Why All Assets Must Lie on or below the Capital Market Line - Essay Example

Capital Asset Pricing Model Question (a Explain why, in equilibrium, all assets must lie on or below the capital market line, but must lie on the security market line. We can answer this question with a brief explanation of what we understand by the terms equilibrium, the capital market line, and the security market line. Equilibrium as a concept in economics means a state where supply equals demand. Economists predict that prices of goods, just like water seeking its own level, adjust based on supply and demand conditions until equilibrium is reached. This applies to petrol, soccer game tickets, iPods, and the stocks of companies. Financial economists who study the world of stock investments define equilibrium similarly, as a condition where demand equals supply. Prior to reaching this state, stock prices go through a series of adjustments depending on the buy-hold-sell decisions of thousands of investors until equilibrium is reached. In real life, equilibrium is a constantly moving target. We cannot say that the stock market is in equilibrium at the end of the day or week or year. Prices move based on the perception of brokers and shareholders, driven by information (Fama, 1970), psychology (Kahneman and Tversky, 1982), or anything under the sun (Barberis, Shleifer, and Vishny, 1998). As investors try to maximise returns or minimise losses, they either push up or pull down stock prices, or keep it level, the differences between the demand of buyers and the supply of sellers being reflected in stock price changes. This is equilibrium, which is not a static point but more of a dynamic process where adjustments constantly take place, reflecting the free agreement of investors in the market that stocks are bought and sold at the right price. Of course, one side thinks the price will go up, while the other side thinks it will go down. By ‘assuming’ equilibrium as an ideal state towards which everything moves, finance academics have discovered a tool that allows them to pin down a moving target – the behaviour of stock prices over the last fifty years, for example – so they can study it, test their theories, develop a mathematical model, and see if the model explains reality. One such aspect of reality that is being studied for the last half a century is the relationship between the return of a stock price and the risk that the return will not be realised. Several years of observations have made academics ask: how should investors decide which stocks to buy? This is what Markowitz did in his paper (Markowitz, 1952), where he drew attention to the practice of portfolio diversification. After observing that stock prices move differently in relation to the general movement of the stock market, he showed that investors could reduce the unpredictability of returns 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 while some go the opposite way, and not at the same rates. Markowitz measured these stock price movements using a statistical tool called ‘standard deviation’, which indicates how far a stock price has moved from its average value. His first observation was that the higher the standard deviation, the higher the average, or expected, return. This looks like common sense, because a stock A whose price swings from £2 to £10 per share surely promises a higher return than a stock B whose price swings from £4 to £8 even if both have an “average” price of £6. Conversely, such large price swings also promise a bigger loss if the investor bought stock B at the wrong time. One of Markowitz’s insights is that every investor wants to get the highest expected return (r) for a given standard deviation (σ), so he suggested that investors put their money in what he called an efficient portfolio. Using historical stock prices, he determined that different stocks have different values of σ and r. Next, he computed what would happen if he mixed stocks and discovered that one could get a higher average r for a lower average σ from a portfolio. This is how the so-called Portfolio Investment Theory was born. With σ as a measure of risk, Markowitz concluded that diversification – owning more than one stock – brings down the risk of a portfolio of stocks while earning relatively higher expected returns. Using a graph, he calculated that the right mix of stocks in the portfolio that gives the best r for a given σ lies along what he called an “efficient frontier” above the σ-r (or risk-return) profiles of all the stocks in the market. Based on this finding, he ‘conceptually’ showed that while all assets (stocks) with their individual σ-r are below the efficient frontier, it is possible to assemble a portfolio of stocks at the same σ but whose r is higher, that is, with a σ-r along the security market line that lies on the efficient frontier. The Security Market Line (SML) plots the market risk versus return of the whole market at a certain time and shows all risky marketable securities. This is represented by the red curve in Figure 1. The SML at two different times 1-1 and 2-2 are also plotted, with the slope of the line adjusting as the market moves towards equilibrium. Thus, Markowitz showed that investors could get the highest rate of return at lower rates of risk by diversifying, investing in a portfolio whose characteristics lie on the efficient frontier marked by the SML. But is this it? Will diversifying funds by investing only in stocks give the investor higher returns? No, because there is another way of getting higher investment returns: combine investments in an efficient portfolio and borrowing and lending money at the risk-free rate, a scheme proposed by Tobin (1958). By mixing an investment in the most efficient stock portfolio – marked by point EP in Figure 1 that gives the highest expected risk premium, or the highest difference between the return r and the risk-free rate of capital, rf, which is the Treasury bill rate, per unit of standard deviation – you can earn anywhere between the risk-free rate up to EP if you lend your money by buying Treasuries, or earn a rate of EP or more if you borrow money at the risk-free rate and lend at a higher rate. The range of possible returns is along the so-called Capital Market Line (CML), a 45-degree line that starts from the risk-free rate rf where the risk is zero because it ‘assumes’ that the U.K. or U.S. governments will never default. This is the reason why many investment funds diversify by investing in stocks and government treasuries or bonds. The CML represented by the yellow line in Figure 1 will intersect the capital market line at the point EP in the curve where the standard deviation is the same as that of the capital markets and where the market risk is therefore equal to 1. This is the so-called equilibrium point where funds are lent or borrowed at the risk-free rate and partly invested in the stock market portfolio whose σ-r (risk-return) profile matches that of the market. To know why, we have to explain the concept of