MODERN PORTFOLIO THEORY ASSUMPTIONS - The frame work of MPT makes many assumptions about investors and markets. Some are explicit in the equations, such as the use of Normal distributions to model returns. Others are implicit, such as the neglect of taxes and transaction fees. None of these assumptions are entirely true, and each of them compromises MPT to some degree.! Investors are interested in the optimization problem described above (maximizing the mean for a given variance). In reality, investors have utility functions that may be sensitive to higher moments of the distribution of the returns. For the investors to use the mean-variance optimization, one must suppose that the combination of utility and returns make the optimization of utility problem similar to the mean-variance optimization problem. A quadratic utility without any assumption about returns is sufficient. Another assumption is to use exponential utility and normal distribution, as discussed below.! Asset returns are (jointly) normally distributed random variables. In fact, it is frequently observed that returns in equity and other markets are not normally distributed. Large swings occur in the market far more frequently than the normal distribution assumption would predict. While the model can also be justified by assuming any return distribution that is jointly elliptical, all the joint elliptical distributions are symmetrical whereas asset returns empirically are not. Empirically reject the elliptical hypothesis, writing intuitively, the failure of elliptical models can be traced to the inadequacy of the assumption of a single volatility mode for all stocks. Correlations between assets are fixed and constant forever. Correlations depend on systemic relationships between the underlying assets, and change when these relationships change. include one country declaring war on another, or a general market crash. During times of financial crisis all assets tend to become positively correlated, because they all move (down) together. In other words, MPT breaks down precisely when investors are most in need of protection from risk.! All investors aim to maximize economic utility (in other words, to make as much money as possible, regardless of any other considerations). This is a key assumption of the efficient-market hypothesis, upon which MPT relies.! All investors are rational and risk-averse. This is another assumption of the efficient-market hypothesis. In reality, as proven by behavioral economics, market participants are not always rational or consistently rational. The assumption does not account for emotional decisions, stale market information, herd behavior, or investors who may seek risk for the sake of risk. Casino gamblers clearly pay for risk, and it is possible that some stock traders will pay for risk as well.! All investors have access to the same information at the same time. In fact, real markets contain information asymmetry, insider trading, and those who are simply better informed than others. Moreover, estimating the mean (for instance, there is no consistent estimator of the drift of a brownian when sub-sampling between 0 and T) and the covariance matrix of the returns (when the number of assets is of the same order of the number of periods) are difficult statistical tasks.! Investors have an accurate conception of possible returns, i.e., the probability beliefs of investors match the true distribution of returns. A different possibility is that investors expectations are biased, causing market prices to be information-ally inefficient. This possibility is studied in the field of behavioral finance, which uses psychological assumptions to provide alternatives to the CAPM such as the overconfidence-based asset pricing model .! There are no taxes or transaction costs. Real financial products are subject both to taxes and transaction costs (such as broker fees), and taking these into account will alter the composition of the optimum portfolio. These assumptions can be relaxed with more complicated versions of the model.! All investors are price takers, i.e., their actions do not influence prices. In reality, sufficiently large sales or purchases of individual assets can shift market prices for that asset and others ( cross elasticity of demand.) An investor may not even be able to assemble the theoretically optimal portfolio if the market moves too much while they are buying the required securities.! Any investor can lend and borrow an unlimited amount at the risk free rate of interest. In reality, every investor has a credit limit.! All securities can be divided into parcels of any size. In reality, fractional shares usually cannot be bought or sold, and some assets have minimum orders sizes.! Risk/Volatility of an asset is known in advance/is constant. In fact, markets often mis-price risk and volatility changes rapidly. More complex versions of MPT can take into account a more sophisticated model of the world as one with non-normal distributions and taxes but all mathematical models of finance still rely on many unrealistic premises.! MPT DOES NOT REALLY MODEL THE MARKET - The risk, return, and correlation measures used by MPT are based on expected values, which means that they are mathematical statements about the future (the expected value of returns is explicit in the above equations, and implicit in the definitions of variance and covariance). In practice, investors must substitute predictions based on historical measurements of asset return and volatility for these values in the equations. Very often such expected values fail to take account of new circumstances that did not exist when the historical data were generated.! More fundamentally, investors are stuck with estimating key parameters from past market data because MPT attempts to model risk in terms of the likelihood of losses, but says nothing about why those losses might occur. The risk measurements used are probabilistic in nature, not structural. This is a major difference as compared to many engineering approaches to risk management.! Options theory and MPT have at least one important conceptual difference from the probabilistic risk assessment done by nuclear power [plants]. A PRA is what economists would call a structural model. The components of a system and their relationships are modeled in Monte Carlo simulations. If valve X fails, it causes a loss of back pressure on pump Y, causing a drop in flow to vessel Z, and so on.! But in the Black–equation and MPT, there is no attempt to explain an underlying structure to price changes. Various outcomes are simply given probabilities. And, unlike the PRA, if there is no history of a particular system-level event like a liquidity crisis, there is no way to compute the odds of it. If nuclear engineers ran risk management this way, they would never be able to compute the odds of a meltdown at a particular plant until several similar events occurred in the same reactor design.! Essentially, the mathematics of MPT view the markets as a collection of dice. By examining past market data we can develop hypotheses about how the dice are weighted, but this isnt helpful if the markets are actually dependent upon a much bigger and more complicated chaotic system—the world. For this reason, accurate structural models of real financial markets are unlikely to be forthcoming because they would essentially be structural models of the entire world. Nonetheless there is growing awareness of the concept of systemic risk in financial markets, which should lead to more sophisticated market models.! Mathematical risk measurements are also useful only to the degree that they reflect investors true concerns—there is no point minimizing a variable that nobody cares about in practice. MPT uses the mathematical concept of variance to quantify risk, and this might be justified under the assumption of elliptically distributed returns such as normally distributed returns, but for general return distributions other risk measures (like coherent risk measures) might better reflect investors true preferences.! In particular, variance is a symmetric measure that counts abnormally high returns as just as risky as abnormally low returns. Some would argue that, in reality, investors are only concerned about losses, and do not care about the dispersion or tightness of above-average returns. According to this view, our intuitive concept of risk is fundamentally asymmetric in nature.! MPT does not account for the personal, environmental, strategic, or social dimensions of investment decisions. It only attempts to maximize risk-adjusted returns, without regard to other consequences. In a narrow sense, its complete reliance on asset prices makes it vulnerable to all the standard market failures such as those arising from information asymmetry, extra nalities, and public goods. It also rewards corporate fraud and dishonest accounting. More broadly, a firm may have strategic or social goals that shape its investment decisions, and an individual investor might have personal goals. In either case, information other than historical returns is relevant.! After the stock market crash (in 1987), they rewarded two theoreticians, who built beautifully Platonic models on a base, contributing to what is called Modern Portfolio Theory. Simply, if you remove their Gaussian assumptions and treat prices as scalable, you are left with hot air. The Nobel Committee could have tested the Sharpe and models—they work like quack remedies sold on the Internet—but nobody in Stockholm seems to have thought about it.! The MPT does not take its own effect on asset prices into account[edit] Diversification eliminates non-systematic risk. As unsystematic risk is not associated with increased expected return, this is considered one of the few free lunches available. Following MPT means portfolio managers can invest in assets without analyzing their fundamentals, specially weighting each asset by the markets weight in the asset. Because the investor purchases assets in proportion to their market weights, there is no relative increase in demand for one asset versus another, and thus no impact on the expected returns of the portfolio.!
Posted on: Wed, 24 Dec 2014 14:00:38 +0000
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