Investment strategy performance of hedge funds

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University of Amsterdam

Faculty of Economics and Business (FEB)

BSc Economics and Business

Investment strategy performance of hedge funds

Name: Hjalti Stefansson

Student number: 10025596

Specialization: Finance & Organization

Field: Finance

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Statement of Originality

This document is written by Student Hjalti Thor Stefansson who declares to take full responsibility for the contents of this document.

I declare that the text and the work presented in this document is original and that no sources other than those mentioned in the text and its references have been used in creating it.

The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.

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1. Introduction

Since the beginning of the nineties hedge funds have been gaining popularity, with each year the total assets under management (AUM) growing. The lack of transparency and the absence of performance reporting standards makes it hard to formulate expectations for hedge fund performance. Fung & Hsieh (2004) created a model for the hedge fund category fund of funds (FoF) to find the different exposures of various hedge fund indexes. They succeeded in

creating a model (the seven factor model) with a high . Only this model was created purely for the fund of funds category.

Therefore, how did different hedge funds strategies perform during 2008 through 2013 and is the seven factor model useful per investment strategy?

Fung & Hsieh (2004) tested the usefulness of their model by applying data, that was not used in the construction of their model, to conditionally forecast the returns of hedge fund FoF indexes. These predictions were very accurate as can be observed in table 1, which is the original table from Fung & Hsieh article of 2004.

Table 1. Actual returns and conditional forecasts of annual returns for hedge fund indexes, 2003 (Fung & Hsieh, 2004)

Type of return HFRI CTI MSCI SPHF

Actual Predicted 18.10% 18.17% 14.48% 12.13% 14.05% 14.84% 10.58% 10.72%

So if the model holds and correctly captures the risk exposures for different hedge fund strategies, perhaps it could be possible with some degree of certainty to forecast the index returns per strategy.

To answer the research question the seven factor model will be used to regress the index return per strategy on asset-based style (ABS) factors. The alphas will be tested for significance after exposure to their risk benchmarks (i.e., the ABS factors) to ascertain how the index strategies have performed. To examine if the model holds per investment strategy a benchmark of the original research of Fung & Hsieh (2004) will be created with the FoF category. So the per regressed strategy to the ABS factors can be compared to that of the FoF.

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Section 2 will cover the literature review, consisting of defining hedge funds and a brief history of the literature written about the subject. Furthermore, in section 3 the

methodology is covered, containing the model that is used in this thesis. In section 4 the data is discussed, that is, where it was obtained, descriptive statistics, and associated biases. In section 5 the results have been displayed and discussed. Finally, in section 6 the conclusion is formulated.

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2. Literature review

In this section a brief history of hedge funds will be discussed and a summary of the research that has been done in this field regarding the analysis of risk exposures of hedge funds.

2.1 Hedge Funds

Hedging is taking an investment position, which reduces the risk of price movements in the underlying asset. For example, going long in stocks that are expected to rise in value and going short in stocks that are expected to drop in value. This is also called the long/short equity hedge, which is the strategy of the first modern hedge fund developed by A.W. Jones in 1949. Nowadays, however, hedge funds have many different investment strategies, which don’t necessarily hedge.

Hedge funds are investment companies, that typically have the business structure of a Limited Liability Partnership or Limited Liability Company, so that they can bypass the requirements mutual funds are subjected to through the securities act of 1933 and the investment company act of 1940. This forces mutual funds to be transparent and have a predictable strategy. Also the public must be regularly updated on the composition of the portfolio. (Bodie et. al, 2014)

Hedge funds conventionally don’t have more than 100 “sophisticated” investors. Generally this means they have a minimum net worth, income requirements and minimum investments usually between $250.000 and $1 million. (Bodie et. Al, 2014)

Hedge funds investment strategies are more flexible in comparison to those of mutual funds. For instance mutual funds have restrictions on how much they may deviate from their prospectus, how much they can sell short, and the use of derivatives is limited. (Bodie et. al, 2014)

The liquidity of hedge funds also differs from that of mutual funds. Whereas you can sell your share/or cash out of a mutual fund, hedge funds often impose lock up periods, i.e., after the investment is made it cannot be withdrawn for a pre specified period. Also to redeem funds there is often a redemption notice of a couple of week or months in advance. (Bodie et. al, 2014)

