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When managing risk, diversify (part 4)

admin — Mon, 06 Apr 2009 20:57:09 +0000

The CAPM establishes a logical relationship between expected rate of returns and portfolio volatility. The greater the latter, the greater should be the mathematical expectancy of high returns. The CAPM shows that the expected returns for a portfolio should exceed that of a risk-free investment; this may be attributed to a risk premium whose amount is proportional to the beta coefficient.
However, empirical studies do not exactly confirm this theory. In a study dating from 1992, two American researchers, Fama and French, considered the monthly returns of stocks quoted in New York from 1963 through 1990.30 These stocks were distributed into 10 portfolios in accordance with their beta coefficients. The first contained those stocks whose beta was weakest; its volatility was assessed at 0.8. The volatility of the second portfolio was assessed at 0.9 and so on. The last portfolio’s volatility was rated at 1.7. Returns should have grown at the same rate as the relative degrees of volatility. Nothing of the sort took place; no correlation emerged. In a more recent study (June 1999) another researcher, John Cochrane, demonstrated that even though a correlation does in fact exist, ‘‘small cap’’ shares provide returns that are higher than their volatility would convincingly lead us to believe.
The trouble with these theories is that statistical tests on returns obtained after the fact fail to render them perfectly justifiable. Practice shows that professional investors base their choices first on historically attested volatility and second on expectations of returns. Portfolio theory is regularly applied. That said, investors often anticipate in an erroneous manner. If they expect prices to rise and choose volatile portfolios in order to make profits, a market downturn will aggravate the effects of disappointing results. It is not because the expected return on a portfolio is 15 percent that it will supply such sizable returns. Risk justifies the fact that an investor demands higher returns than is the case with risk-free rates, and quite rightly so. The CAPM shows us that the more risks are incurred, the higher the returns an investor must demand. However, this is not tantamount to asserting that the higher the risk, the more favorable the returns obtained! Were this the case, it would behove us to take a maximum number of risks, to run up debts and to invest borrowed money in a market portfolio clearly reflecting systemic risk. In the long run, each and every gambler would make a fortune! One would be better off going for broke and putting borrowed money into play on the roulette wheel or on horse races. Were rewards proportional to the risks incurred, gambling would invariably be the best bet. Statistical tests apply to history-based returns or volatility; as for the model, it functions with expectations of returns rather than time-based averages and with estimates of responsiveness instead of past volatility. Expectations of returns may indeed prove to be proportional to the risk incurred, and yet obtained returns may turn out to be disappointing.
Another criticism is that such tests ought not be restricted to stock market securities. When calculating the beta coefficient, the reference market needs to include all the financial instruments and all assets in which the fortune of the world may be invested: unquoted equities, real estate, raw materials, precious metals, the art market and so on. That said, such criticism is basically technical.
More criticism should rather be addressed to the hypotheses that underpin the CAPM. As we saw above, this reasoning is predicated on a strong hypothesis according to which everyone has the same vision of the future. All investors are said to form identical anticipations; as a result, there supposedly exists but only one envelope of efficient portfolios. This assumption is also part and parcel of a well-known economic framework in which markets are always in equilibrium. This basis for CAPM does not hold water. Markets are never well-balanced; any equilibrium is always shifting. Equilibrium between supply and demand is achieved through prices; continual changes in the latter reflect a perpetual displacement of the point of equilibrium.
The second basis for the CAPM logic consists in the would-be existence of a single efficient envelope of portfolios, the set of all the superior portfolios possible in Markowitz’s framework. Yet in order for this envelope to be unique, it would be necessary for all investors to hold the same predictions. However, if everybody shared the selfsame vision of the future, there would be neither buyers nor sellers! In reality, when we talk about markets we evoke transactions; any transaction features the divergent viewpoints of the buyer and the seller. So there can be no single efficient envelope of portfolios. In practice, many investors believe that their idea of the future is more prescient than that of their neighbors. They do not invest in the same portfolio as the rest of the market. Moreover, when there are several points of view, there also exist several portfolio envelopes. One may even wonder whether the number of efficient envelopes is not equivalent to the number of investors, in so far as each of the latter foresees the future differently. If this is the case, one must admit that portfolio structures may differ greatly among particular investors, which does not necessarily call into question the analytical frame of reference. We must not forget that investors have differing horizons; while some of these are short term, others are long term.
Predictions for the future are relevant to a given horizon of investment. When you think of investing over two to three years, you formulate hypotheses on that time span. But if you are a long-term investor (+ 8 years), you tend to rely on trend analysis. When there are sellers and buyers, there also exist several points of view. And if there is a market, sellers and buyers do exist. The market arbitrates their differences. There is no such thing as a consensus about the future. At any given point in time, one may find many efficient envelopes of possible portfolios.

