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Portfolio Risk Measurement and ManagementIt is an axiom of financial economics that a rational investor will seek to minimize the risk of their portfolio, and to maximize their return. Indeed, to explain this axiom more explicitly, there are two principles that financial economics assumes about rational investors:
These two statements say a lot about the risk/return preferences of rational investors. However, they certainly don't mean that all rational investors have the same risk/return preferences! Different investors have different risk/return preferences. Nevertheless, the principles of return maximization and risk minimization make it possible to make a lot of generalizations about how to construct investment portfolios. An interesting practical aspect of this, which the traditional financial economics textbooks tend not to mention very much, is the question of how many actual investors conform with these assumptions about what it takes to make someone a rational investor. Psychological evidence, such as Kahneman and Tversky's prospect theory, and Richard Thaler's concept of mental accounting shows not just that there are limits to human rationality, but that there are systematic ways in which people are irrational in their decision making. Having said that, it is undoubtedly useful to explore issues of risk and return from the standpoint that of the hypothetical "rational investor". What is Risk?Risk, in these conversations, is defined quite simply as the standard deviation of returns. In other words, risk captures the variability of returns. There are a lot of little quibbles that one can have with this definition, but it does in fact do a very good job of reflecting the essential characteristics of what market risk is. In "big picture" terms, the market risk of which we speak here is risk due to movements in market prices. Other classes of risk, such as operational risks or sovereign risk, are not captured by this framework. To provide a small illustration of what it means to say that a portfolio has a risk of X%, this means that the standard deviation of returns for the portfolio is X%. Standard deviations on the normal curve follow the old principle 65-95-99. In other words, 65% of outcomes will be within one standard deviation of the mean, 95% will be within two standard deviations, and 99% will be within three standard deviations. So, for a portfolio whose mean expected return is 10%, with risk of 8% (these numbers are all annualized by convention), there is a 65% chance that the return over the next year will be between 2% and 18%. All sorts of subtle elaborations are possible, but the basic idea of market risk is very simple, and (usefully) very amenable to calculations using standard statistical methods. DiversificationDiversification is the one tool, freely available to everybody, that enables investors to reduce the risk of their portfolio. A wise portfolio manager will consider portfolio-wide needs when deciding how to construct a portfolio. Portfolio construction should not just be the accidental coming-together of securities that seem attractive to hold; rather, one should give careful consideration to the impact of each security on the overall portfolio characteristics. The next section, for example, shows why it can still be worthwhile to add a security to a portfolio when the security has higher risk (and equal expected return). Example: Combining a Hedge Fund with EquitiesThe most valuable aspect of a hedge fund may not be that it offers higher returns, or that it offers lower risk. The unique value-adding potential of a hedge fund is the way it can reduce the investor's overall portfolio risk by offering "extreme diversification". Consider the example of an investor who can construct their portfolio out of two possible assets: a hedge fund, or equities. Assume that the hedge fund and the equity market both have expected returns of 13%. Assume also that the hedge fund has an expected risk of 14%, while the equity market has an expected risk of 12%. Since the risk of the hedge fund is higher than the risk of the equity market, one might think that it would be best for the investor to avoid investing in the hedge fund. However, this is not the case. The missing ingredient that one needs to consider is the correlation between the hedge fund and the equities market.
The chart above contains three different lines plotting the total risk of the portfolio against the proportion of equities in the portfolio. The left side of the chart shows the risk for 0% equities, 100% hedge fund. This is 14%. The right side of the chart shows the risk for 100% equities, 0% hedge fund. This is 12%. The lines in between these point show how the risk changes with different concentrations of assets:
This is just one particular numerical example, but it illustrates the general principle that introducing low-correlation assets into a portfolio can reduce risk quite appreciably. At a correlation of 1.0, there would be no advantage at all in allocating assets into the hedge fund. At a correlation of 0.7, one has the potential to reduce the risk to 11.7% by allocating assets into the hedge fund. This is a fairly marginal benefit: only 30 basis points of risk reduction. A practical person might be inclined to say that a theoretical risk reduction of 30 basis points means little in practice, because of the danger that reality can turn out differently from a mathematical model. However, at a correlation of 0.0, the potential risk reduction becomes hard to ignore. The potential is to get the risk down to 9.1%, which eliminates (through diversification), almost one quarter of the existing risk in an equities portfolio. This is very considerable risk reduction. We could simply accept this risk reduction "as is", or we could convert it into higher return by leveraging the portfolio. For example, the expected return of all our portfolios including equities and hedge fund is 13% (remember this is the expected return that we assumed both for hedge funds and for equities). Our diversified portfolio with a risk of 9.1% has this 13% expected return. To take the level of risk back up to 12% (the level of equities on their own), we could increase the portfolio weight of risky assets to 131.56%, and hold -31.56% cash in this leveraged portfolio. We assume that the cash interest rate is 5%. The final result is a portfolio with risk = 12% (just as for a plain equities portfolio), but expected return boosted up to 15.52%. This is a nice return enhancement of 252 basis points, for zero incremental risk. Surely every rational investor would seek-out a solution of this kind, if they were able to access it? Well, perhaps maybe not, because some investors use Thaler's mental-accounting principle of ignoring the fungibility of money, and instead concerning themselves primarily with the labels attached to different sub-parts of their portfolio (specifically, they might shun having any leverage or hedge funds, without regard to the consequences for the overall risk/return profile of their portfolio). So, to pose another question of great practical importance, is it possible to find hedge funds that offer the sort of risk/return characteristics shown in this example? Sometimes yes, but you do need to watch out for the great pretenders. Some hedge funds are constructed in an explicitly market-neutral way. Typically, this would mean that every long asset was offset by a similar short asset. For example, the hedge fund manager might bet on copper vs. steel, oil vs. natural gas, Euro vs. Japanese Yen, Swedish bonds vs. British bonds, etc. Each bet is essentially a relative bet, that one asset will outperform another asset. When this sort of portfolio construction is done rigorously (especially with the assistance of sophisticated factor models), the resulting portfolio tends to have zero correlation with equities markets. Yet, if the hedge fund manager has skill in picking misvalued assets, the expected return from this sort of portfolio can be quite reasonable. A rigorously constructed market neutral hedge fund will have zero correlation with equity markets, and it will offer attractive long-term returns. However, as somebody once said, "hedge fund" means a remuneration structure, not a portfolio management style. There are many "wannabe" investment managers who love the idea of charging 2+20 fee structures. so, they often cobble together a fairly standard long-only investment style, then add a bit of short selling in order to get a product that they can market to a gullible public as a hedge fund. My SuggestionMy suggestion is that all so-called market neutral hedge funds should be required to report in detail on their correlations with major asset classes. That way, investors would have a reliable piece of information to help them decide whether they are truly likely to gain significant benefits from something claiming to be a hedge fund. See alsoOur page about Performance Fees, which mostly applies to hedge funds. |
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