The compensation structure of hedge fund managers resembles the payoff diagram of a long call option, that is, as soon as a high water mark has been reached (some fixed

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percentage that the returns have to surpass) he or she gets a fraction of the additional profit. This incentive fee is usually 20%. (Bodie et. al, 2014)

Hedge funds built up fame through large returns in a short time span. For instance in 1986, the Tiger fund and the Jaguar fund profited through global macro strategies. They expected the U.S. dollar to depreciate against the European currencies and the yen. So they made large investments in foreign currency call options and made substantial profits. The following years hundreds of new hedge funds were established (Eichengreen & Mathieson, 1999). Also George Soros’ Quantum Fund achieved a similar feat, by betting on a

depreciation of the British pound and the Thai Baht. These success stories led to an increase in the popularity of hedge funds (Connor & Woo, 2003).

Since 1997 the total assets under management (AUM) of the hedge funds industry has grown from $118 billion to $2508 billion in 2014. (Barclayhedge, 2015). In figure 1 the progress of this growth is illustrated. After the start of the global financial crisis in 2007 over 25% of the total AUM has dropped and by now surpassed the amount from before the crisis.

Figure 1. Total assets under management for the hedge fund industry, 1997-2014 (Barclayhedge, 2015)

In the past few decades several strategies within the hedge fund industry have emerged, which are also defined in the Lipper Global Classification 2014.

1. Convertible Arbitrage: attempts to gain profits of pricing differences in the

conversion factor of a security by taking a long position in the convertible security and a short position in the underlying common stock.

$- $500,000 $1000,000 $1500,000 $2000,000 $2500,000 $3000,000 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 In b il li o n s

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7 2. Dedicated Short Bias: an investment strategy that constantly has a “net-short”

exposure to the market by taking long and short positions. It tries to profit from market declines by making investment in short positions. During the bull markets of the 80’s and the 90’s the hedge funds with a dedicated short strategy (i.e. only taking short positions) were almost entirely wiped out. As a result the dedicated short bias became more popular, which has a more balanced approach.

3. Emerging Markets: invests in debts and/or equity in emerging market countries. The

difference between conventional emerging market funds, is that hedge funds strategies can use leverage to stimulate the profits of their portfolios. Emerging markets hedge fund strategies do not necessarily hedge portfolio risk, either there is no derivatives market for hedging the risk or the fund manager wants to keep market exposure.

4. Equity Market Neutral: this strategy seeks to make positive returns through superior

stock selection with long and short positions that have a total net exposure of zero. It involves buying underpriced stock – the long position – and selling the overpriced stock – the short position.

5. Event Driven: takes place when specific corporate or market events occurs (i.e.

mergers, bankruptcies, share buy backs, litigation, etc.), by taking significant positions in numerous asset classes attempting to gain profits of possible mispricing.

6. Fixed Income Arbitrage: Simultaneously buying and selling a security on different

markets because fund managers believe there is a price discrepancy through which they can profit.

7. Fund of Funds: funds are allocated to multiple different hedge funds to be managed. 8. Global Macro: Is the broadest hedge fund strategy, investing in large trends, i.e.

major equity, foreign exchange, and commodity markets.

9. Long/Short Equity Hedge: Equity-oriented positions, that combines long holdings of

equities and short holdings of stocks or stock indexes. This strategy can be long or net-short, but not market neutral (i.e. net exposure of zero)

10. Managed Futures: This strategy uses financial, currency or commodity futures to

benefit from market trends.

11. Multi Strategy: a strategy where single- or multi-manager hedge funds have

multiple strategies that contribute to the total performance of the fund. Also, not one investment process may account for 75% of the risk capital.

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8 2.2 Seven factor model

The roots of the model used in this thesis are found with the creation of the capital asset pricing model (CAPM) by Treynor, Sharpe, Litner and Mossin. All who advanced the work laid down by Markowitz with his modern portfolio theory. The CAPM is a pricing model of the expected return of a risky asset.