When managing risk, diversify (part 3)

admin — Thu, 26 Mar 2009 20:56:07 +0000

It has been shown that portfolio risk is reduced by introducing shares from emerging countries, whose volatility is nonetheless much greater than that of industrialized countries. The key to the mystery is that the shares of the former are only weakly correlated to those of the latter. Portfolio performance is enhanced once shares of emerging countries are brought into the mix. At least that is the case in normal times. Financial crises occasionally breed correlations that foil the best-laid mathematical schemes.
During a stock market crash in a given country, it often happens that the local currency also bites the dust. Losses for a foreign investor are even more agonizing than those suffered by a domestic investor; this is due to the correlation that appears in times of financial crisis between exchange rate risk and overall market risk. In the Mexican crisis from December 1994 to March 1995, shares dropped by about 30 percent. That said, over the same period an investor who had acquired Mexican stocks with dollars would have endured a loss of 65 percent – 35 percent more – on account of the devaluation of the Mexican peso in relation to the American dollar.
A financial crisis makes correlations appear in places where they were not expected. The ‘‘tequila’’ effect of the Mexican crisis made investors massively sell off their shares in emerging countries. So it was that the crash spread to numerous Latin American countries and also had a ripple effect across the Pacific, in Indonesia, Thailand and the Philippines.
In fact the risk of a security is composed of two distinguishable sets of risks. Systematic risk is that which cannot be eliminated through diversification strategies. It is the risk inherent to the system, the market risk. Specific risk is proper to the financial asset under consideration. It is a reflection of the risk that something happens and affects the asset (and the asset alone). This risk disappears by dint of diversification.
These two risks are independent; their correlation coefficient is 0. Total risk is the sum of the two. Three experts – William Sharpe, John Lintner and Fisher Black – have put this observation to work by building the Capital Asset Pricing Model (CAPM). The CAPM indicates the price of risk. You may recall that Louis Bachelier established that: ‘‘The mathematical expectancy of the speculator is zero.’’ As for the CAPM, it establishes a simple rule on the basis of two hypotheses: markets are in equilibrium; all investors believe in Markowitz’s theory and they choose their investment out of the same set of efficient portfolios. The rule postulates that the mathematical expectancy for an investment in a security or a portfolio must be proportional to the systematic risk. Since specific risk may be eliminated by diversification, it will not be remunerated by the market. On the other hand, the value of a portfolio has to include remuneration for the investor of an amount in proportion to the degree of systematic risk.
Market risk is attributable to the ongoing evolution of financial assets; it dictates the fluctuation of a given security. Some stocks react strongly to market movements; others do not. The degree of sensitivity to overall market fluctuation proper to a given security is known as the beta coefficient (the estimated coefficient of independent variables in a regression equation). It historically measures the systematic risk proper to a given security on the basis of comparison between the price fluctuations of the security and the fluctuations of the financial market taken as a whole. A security with a 1.0 beta presents the same risk as the market. With a beta lower than 1.0, its risk is also lower than that of the overall market; the security attenuates market fluctuations. With a beta higher than 1.0, the security tends to amplify market fluctuations. With a beta of 2.0, the instrument moves twice as much as the market. If the market rises by 10 percent, it goes up by 20 percent; when the market falls, it goes just as precipitately down. Yet for a given security, the beta does not necessarily hold steady. In other words, it takes on different values in accordance with the periods for which it is measured. On the other hand, the beta value of a market portfolio shows more stability over the course of time. It measures the responsiveness of this portfolio to market fluctuations; it quantifies its volatility.

