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| Quantitative Tools |
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| Introduction |
| In this section, we describe the different risks associated with investing in hedge funds. For each of these risks, a technique is proposed. Aside to the classical statistical measures used in the hedge funds and in the long-only industries, new recent measures have been developed by academics focusing only on the behavior of negative returns. We focus on each of them in the following sections. |
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| Extreme
Risk Analysis - Use AlternativeSoft's Platform, Fund Selection module |
| Extreme risks are extreme events occurring rarely. These extreme events are not captured by normal distributions. The third and fourth moments
(i.e. skewness and kurtosis), Value-at-Risk, Modifed
Value-at-Risk, Conditional Value-at-Risk, Maximum possible
time-under-water, maximum possible future drawdown, Omega,.... are
necessary. The difference between normal risk (measured with volatility) and extreme risk (measured with volatility, skewness and kurtosis) is called extreme risk. These extreme
risk measures are all available in
AlternativeSoft's platform.
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| Portfolio
Construction with Volatility, Skewness and Kurtosis -
Use AlternativeSoft's Platform,
Portfolio Construction module |
| Skewness measures the asset return asymmetries. A negative skewness implies more than 50% of the returns on the right of the mean or that the returns on the left of the asset's mean are farther on the left than on the right. The distribution is negatively skewed. The explanation of the asset's skewness has three theoretical sources: |
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Investor Preferences (Grossman, Zhou, 1996). |
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Transaction Costs (Constantinides, 1997). |
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Stochastic Processes with Changing Volatility and Jumps (Bates, 1996). |
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| Kurtosis measures the degree of fat-tailness of the asset returns. Sudden extreme positive or extreme negative returns increase the kurtosis. For a normal distribution asset, its kurtosis equals 3. If a distribution has a kurtosis of 6, there is a high probability in the future to have high positive or negative returns. Kurtosis can be explained by overreaction to information, by crashes, and by leverage. Risk averse investors do not like negative skewness or kurtosis higher than 3. Nevertheless, investors are buying, selling and constructing portfolios without asking a premium for these two moments (i.e. skewness and kurtosis). This is why skewness and kurtosis have to be included in a portfolio optimization as soon as they are significant. The portfolio risk including skewness and kurtosis will be higher than the portfolio risk measured with volatility only. The following graph exhibits the effect of accounting for skewness and kurtosis, on the horizontal axis. |
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| Source: AlternativeSoft's platform. |
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Portfolio expected annual return |
11.75% |
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Skewness |
-0.18 |
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Normal monthly Value-at-Risk at 99% |
-1.60% |
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Modified monthly Value-at-Risk at 99% |
-2.26% |
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| The portfolio (i.e. red dot in the graph) has an expected annual return of 11.75%, a Normal monthly Value-at-Risk of -1.60% and a Modified Value-at-Risk of -2.26% (i.e. the portfolio can loose more than -2.26% each 1 over 100 months). This means the Modified VaR shows a riskier portfolio than the Normal VaR, because the Modified VaR accounts for skewness and kurtosis. |
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| Bear
Correlation - Use AlternativeSoft's Platform, Fund Selection module |
| A risk-averse investor does not want to have negative returns. Consequently, banks and managers are constructing portfolios with low correlation coefficient with respect to equity or bond indices. This methodology is not accurate for two reasons: |
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The correlation is only valid for normal distributions |
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The correlation is only valid if the portfolio assets follow elliptical multivariate distributions |
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| In an ideal world, we would like to be highly correlated during positive index returns
(i.e. high bull correlation) and not correlated during negative index
returns (low bear correlation), like with a long call option. One needs to decompose the linear correlation in two correlation
coefficients: the bull and the bear correlation. These techniques reveal the
fund behavior during negative index returns. The correlation during negative markets and the respective portfolio returns is called 'bear correlation'. The table below shows the correlation and the bear correlation for
GAM Diversity (i.e. a fund of hedge funds) and two indices. |
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| Source: AlternativeSoft's platform. |
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| Maximum
Possible Drawdown - Use AlternativeSoft's Platform, Fund Selection module |
| Historical drawdown measures the peak to through of an asset, a mutual fund, a hedge fund, a fund of funds or a portfolio. The issue with this measure is that it relies on old data, sometimes from 1998, during the Russian crisis. There are two solutions to solve this issue: |
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Use a shorter time window which does not include 1998 |
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Derive a formula computing the future possible drawdown, using the current volatility and the current annualized return |
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| The opposite is true. A fund with a short track record and a risky strategy has, for sure, not seen its maximum drawdown. In order to solve that, AlternativeSoft has developed a
proprietary measure called 'Maximum possible drawdown'. It measures,
for the future, how much a fund can loose during any specific time window. This formula is applied in the table
below for the fund of funds 'GAM Diversity' and two indices. |
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| Source: AlternativeSoft's platform. |
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| Portfolio
Simulation - Use AlternativeSoft's Platform,
Portfolio Construction module |
| In the hedge funds industry, managers use leverage, options, futures, forwards, short positions, long positions, and illiquid instruments. These strategies have two common risks: liquidity and credit risks. When markets crash, liquidity dries up and investors turn to government bonds (i.e. no credit risk). |
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| The portfolio behavior during market turmoil can be simulated with a non-normal distribution. The investor is aware that during a crash, many hedge funds will disappear or lose more than 20% of their value, as in August 2007. The graph below shows the portfolio simulation for the next 3 years. In 3 years, the portfolio has 50% probability to be higher than 45.4%. The portfolio has only 1% probability, in 3 years, to be below 13.6%, if portfolio skewness and kurtosis are taken into account. If only volatility is taken into account, the portfolio has 1% probability, in 3 years, to be below 25.2%. The difference between 25.2% and 13.6% is due to the portfolio negative skewness. |
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| Source: AlternativeSoft's platform. |