Ross developed the Arbitrage Pricing theory (APT) in 1976. This theory has it resemblance with CAPM, because it also tries to predict the security market line. It tries to display the expected return in a linear model with macro-economic factors or market indexes.

William F. Sharpe introduced style analysis in 1992. He regressed mutual fund returns on various indexes of asset classes. The coefficients of the regression would then measure the funds capital allocation to that asset class. Knowing that mutual funds are very limited in their use of short positions and leverage, the regression coefficients were restricted to be

nonnegative and sum up to one. After achieving a high (above 0.90), the unexplained variance was attributed to either security selection, market timing, and or changes in the weights assigned to asset classes (Bodie et al., 2014).

Usually performance models regress a funds historical returns on one or more benchmarks. The slope of the coefficients indicate benchmark-related performance and the alpha (constant) measures performance “benchmark risk”. This method traces back to Jensen’s original work in 1968. The drawback with this type of regression is, that it is sensitive to nonlinear relationships between the funds return and the benchmarks. (Fung & Hsieh, 2001)

Fung & Hsieh (2001) followed the suggestions of Glosten and Jagannathan (1994) to model hedge fund returns to the popular “trend-following” strategy. Fung & Hsieh (1997) found that hedge fund managers use dynamic trading strategies, which generate option like returns with seemingly no systematic risk. The linear-factor models of investment styles using asset based benchmarks, as suggested by Sharpe (1992), don’t have these characteristically nonlinear returns often found among hedge funds. This may mislead investors into thinking that there is no systematic risk.

Treynor and Mazuy (1966) and Henriksson and Merton (1981) added nonlinear functions of the benchmark return as regressors to solve for option-like return features. Glosten and Jagannathan (1994) also suggested a cure for this by using benchmark-style indexes, which have embedded option-like features. (Fung & Hsieh, 2001)

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Fung & Hsieh (2001) were trying to find portfolios of bills and options that have similar returns of trend-following funds. They used a concept introduced by Goldman et al. (1979) by combining a long lookback call (i.e., the right to buy the asset at the lowest price during the life of the option) and a long lookback put (i.e., the right to sell the asset at the highest pricing during the life of the option). Combining the two gives the ex post maximum payout of any trend-following strategy. Fung & Hsieh (2001) called this the “primitive trend following strategy” (PTFS).

Fung & Hsieh (2004) identified four subgroups of hedge funds and commodity funds: trend-following funds, merger arbitrage funds, fixed-income hedge funds, and equity long-short hedge funds. To find relevant observable market variables for their model they examined these subgroups.

For the trend-following funds they created lookback straddle option portfolios for bonds (i.e., futures contracts on the U.S. 30-year treasury bonds (CBOT), UK Gilts (LIFFE), German Bunds (LIFFE), the French 10-year government bond (MATIF), and the Australian 10-year government bond (SFE)), currencies (i.e., futures contracts on the British pound, Deutschemark, Japanese yen, and Swiss franc on the CME) ,and commodities (i.e., futures contracts on soybean (CBOT), wheat (CBOT), corn (CBOT), gold (NYMEX), silver (NYMEX), and crude oil (NYMEX). (Fung & Hsieh, 2001).

For the merger arbitrage funds they found that the corresponding index had a low correlation with the S&P500, except when there was a sharp decline in the S&P500. So they concluded that the merger arbitrageurs are exposed to risk that can be proxied by an out-of-the-money short put option on the S&P500.

Fung & Hsieh (2002) found that the fixed-income hedge funds are usually exposed to the yield spread, that is, they buy bonds with a lower credit rating and/or less liquidity and then hedge the interest rate risk by shorting U.S. T-bonds.

For the equity long-short hedge funds Fung & Hsieh (2004) found that they are exposed to the stock market (S&P500) and to the spread between the returns of small-cap (Russel 2000) and large-cap firms (S&P500).

To sum up, they constructed a model to regress the index returns of Fund of funds (FoF) Hedge Funds Research, Lipper Tass, CFSB/Tremont, and MSCI to the seven asset based style factors, which are the S&P500, small cap minus large cap, the change in the risk free rate, the change in the lower rated bonds minus the risk free rate, and lookback straddles on bonds, currencies and commodities. They found a high for all the indexes and could therefore reliably benchmark the risks and returns of FoF for hedge funds.