systematic or market risk that is represented by the symbol, β, or beta. The first to gain an insight into the effect of market risk or beta on portfolio returns were Sharpe (1964) and Lintner (1965). Both made the observation that stocks are exposed to two kinds of risk: systematic or market risk and unsystematic risk. The first risk affects the market as a whole and cannot be diversified away; the second risk affects the company whose stocks are traded in the market and can be diversified, that is, lessened by investing in a portfolio of stocks. Therefore, the expected return of a stock is dependent only on beta, which becomes the sole determinant of the expected risk premium, or the excess return over and above the risk-free rate. This is represented by the equation: r-rf = β (rm-rf) where r-rf is the stock’s risk premium and rm-rf is the market’s risk premium. The insight from this equation explains why in equilibrium, all assets must lie on or below the capital market line, but must lie on the security market line. Since beta is the only determinant of return, the most efficient portfolio given the ideal condition of equilibrium must lie on the point when the slope of the CML and SML coincide, because this is where returns are in direct proportion to beta, and is the point where these two lines intersect the efficient frontier, which is at point EP as shown in Figure 1. The model derived by Sharpe and Lintner is called the Capital Asset Pricing Model (CAPM). Question (b): To what extent does recent empirical evidence suggest that beta is dead. News of the death of beta was first asked by Wallace (1980), brought about by the observation that stock returns in the 1970s did not rise in proportion to the rise in beta. While risks were rising at a faster rate, returns were not, so critics of CAPM like Fama (1998; with French, 1992) attributed returns not only to beta but also to market capitalisation and the book-to-market value. Behavioural finance proponents like Shiller (2000) attributed actualised returns to other factors like irrational market psychology and calendar anomalies. Both sets of critics added to the “beta is dead” chorus. While Fama and French (1992) concluded from empirical studies that there is a flat relationship between market beta and average return even when beta is the only explanatory variable, studies by Chan and Lakonishok (1993) and Grinold (1993) accepted that there is inconclusive evidence that the relationship between beta and returns may actually hold as suggested by CAPM. The debate between the different groups continue as to the usefulness of beta as a factor that can predict expected returns, even though the relationship between these two variables is not as strong as it was thought to be. This, however, does not prevent analysts from continuing to use beta to construct their investment portfolios, perhaps taking a lesson from Black (1993), who proposed that beta is a valuable investment tool if the line is as steep as the CAPM predicts, but that it is even more valuable if the line is flat. What this means is that investment analysts have in beta a tool that they can use to study the past behaviour of a stock with respect to the market. Whether the analyst believes or not that past information is useful in predicting future stock price, since this information somehow forms part of the analyst’s deposit of knowledge that he or she can use to make an investment recommendation, it becomes useful. Several other academics like Clare, Priestley, and Thomas (1997) and Hsia, Fuller, and Chen (2000) proposed other alternatives to beta like alternative estimation models and multifactor empirical approaches. Given the evidences presented by all these authors, one thing is clear: beta as an exact predictor of future prices may seem to be dead because historical stock price behaviour may not be the best way to predict future prices, and because several other factors aside from beta determine the value of expected returns. However, beta is still alive in the sense that stocks with higher beta continue to give higher returns compared to stocks with lower beta. As we already saw above, this conclusion may be due mainly to the way hindsight becomes part of the formula, since beta is calculated from actual or historical returns, rather than being an accurate gauge of how the stock price will behave in the future. In the meantime, the debate goes on, and this can only be good for investors and the analysts and academics studying the market. Beta may not explain everything, but the CAPM – elegant, persuasive, and valuable – contains simple insights and relationships that have yielded a wealth of understanding and practical solutions that continue to help us understand better our real world. Like the elementary physics models of Newton paving the way for the quantum models of Einstein, CAPM has to be given the chance to evolve in ways that will lead to greater economic understanding, practical financial solutions, and better models of asset pricing. Beta is still useful, so let us not kill it yet. Works Cited Barberis, Nicholas, Andrei Shleifer, and Robert Vishny. “A Model of Investor Sentiment.” Journal of Financial Economics 49 (1998): 307-343. Black, Fischer. “Beta and Return.” Journal of Portfolio Management 20 (Fall 1993): 8-18. Chan, Louis and Josef Lakonishok. “Are the Reports of Betas Death Premature?” Journal of Portfolio Management 19.4 (Summer 1993): 51-62. Clare, Andrew, Richard Priestley, and Stephen Thomas. “Is Beta Dead? The Role of Alternative Estimation Methods.” Applied Economics Letters 4.9 (1997): 559-562. Fama, Eugene. “Market efficiency, long-term returns, and behavioural finance.” Journal of Financial Economics 49 (1998): 283-306. Fama, Eugene and Kenneth French. “The Cross-section of Expected Stock Returns.” Journal of Finance 47 (1992): 427-465. Fama, Eugene. “Efficient Capital Markets: A Review of Theory and Empirical Work.” Journal of Finance 25 (1970): 383-417. Grinold, Richard. “Is Beta Dead Again?” Financial Analyst Journal 49.4 (July/August 1993): 28-34. Hsia, Chi-Cheng, Beverly Fuller, and Brian Y. J. Chen. “Is Beta Dead or Alive?” Journal of Business Finance and Accounting 27.3 (2000): 283-311. Kahneman, Daniel and Amos Tversky. Intuitive Predictions: Biases and Corrective Procedures. Cambridge: Cambridge University Press, 1982. Lintner, John. “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, Harry. “Portfolio Selection.” Journal of Finance 7 (1952): 77-91. Sharpe, William. “Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk.” Journal of Finance 19 (1964): 425-442. Shiller, Robert. Irrational Exuberance. Princeton, NJ: Princeton University Press, 2000. Tobin, James. “Liquidity Preference as Behavior toward Risk.” Review of Economic Studies 25 (1958): 65-86. Wallace, Anise. “Is beta dead?” Institutional Investor 14 (1980): 22-30. Figure 1. Capital Market Line Where: EP is the Efficient Market Portfolio Rf is the Risk-free Rate 1-1 and 2-2 are Security Market Lines at Time 1-1 and Time 2-2 Read More