disaster. In a normal period (so the thinking goes), some stocks in a diversified fund will go down and others will go up, and let's keep our fingers crossed that the latter will compensate for the former. The chances get better, active managers believe, as the number of stocks in the portfolio grows; ten is better than one, and a hundred is better than ten. An index fund, by definition, affords this kind of diversification if the index it mirrors is also diversified, as they usually are. The traditional stock mutual fund, with upward of a hundred stocks constantly in motion, also offers diversification. We have all heard this mantra of diversification for so long, we have become intellectually numb to its inevitable consequence: mediocre results. Although it is true that active and index funds offer diversification, in general neither strategy will yield exceptional returns. These are the questions intelligent investors must ask themselves: Am I satisfied with average returns Can I do better The theory The MTP indicates to split the investments between a money-market fund and a broad-based, passively managed stock fund. That fund should concentrate on minimizing fees and transaction costs, period. It should avoid the temptation to actively manage its portfolio, trying to chase the latest hot stock or trying to foresee market movements. An index fund or other approximation to the market portfolio that passively holds a bit of every stock is ideal. The portfolio advice is not so remarkable for what it does say, which given the setup is fairly straightforward, as for what it does not say. Compared with common sense and much industry practice, it is radical advice (Elton et al., 2003). One might have thought that investors willing to take on a little more risk in exchange for the promise of better returns should weight their portfolios to riskier stocks, or to value, growth, small-cap, or other riskier fund styles. Conversely, one might have thought that investors who are willing to forego some return for more safety should weight their portfolios to safer stocks, or to blue-chip, income, or other safer fund styles. Certainly, some professional advice in deciding which style is suited for an investor's risk tolerance, if not a portfolio professionally tailored to each investor's circumstances, seems only sensible and prudent. The advertisements that promise "we build the portfolio that's right for you" cater to this natural and sensible-sounding idea. The two-fund theorem leaves open the possibility that the investor's horizon matters as well as his risk aversion. What could be more natural than the often repeated advice that a long-term investor can afford to ride out all the market's short-term volatility, while a short-term investor should avoid stocks because he may have to sell at the bottom rather than wait for the inevitable recovery after a price drop The fallacy lies in the "inevitable" recovery. If returns are close to independent over time (like a coin flip), and prices are close to a random walk, a price drop makes it no more likely that prices will rise more in the future. This view implies that stocks are not safer in the long run, and the stock/bond allocation should be independent of investment horizon. This proposition can be shown to be precisely true in several popular mathematical models of the portfolio decision. If returns are independent over time, then the mean and variance of continuously compounded returns rises in proportion to the horizon: The mean and variance of ten-year returns are ten times those of one-year returns, so the ratio of mean to variance is the same at all horizons. More elegantly, Merton (1969) and Samuelson (1969) show that an investor with a constant relative risk aversion utility who can continually rebalance his portfolio between stocks and bonds will always choose the same stock/ bond proportion regardless of investment horizon, when returns are independent over time. Hedging demands Market-timing addresses whether you should change your allocation to stocks over time as a return signal rises or falls. Hedging demands address whether your overall allocation to stocks, or to specific portfolios, should be higher or lower as a result of return predictability, in order to protect you against reinvestment risk. A long-term bond is the simplest example. Suppose you want to minimize the risk of your portfolio ten years out. If you invest in apparently safe short-term risk-free assets like Treasury bills or a money-market fund, your ten-year return is in fact quite risky, since interest rates can fluctuate. You should hold a ten-year (real, discount) bond. Its price will fluctuate a lot as interest rates go up and down, but its value in ten years never changes. Another way of looking at this situation is that, if interest rates decline, the price of the ten-year bond will skyrocket; it will skyrocket just enough so that, reinvested at the new lower