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3. Methodology

In this thesis the performance of all the hedge fund investment category (as defined by Lipper Tass) indexes will be benchmarked against market observable risk factors to ascertain how these indexes have been performing and to get more insight in the relative value of this model for different types of hedge fund strategies. A benchmark is created with what Fung & Hsieh did in their original work of 2004, that is, regressing their ABS factors on the index returns of fund of funds hedge fund strategy. Therefore, a comparison can be made between their original research and the extension of that research done in this thesis (i.e. per investment category). The asset-based style factors of Fung & Hsieh (2004) provide a good explanatory power (i.e. high ). The β’s of these ABS factors represent the degree of exposure (or factor loading) to the benchmark risk and returns per investment category. The index returns per investment strategy is therefore regressed against these risk factors to find if it has a similarly high explanatory power as in the original model in Fung & Hsieh (2004).

The variable S&P500 is the monthly return of S&P500 index. The variable small – large is the monthly returns of the Russel2000 minus the monthly returns of the S&P500. The 10Yield variable is the difference in the month-end 10 year Federal treasury yield. The CRspread is lower rated Baa bonds return minus the 10 year federal treasury yield. Bond Opt is a portfolio of lookback straddle on bond options. The ForOpt is a portfolio of lookback staddle on foreign exchange futures contracts. Finally, CommodityOpt is a portfolio of lookback straddles on commodity futures contracts

Usually, the returns of a traditional asset class index is calculated via a method of equally weighted, price weighted, or value weighted method. However with the average returns per investment strategy of hedge funds these methods have some issues. The distribution of the assets under management of hedge funds is skewed towards the top funds. Less than 25% of the funds hold over 75% of the industry’s capital. So equally weighted returns will then not

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reflect this situation. Also, with an equally weighted calculation the focus will shift to newly established funds, where the backfill bias is the largest. (Fung & Hsieh, 2004)

In their publication of 2004 Fung & Hsieh elaborate why an assets under management weighting scheme would also create problems. First, the quality of the data in historical series of assets managed by hedge fund managers is less reliable than those of conventional asset class returns. Second, most hedge fund strategies have a maximum capacity. This means that large successful hedge funds can close the fund to new capital and stop reporting to the data vendors, thereby distorting the index return series. Third, a return index of hedge funds should represent the risk capital used to achieve the performance, the use of leverage could distort this image. To assume that all hedge fund managers operate a specified leverage ratio is unrealistic. This would bias the index return towards under levered funds and, at the extreme, over accentuate the performance of asset gatherers.

To avoid all these problems Fung and Hsieh use an index of fund of funds, in which all the biases are the least. In this study the assets under management weighting scheme will be used simply because of the absence of a better alternative. Further research for this issue is needed.

After the regressions, that have been done for the complete period, the period was subdivided into 2 intervals and the regressions were performed again. This way a comparison could be made if the models per period differ from each other and/or from the complete period model.

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4. Data

4.1 Choice of databases

The Lipper Tass database was used to acquire the hedge fund index returns per strategy. The Dow Jones Credit Suisse hedge fund indexes were used (reported on the database of Lipper Tass). The requirements that Credit Suisse has for the funds in its database are: A minimum of $50 million assets under management, a minimum one-year track record, and current audited financial statements. Each category index contains at least 85% of the AUM in the respective category and the returns are asset weighted (Credit Suisse, 2015). Furthermore, Lipper Tass provides an index of FoF, which was also used in this regression to benchmark the original results obtained by Fung & Hsieh (2004).

Datastream and the website of the Federal Reserve System were used to obtain the ABS factors. Ang & Kristensen (2012) found that the optimal length of a dataset is between 1.5 and 8.5 years using monthly data. This also falls under what is usually done in research, which is 5 years using daily, weekly, or monthly data (Lewellen & Nagel, 2006) The dataset has to be large enough to generate a high enough power, but also short enough to maintain its relevance. In this thesis a interval of 6 years is therefore used from 2008 to 2013 (72 months).