When managing risk, diversify (part 2)

admin — Thu, 05 Mar 2009 20:55:17 +0000

It is often supposed that investors do not like risk; they are convinced that the good surprises fail to compensate for the bad ones. They would consequently prefer the same returns while incurring a lower degree of risk.
The more the correlation coefficient is negative, the more one endeavors to diminish average risk by applying negatively correlated instruments. If the investor is indeed ‘‘risk-averse’’, he will make sure that the latter are as negatively correlated as is feasible. Then again, the mere fact that the financial instruments are not strictly correlated enables diversification to play an appreciable role.
The correlation of two financial instruments takes on a value between – 1 and + 1. The lower the correlation between a financial asset and a portfolio, the more the volatility of the latter is diminished once the former is added to the portfolio. If one adds securities that are negatively correlated with the portfolio, then the volatility of the latter will be very much diminished. If the new financial assets have no correlation with the portfolio (its coefficient correlation is 0), adding such a security will nonetheless reduce the volatility of the portfolio. Even with a positive correlation coefficient, provided that it is less than 1, adding a supplementary asset diminishes the risks incurred by a portfolio. If we limit ourselves to stock portfolios, studies show that maximal risk diversification is attained with at least 20 shares of firms operating in heterogeneous industrial sectors. Needless to say, if you specialize in stocks for skis, ice skates, fur jackets and 17 shares in industries related to cold weather, your portfolio will be poorly diversified notwithstanding your 20 shares! In contrast, you must try to introduce shares that are not positively correlated. It is also necessary for the probability distributions and the degrees of correlation between them to remain stable for a sizable length of time. The more we study long periods of time, the less reliable are the available statistics. How long is long enough? During calm spells studies by institutional investors analyze and survey the degrees of correlation that may exist between the different categories of financial assets: the stocks of large-scale groups, medium-sized companies, government bonds, corporate bonds, junk bonds, real estate, hedge funds and so on. One must remember that securities that are riskier than a portfolio when taken individually may, in spite of everything and provided that they are not correlated with the portfolio, reduce the overall risks of the latter.
Such factors help to explain the interest in international diversification; it can be expected that economic crises will not take place simultaneously in every country. This approach is supported by the observation that in each country, stocks evolve as a function of the ups and downs of the local economy. Money flows likewise introduce negative correlations between stock market performances and exchange rates. Lowering risk through international diversification largely compensates for the risk linked to exchange rates. Yet with the ongoing internationalization of the activities of quoted companies, the impact of purely local or national factors tends to diminish. A French economist, Bruno Solnik, has shown that for an internationally diversified firm, asset returns are determined to a significant extent by non-domestic (rather than domestic) factors. Moreover, the sensitivity of individual company returns to non-domestic factors is integrally linked to the scope of their international activities, as represented by the relative importance of foreign sales in relation to total sales.

When managing risk, diversify (part 1)

admin — Sat, 14 Feb 2009 20:54:18 +0000

When he drastically modified the risk theory of financial markets, Markowitz reasoned in terms of a portfolio. A portfolio is a whole group of financial assets. Its overall profitability is the sum total of the return on each asset weighted in terms of the proportion represented by its value with regard to that of the entire portfolio. Portfolio profitability is the weighted average of returns on the securities included in it. Yet the risk incurred is another story entirely. A portfolio’s volatility is less than the average volatility of the securities from which it is constituted; that is why diversification is basically praiseworthy.
Markowitz’s singular contribution consisted in providing precise instruments to measure diversification. These instruments allow for the constitution of a portfolio supplying optimal returns for minimal risk; Markowitz terms this an efficient portfolio. No efficient portfolio is superior to any other. Each is simply the best in its category of risk; it offers the highest expectations of returns for a given risk. And in a rigorously equivalent manner, it offers minimal risk for a given expectation of returns. If an efficient portfolio offers comparatively higher returns, it must also present more risks.
Instances of random deviation have a tendency to cancel each other out in a portfolio. This is called diversification. There is an important parameter known as the correlation coefficient, whose role is to assess the benefits obtained through diversification. The correlation coefficient measures the degree of correlation between two variables. The greater their tendency to move in concert at the same time, the higher their correlation coefficient. The range of values this takes is between – 1 and + 1. If the phenomena are perfectly correlated, the coefficient is +1. If they are inversely correlated, the coefficient is – 1. If they are not correlated at all, the coefficient is equal to 0. As for two positively correlated shares, the periods of strong returns for the first correspond to the periods of strong performance for the second; the same for poor performance. When the shares are negatively correlated, underachievers accompany overachievers. When there is no correlation at all, A’s performance has nothing to do with B’s.
Diversification brings together two random variables that are not strictly correlated and thereby diminishes average risk. The interest of Markowitz’s theory basically consists in his having mathematically expressed the fact that the important parameter is the correlation coefficient and that what matters is to estimate correlations involving multiple phenomena.