rates, it provides the same ten-year return as it would have if interest rates had not changed. Changes in the ten-year bond value hedge the reinvestment risk of short-term bonds. If lots of investors want to secure the ten-year value of their portfolios, this will raise demand for ten-year bonds and lower their prices (Jones, 2002). In general, the size and sign of a hedging demand depend on risk aversion and horizon and, thus, will be different for different investors. If the investor is quite risk averse - infinitely so in my bond example - he wants to buy assets whose prices go up when expected returns decline. But an investor who is not so risk averse might want to buy assets whose prices go up when expected returns rise. If the investor is sitting around waiting for a good time to invest, and is willing to pounce on good (high expected return) investments, he would prefer to have a lot of money to invest when the good opportunity comes around. It turns out that the dividing line in the standard (CRRA) model is logarithmic utility or a risk aversion coefficient of 1 - investors more risk averse than this want assets whose prices go up when expected returns decline, and vice versa. Most investors are undoubtedly more risk averse than this, but not necessarily all investors. Horizon matters as well. A short horizon investor cares nothing about reinvestment risk and, therefore, has zero hedging demand. In addition, the relationship between price and expected returns is not so simple for stocks as for bonds and must be estimated statistically. The predictability evidence reviewed above suggests that high stock returns presage lower subsequent returns. High returns drive up price/dividend, price/earnings, and market/book ratios, all of which have been strong signals of lower subsequent returns. Therefore, stocks are a good hedge against their own reinvestment risk - they act like the long-term assets that they are. This consideration raises the attractiveness of stocks for typical (risk aversion greater than 1) investors. Precisely, if the two-fund analysis of figure 1 suggests a certain split between stocks and short-term bonds for a given level of risk aversion and investment horizon, then return predictability, a long horizon, and typical risk aversion greater than 1 will result in a higher fraction devoted to stocks. Again, exactly how much more one should put into stocks in view of this consideration is a tough question. (Jones, 2002). Campbell and Vicera's (1999) calculations address this hedging demand as well as market-timing demand, and figure 5 also illustrates the strength of the hedging demand for stocks. Campbell and Vicera's investors want to hold almost 30 percent of their wealth in stocks even if the expected return of stocks is no greater than that of bonds. Absent the hedging motive, of course, the optimal allocation to stocks would be zero with no expected return premium. Almost a 2 percent negative stock return premium is necessary to dissuade Campbell and Vicera's investors from holding stocks. At the average (roughly 6 percent) expected return, of the roughly 130 percent of wealth that the risk aversion 4 investors want to allocate to stocks, nearly half is due to hedging demand. Thus, hedging demands can importantly change the allocation to stocks. However, hedging demand works in opposition to the usual effects of risk aversion. Usually, less risk averse people want to hold more stocks. However, less risk averse people have lower or even negative hedging demands, as explained above. It is possible that hedging demand exactly offsets risk aversion; everybody holds the same mean allocation to stocks. This turns out not to be the case for Campbell and Vicera's numerical calibration; less risk averse people still allocate more to stocks on average, but the effect depends on the precise specification. Bibliography: 1. Elton, E.J, Gruber, M.J, Brown, S.J and W.N. Goetzmann, Modern Portfolio Theory adn Investment Analysis 6e, Wiley, 2003 2. Lewis MK and Mizen PD, Monetary Economics, Oxford University, 2000. Chapter 6 Pilbeam, K 1998. International Finance, london: Macmillan, Chapters 7-8 3. Jones, C.P., Investments- Analysis and Management 8e, Wiley, 2002. Ch. 19-20 Howells & Bain, The Economics of Money, Banking and Finance: An European Text. Longman. Chapter 2 4. Bodie, Z., Kane, A. and A. Marcus, Essentials of Investents 6e, McGraw-Hill, 2005. Chapter 9 5. Campbell, John Y. and Luis M. Vicera, 1999, "Consumption and portfolio decisions when expected returns are time varying," Quarterly Journal of Economics, forthcoming. 6. Merton Robert C., 1969, "Lifetime portfolio selection under uncertainty: The continuous time case," Review of Economics and Statistics, Vol. 51, No. 3, August, pp. 247-257. 7. Samuelson, Paul A., 1969, "Lifetime portfolio selection by dynamic stochastic programming," Review of Economics and Statistics, Vol. 51, No. 3, August, pp. 239-246. Read More