4.2 Investment Strategies

The primary investment categories used in this study, as defined by Lipper Global

Classification 2014, are: convertible arbitrage, dedicated short bias, emerging markets, equity market neutral, event driven, fixed income arbitrage, fund of funds, global macro, long/short equity hedge, managed futures, and multi strategy.

In table 2 the descriptive statistics per investment strategy have been denoted and in figure 2 the indexed returns per investment strategy are displayed. Three of the eleven

investment strategy indixes had an overall negative return. These were The Tass average FoF, dedicated short bias, and equity market neutral. This is also observable in figure 2. The strategies with the highest monthly average returns were global macro, multi strategy, and convertible arbitrage.

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Table 2. Descriptive statistics for investment strategy index returns

Mean Stand. dev.

Min. Max. Skew. Kurt.

TassFoF -0.0007 0.0155 -0.0541 0.0369 -1.0280 5.2071 Convertible arbitrage 0.0040 0.0288 -0.1259 0.0581 -2.2847 12.2395 Dedicated short bias -0.0111 0.0458 -0.1128 0.0966 0.3927 2.8760 Emerging markets 0.0022 0.0316 -0.1363 0.0696 -1.4938 7.6374 Equity market neutral -0.0031 0.0505 -0.4045 0.0366 -7.1236 57.1967 Event driven 0.0038 0.0211 -0.0575 0.0422 -1.0312 3.9926 Fixed income arbitrage 0.0032 0.0243 -1.4035 0.0433 -3.6314 20.0187 Global macro 0.0049 0.0177 -0.0663 0.0444 -1.1042 6.5102 Long short equity hedge 0.0033 0.0263 -0.0781 0.0523 -0.8404 3.8335 Managed Futures 0.0021 0.0311 -0.0542 0.0661 0.02217 2.0553 Multi strategy 0.0040 0.01968 -0.0735 0.0428 -1.7079 7.5231

Figure 2. Index returns per investment strategy

The indexed returns per investment category from 2008 through 2013 with December 2007 as base. 0 20 40 60 80 100 120 140 160 31 -11 -2007 29 -2 -2008 31 -5 -2008 31 -8 -2008 30 -11 -2008 28 -2 -2009 31 -5 -2009 31 -8 -2009 30 -11 -2009 28 -2 -2010 31 -5 -2010 31 -8 -2010 30 -11 -2010 28 -2 -2011 31 -5 -2011 31 -8 -2011 30 -11 -2011 29 -2 -2012 31 -5 -2012 31 -8 -2012 30 -11 -2012 28 -2 -2013 31 -5 -2013 31 -8 -2013 30 -11 -2013

Multi Strategy Managed Futures Long/Short Equity Hedge Global Macro Fixed Income Arbitrage Event Driven

Equity Market Neutral Emerging markets Dedicated Short Bias Convertible Arbitrage TASSFOF

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14 4.3 Asset-Based Style factors

The seven Asset-Based Style factors, that are used in this study, can be subdivided into 3 categories, i.e., trend following risk factors, equity-oriented risk factors, and bond oriented risk factors.

1. The trend-following risk factors: these are the bond trend-following factor (variable:

PTFSBO), currency following factor (variable: PTFSFX), and commodity trend-following factor (variable: PTFSCOM). All obtained from the website of Duke university1, where Fung & Hsieh wrote their 2001 paper.

2. Equity-oriented risk factors: these are the equity market factor (i.e. the Standard &

Poors 500 index monthly return; Datastream code: S&PCOMP(RI))(variable: S&P500) and the size spread factor (i.e. the Russell 2000 index monthly returns minus the S&P500 monthly total return; Datastream code for Russell 2000: FRUSS2L(RI))(variable: R2-S&P500).

3. Bond-oriented risk factors: these are the bond market factor (i.e. the monthly

change in the 10-year treasury constant maturity yield (month end-to-month end); available at the Board of Governors of the Federal Reserve System2)(variable: 10YTY) and the credit spread factor (i.e. The monthly change in the Moody's Baa yield less 10-year treasury

constant maturity yield (month end-to-month end); available at the Board of Governors of the Federal Reserve System3)(variable: Baa-10YTY).

