Thursday, April 12, 2012

Modern Portfolio Theory & CAPM.

Conventional wisdom amongst investors recommends maintaining a diversified portfolio. The reasoning behind this, however, is not so common knowledge. One theory put forth by Harry Markowitz, Modern Portfolio Theory, asserts that asset returns represent normally-distributed random variables, each with their own variances, and quantifiable risk being represented by standard deviation (Markowitz, 1999). While variants of Modern Portfolio Theory are still in use in the financial industry, and its main theorists had won the Nobel Prize for its creation, it has recently been the subject of increased criticism, citing its dependence on rational investor behaviour and market efficiency (The Economist, 2009). Building on Markowitz’s earlier work on Portfolio Theory,William Sharpe (1964) proposed the Capital Asset Pricing Model (CAPM) for pricing risky securities. Sharpe says an investor might think of the CAPM this way. "First, I would say to you, ‘what do you think you should pay to get a dollar in bad times? Should you pay more than to get a dollar in good times?' And you would probably say, ‘Yes, I think so.' If you said, ‘No,' I'd say, ‘Well there aren't as many dollars available in bad times so don't you think the price of scarcer goods should be higher than more plentiful goods?' And hopefully you'd see that this makes sense. So I'd try to convince you that, all things being equal, the price of a dollar in bad times should be higher so, therefore, the return on what you pay for it should be worse. You pay more to get the dollar so the return on your investment is going to be worse."Sharpe is also known for creating the Sharpe Ratio, which is a risk-adjusted measure of investment performance. This continues to be one of the most widely-used performance measures for investment managers. Sharpe originally called the Sharpe Ratio the Reward to Variability Ratio but other scholars insisted on naming the idea for its founder.
William Sharpe

Before Markowitz formalized his portfolio theory in 1952 (Markowitz, 1999), investors had already held the belief that diversification of portfolios could reduce risk while preserving an adequate level of returns. Portfolio theory assumes that investors are risk-averse; that is, given two securities with identical returns, investors will prefer the security with the lower risk (Markowitz, 1999). What Markowitz (1952) contributed, however, was a formalization to diversification. Prior to Portfolio Theory, informed investors understood that it was in their best interests to maintain a diverse set of securities in a given portfolio. Markowitz (1952) demonstrated that correlation between securities can be quantified and as long as securities are not perfectly positively correlated, their combination in a portfolio will result in reduced overall portfolio risk. His work put risk at the center of investing, and attempted to measure the appropriate amount of risk to undertake, as higher returns are dependent on greater risk, and the greater the risk, the greater the possibility of loss. Further, he explained that the variance of the overall portfolio is a function of the variances and covariances of the individual securities comprising the portfolio (Markowitz, 1999). His landmark 1952 paper showed how a subset of the possible portfolio compositions, the efficient frontier, represented the lowest level of risk for a given level of return.Markowitz showed how an investor’s portfolio choice can be reduced to balancing just two dimensions: the expected return on the portfolio, and its variance or standard deviation, depending on the circumstances.At the RAND Corporation, he researched optimization techniques, developing the critical line algorithm for the identifications of the optimal mean-variance portfolios. This was found to be lying on what was later named the Markowitz Frontier.A Markowitz Efficient Portfolio is one where no added diversification can lower the portfolio’s risk for a given return expectation, while the Markowitz Efficient Frontier is the set of all portfolios that will give the highest expected return for each given level of risk. These concepts of efficiency were essential to the development of the capital asset pricing model .Building on the quantified risk concept described by Markowitz (1952), Sharpe described a pricing theory for risky securities comprising two components: a risk-free rate of return equal to the return of a security with no default risk (such as a US Treasury bill) and systematic risk (“beta”) coefficient of risk responsiveness relative to market risk premium (Sharpe, 1964). The result of this relationship is encapsulated graphically in the Security Market Line.
Harry Markowitz

 While Markowitz (1999) pointed out that even Shakespeare included wisdom about portfolio diversification in The Merchant of Venice, it was not until Markowitz (1952) and Sharpe (1964) that widely accepted quantitative models of the relationships between risk, return, and asset pricing gained acceptance. Although Portfolio Theory and the Capital Asset Pricing Model are key theories in finance, contemporaries of Markowitz (1952) and Sharpe (1964) have identified a number of opportunities for these theories to be developed further. It is possible, for example, that returns may not be best represented by a normally-distributed random variable in all cases. There are also special groups in the population that behave contrariwise to the typical “rational investor” either for psychological or, in some cases, even religious reasons: Islam is the fastest-growing religion in the US (Dar & Presley, 1999). Islamic law forbids earning interest on debt but allows—even encourages—investors to earn a return for taking on risk in their investments (Chiu, Newberger, & Paulson, 2005). Consequently, there are legitimate explanations for rational investors to make decisions that under previous assumptions would be classified as nonrational. Very interesting Game theory is another revolutionary development of the 20 th Century that at one time was hoped to elucidate investor behaviour. Due to the complexities of large systems, particularly involving human behaviour, it too has proved to be somewhat underwhelming in terms of predictive ability. I have long believed that such studies of economics are excellent tools to identify themes and understand behaviours, but that human behaviour is too complex for these models to propose appropriate interventions. While blood levels of a certain nutrient may show a deficiency is causing a certain symptomology, supplementation of this nutrient may not have the desired effect because of complex interactions that were not readily apparent from observations. I believe this is so with economics and financial markets as well. Even if individual causal interactions could be identified from existing models, they might still not be applicable in situ
Thus, I believe that the concepts Markowitz (1952) and Sharpe (1964) put forth in their theories, such as quantification of risk and interactions of risky assets, are important for future research; yet, research must still be done to find parsimonious models with predictive power, as well as interventions that can be practically applied to real-world investment decisions.

Sharpe's View of the Future of Financial Economics
In his recent book, Investors and Markets, Sharpe called for a new approach to the teaching and practice of Finance. "It's time to move beyond the simplifying assumption that probability distributions of economic events are normal or log-normal and that people only need to consider the mean and the standard deviation of a distribution," he says.
"I think, increasingly, we need to go beyond that - and there's no reason that we can't. You can have distributions that are as complex as you like and you can have characterizations of people's preferences that are reasonably complex. So I think practitioners should go beyond simple paradigms and I have been calling for academics teaching in business schools to do so."

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