Factor Models and Portfolio Impact of Hedge Funds
What you'll learn
- LOS 33.hDescribe how factor models may be used to understand hedge fund risk exposures.
- LOS 33.iEvaluate the impact of an allocation to a hedge fund strategy in a traditional investment portfolio.
Factor Models
Analysis of Hedge Fund Strategies
In this LOS, we will consider the use of a conditional linear factor model to quantify the risk exposures of various hedge fund strategies.
By conditional, we mean a model that takes into account that a fund may behave one way during normal market conditions, but perform differently during a period of market turbulence (such as the economic crisis of 2007 to 2009).
By determining a fund’s actual risk exposures, events such as the widespread closure of hedge funds that happened after the global financial crisis are less likely.
Conditional Factor Risk Model
Suppose we use the following conditional linear factor model to explain the return of hedge fund i in period t:
where:
| Symbol | Meaning |
|---|---|
| Intercept for hedge fund | |
| Exposure during normal periods to risk factor | |
| Dummy variable that equals zero during normal periods, and one during a financial crisis | |
| Incremental exposure to risk factor during financial crisis periods | |
| Random error with zero mean |
Any returns not explained by the model’s risk factors would be attributed to either omitted risk factors, alpha (i.e., hedge fund manager skill), or randomness (error).
Hasanhodzic and Lo (2007) used the following six factors:
1. Equity risk (SNP500): S&P 500 total return index.
2. Interest rate risk (BOND): Bloomberg Barclays Corporate AA Intermediate Bond Index.
3. Currency risk (USD): U.S. Dollar Index.
4. Commodity risk (CMDTY): Goldman Sachs Commodity Index (GSCI) total return.
5. Credit risk (CREDIT): Spread between Moody’s Baa and Aaa corporate bond yields.
6. Volatility risk (VIX): CBOE Volatility Index (VIX).
A stepwise regression process is useful for creating linear conditional factor models that avoid multicollinearity problems, because it avoids the use of highly correlated risk factors. Use of a stepwise regression process resulted in the BOND and CMDTY factors being dropped due to multicollinearity issues. (CREDIT and SNP500 respectively produced higher adjusted .)
This left the following four factors for measuring risk exposures:
1. Equity risk (SNP500).
2. Currency risk (USD).
3. Credit risk (CREDIT).
4. Volatility risk (VIX).
Each hedge fund strategy has different exposures to these various risk factors. These risk factors stem from taking long or short positions in financial instruments that are exposed to these risks.
For example, arbitrage strategies are often exposed to credit spread risk and market volatility risk. Event driven strategies and L/S equity strategies generally have significant exposure to equity (market beta) risk.
We will assume a 20% allocation to a hedge fund strategy from a conventional portfolio comprised of 60% stock and 40% bond. After the allocation, the new weights will be 20% hedge fund, 48% stock, and 32% bond.
Portfolio Contribution of Hedge Fund Strategies
Performance Contribution to a 60/40 Portfolio
For most strategies, when added to a conventional portfolio:
Total portfolio standard deviation decreases.
Sharpe ratio increases.
Sortino ratio increases.
Maximum drawdown decreases (in approximately one third of portfolios).
The interpretation of these results is that hedge fund strategies generally increase risk adjusted return and provide diversification to a traditional portfolio of stocks and bonds.
Risk Adjusted Performance
The Sharpe ratio is one risk adjusted measure of performance. The risk metric used to calculate the Sharpe ratio is standard deviation, with the result that both downside and upside deviations result in a lower Sharpe ratio.
The Sortino ratio is a similar risk adjusted measure of performance; however, only downside deviations are considered to reflect risk: risk is measured as variability below a predefined level of return. Because of the left tail risk present in many hedge fund strategies, the Sortino ratio is generally seen as a superior measure of the risk adjusted performance of hedge funds.
When 20% allocations to various hedge fund strategies are added to the traditional stock/bond portfolio, particularly high Sharpe ratios are achieved from allocations to these strategies:
Systematic futures.
Distressed securities.
Fixed income arbitrage.
Global macro.
Equity market neutral.
The highest Sortino ratios were attained via allocations to the following hedge fund strategies:
Equity market neutral.
Systematic futures.
Long/short equity.
Event driven.
Allocations to the following strategies were found to be effective in generating superior risk adjusted performance, based on comparatively high Sharpe and Sortino ratios:
Systematic futures.
Equity market neutral.
Global macro.
Event driven hedge fund strategies.
On the other hand, it was observed that the following fund strategies do not significantly enhance risk adjusted performance:
Fund of funds.
Multi strategy.
While all of the hedge fund strategies expose the overall portfolio to various kinds of additional portfolio risks, allocating a portion of a stock/bond portfolio to hedge funds generally reduces risk and increases returns.
Risk Metrics
One key reason for investors to allocate a portion of their portfolio to hedge fund strategies is to reduce risk.
Standard Deviation
Perhaps not surprisingly, it was found that the following strategies resulted in the lowest standard deviations of returns for the overall portfolio:
Dedicated short biased.
Bear market neutral.
These funds also produced notably low standard deviations:
Systematic futures.
FoF: macro/systematic.
Equity market neutral.
The risk reduction ability of these strategies has been found to be substantial. Not surprisingly, they are also some of the strategies that most improve risk adjusted returns.
Funds that were found to have little positive impact on reducing standard deviations of the overall portfolio include:
Event driven: distressed securities.
Relative value: convertible arbitrage.
An explanation for event driven: distressed securities’ lack of ability to reduce standard deviation is that these funds tend to take long positions in securities, and outcomes are either mild successes or grand failures.
Relative value: convertible arbitrage funds do little to improve standard deviation, likely because this strategy’s leveraged nature becomes a liability during times of market volatility.
Drawdown
Drawdown is defined as the peak to trough decline for a portfolio, generally quoted as the percentage drop between a point of high portfolio value and the subsequent trough. The high water mark refers to the maximum value the portfolio has ever reached.
Drawdown is useful for quantifying the risk and past performance of various investment strategies, and for comparing one strategy’s risk to another.
The hedge fund strategies that produced the smallest maximum drawdowns are various opportunistic strategies:
Global macro.
Systematic futures.
Merger arbitrage.
Equity market neutral.
Use of the conditional risk model can show that these strategies perform relatively well during periods of market crisis because they have minimal exposure to credit risk or equity. Furthermore, these strategies benefit from their liquid nature. Those properties make opportunistic strategies useful diversifiers for traditional assets.
Other hedge fund strategies did little to mitigate the traditional portfolio’s maximum drawdown:
Long/short equity.
Event driven: distressed securities.
Relative value: convertible arbitrage.
These results are somewhat expected. Using the conditional risk model, we can demonstrate that these particular strategies have significant exposure to equity risk, and furthermore during crisis periods they have significant exposure to credit risk as well.