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The Actuary The magazine of the Institute & Faculty of Actuaries
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Hedge fund investment

The basic proposition put forward by the hedge fund industry is an investment diversification argument. The argument is based on two main assumptions.
1 Hedge funds have a low correlation with the traditional asset classes of equities, bonds, and property.
2 The returns over a given period from hedge funds are comparable to the returns on these traditional asset classes.
If we accept these two assumptions and some modern portfolio theory, then it follows that by investing a portion of your portfolio in hedge funds, you should be able to get a return comparable to that on your traditional portfolio, but with lower risk. Risk in this case is measured by the standard deviation or volatility of the portfolio’s return.

Low correlation?
An examination of the various hedge fund databases shows that there are plenty of hedge funds whose returns historically have a low correlation with the returns on the traditional asset classes.
There are, however, some problems with a summary measure like the coefficient of correlation between two asset classes. The main problem is that the coefficient of correlation is not constant. It may be the case that in volatile markets, the returns from the hedge fund and the traditional asset classes may be highly correlated. For example, the returns on long/short equity hedge funds will tend to exhibit a high positive correlation with equity markets in times of market stress. This is because long/short equity hedge funds are in general in a net long position. It is also worth noting that approximately 50% of all hedge funds are long/short equity hedge funds.
In choosing a hedge fund or fund of funds for risk reduction purposes you would need to compare the historical returns on the hedge fund with those of your existing portfolio to see what risk reduction would have been achieved historically. Using a summary measure like the coefficient of correlation to estimate the risk reduction may be unreliable.

Comparable returns?
The second assumption underlying the argument for investing in hedge funds is that the absolute returns on hedge funds are comparable to those on the traditional asset classes. If you look at the websites for the hedge fund indices you will get statistics like those in table 1.
On the face of it, therefore, hedge funds appear to be a good investment. However, there are a number of problems with some of the hedge fund index statistics. These can be categorised into three main groupings: survivorship bias, selection bias, and stale or managed pricing.

Problems with hedge fund index statistics
Survivorship bias occurs because some indices do not include the returns of those funds which left the index during the period of observation, ie the index return is only based on those funds which were in the index from the start to the end of the observation period. As the funds which leave the index are generally the poor performers, the index return will be overstated compared with the universe of all funds. Academic research has suggested that the amount of overstatement could be of the order of 23% per annum. Even at 3% per annum, the return on the Van hedge fund index still compares well with the S&P 500 total return.
Research also suggests that the omission of the returns for funds leaving the index also understates the volatility and kurtosis of the hedge fund index return. Kurtosis is a measure of the thickness of the tails of a distribution relative to that of a normal distribution with the same standard deviation. The higher the kurtosis, the greater the likelihood of extreme outcomes.
Risk-adjusted return is normally measured by the Sharpe ratio. This is defined as the excess return over the risk-free rate divided by the volatility of the return (as measured by standard deviation). If the distribution of returns is not normally distributed, then the use of this measure for calculating risk-adjusted returns is questionable. This is because the volatility measure is not a reliable measure of risk when returns are not normally distributed. Two distributions with different kurtosis can have the same mean and standard deviation. The distribution with the higher kurtosis is clearly more risky but, measured by standard deviation, the two distributions appear to have the same risk. Survivorship bias therefore has a double effect on risk-adjusted return measures such as the Sharpe ratio. It increases the top line and reduces the bottom line, thereby overstating the calculated risk-adjusted return.
Survivorship bias is not confined to hedge fund indices. A similar problem occurs with some mutual fund indices.
The second problem with some of the indices is that funds can choose to participate in the index. If a fund has poor performance it may not report its results to the database. If a fund chooses to report its results to the database then the database may take account of its history prior to joining. This feature is also likely to overstate index returns compared with the universe of hedge fund returns. It is not possible to quantify the effect of this on hedge fund index returns.
The third problem is stale or managed pricing. Some hedge funds deal in illiquid assets which are not traded on a market. The pricing of these assets is a matter of judgement, and it is open to manipulation. Again, it is difficult to quantify the effect of this on hedge fund index returns. We also have the same problem in property funds where property valuations are subjective.
Over the long term, managed pricing is more likely to affect the volatility of returns than the mean return. The effect is to reduce the volatility of returns. This will lead to an overstatement of the Sharpe ratio.

Regulatory position
If we accept the rationale for investing in hedge funds albeit with the health warnings discussed above the next question we might ask is whether a life assurance company could market a hedge fund. This could be achieved by wrapping it in a unit-linked life policy.
This would be difficult under the FSA’s interim prudential sourcebook rules. The main reasons for this are the application of the ‘look-through’ rules and the definitions of a permitted derivative.
The look-through rules require a company to look through to the assets underlying collective investment schemes to see whether these assets would themselves be permitted. On a look-through basis, the assets held by hedge funds might not pass the UK’s admissibility tests, particularly if the assets are freestanding derivatives.
The look-through rules do not apply in all European countries which have adopted the Third Life Directive. In those countries where look-through rules do not apply, it may be possible to wrap hedge funds in unit-linked life policies.

Hedge fund selection criteria
If you are satisfied that a hedge fund has historically achieved returns comparable to those of your existing portfolio, and that its returns have a low correlation with that portfolio, then what other selection criteria should you use?
The first thing you would need to do is carry out an appropriate due diligence test on the fund. This would include looking at the integrity and competence of the key staff, assessing the fund’s risk management processes, determining how the fund actually generates value, and assessing the quality of the fund’s custodian/bankers/brokers, etc.
Funds which are regulated by European regulators or the various US regulators are subject to much more stringent disclosure requirements than are their offshore counterparts. In particular, performance information must be prepared to specified standards. Onshore funds are also subject to much more stringent ‘fit and proper person’ tests than their offshore counterparts.
A significant proportion of hedge funds have long ‘lock-up’ periods; for example you may not be able to redeem within the first 12 months and no more frequently than half-yearly thereafter. These long lock-up periods may indicate high levels of leverage and/or investment in illiquid assets.
Finally, it is also important to examine whether the historic returns from the hedge fund are normally distributed or close to it. Part of the test for normality will be a review of the kurtosis of historic returns.

Jargon buster
Modern portfolio theory this looks at investment markets as a whole. Investments are described in terms of their expected long-term rate of return and expected short-term volatility. The volatility is equated with risk, measuring how much worse than average an investment’s bad years are likely to be. An acceptable level of risk tolerance is identified and then a portfolio is found with the maximum expected return for that level of risk.
Coefficient of correlation measures the strength and direction of the relationship between X and Y, where X and Y could be, for example, investment returns on two asset classes over a period.
Long position state of actually owning a security, contract or commodity.
Short position the promise to sell a certain quantity of a good in the future at a particular price.
Leverage the degree to which an investor or business is utilising borrowed money.

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