For the ABS factors the only two positive returns over the chosen interval were the S&P500 and the spread between Russel2000 and the S&P500 (table 3). Most noticeable about this is that the overall performance of the Russel2000 spread had the highest return during the chosen period of all the strategies and ABS factors. The Russel2000 spread also had the highest volatility, while maintaining a positive return in contrast to the Primitive trend following strategies (lookback straddles on bonds, currencies ,and commodities).

Finally the last noticeable variables in this model are the lookback straddles for bonds currencies and commodities, which are all negative and have high volatilities. Figure 3 illustrates this, where the overall performance index of all the ABS factors is graphically represented. 1 https://faculty.fuqua.duke.edu/~dah7/HFRFData.htm 2 http://www.federalreserve.gov/releases/h15/data/Business_day/H15_TCMNOM_Y10.txt 3_{http://www.federalreserve.gov/releases/h15/data/Business_day/H15_BAA_NA.txt}

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Table 3. Descriptive statistics for ABS factors

Mean Stand. dev.

Min Max Skew. Kurt.

S&P500 0.0069 0.0611 -01664 0.1599 -0.6298 -0.6278 Russel2000 - S&P500 0.0103 0.0800 -0.2242 0.2002 0.5326 3.8388 10year treasury yields -0.0001 0.0029 -0.0108 0.0064 -0.5568 4.6582 Baa – 10year treasury yields -0.0000 0.0033 -0.0079 0.0153 1.2330 8.8073 Lookback straddle Bonds -0.0199 0.1680 -0.2663 0.505 1.3313 4.3409 Lookback straddle Foreign Exchange -0.0235 0.2046 -0.2575 0.6922 1.4898 5.3576 Lookback straddle commodities -0.0074 0.1544 -0.2465 0.4144 0.7636 2.8357

Figure 3. Index returns ABS factors

The indexed returns per ABS factor from 2008 through 2013 with December 2007 as base.

0 50 100 150 200 250 300 31 -11 -2007 29 -2 -2008 31 -5 -2008 31 -8 -2008 30 -11 -2008 28 -2 -2009 31 -5 -2009 31 -8 -2009 30 -11 -2009 28 -2 -2010 31 -5 -2010 31 -8 -2010 30 -11 -2010 28 -2 -2011 31 -5 -2011 31 -8 -2011 30 -11 -2011 29 -2 -2012 31 -5 -2012 31 -8 -2012 30 -11 -2012 28 -2 -2013 31 -5 -2013 31 -8 -2013 30 -11 -2013

S&P500 Russel2000 - S&P500

10YearTreasuryYield Baa - 10YTY

Lookback straddle bonds Lookback straddle currencies Lookback straddle commodities

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16 4.4 Biases

Hedge funds are not obligated to disclose their returns, leverage, and investment strategies. This happens on a voluntary basis (to be transparent and/or to attract new investors) to hedge fund data vendors, which supply data to accredited investors. The returns that are disclosed to the data vendors by hedge funds are usually biased.

Firstly, there is instant history (also backfill bias). Hedge funds start reporting when they already have a good track record, i.e. the returns of a hedge fund since inception have already been “good” for some time before it starts reporting them to the data vendors. While funds that perform “poorly” never start reporting to these databases. This causes an upward bias of the overall performance of the hedge funds that are in the database. Fung & Hsieh (2000) found that for a sample of the Lipper Tass database from 1994 to 1998 there was a 1.4% instant history bias per year.

Secondly, the existence of survivorship bias also causes an upward shift of the overall returns of hedge funds. The reason for this is that funds that perform poorly stop reporting to the databases, so that the funds that still remain in the database are the ones that are

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5. Results

In this section the regressions results for the complete model will be discussed and the period subdivided into two time intervals.

5.1 Regression results

In table 5 the regression results are found for the monthly indexed returns per strategy against the ABS factors of Fung & Hsieh (2004).

For the TassFoF return index significant coefficients were found for the S&P500, small-cap minus large-cap (Russel2000 – S&P500), and the credit spread (Baa bonds – 10 year treasury yield) with a of 0.58. This implies that this index has significant exposures to these market observable factors. The index has a positive exposure towards the S&P500, a negative exposure towards the small – large cap spread and a negative exposure towards the credit spread. Overall the TassFoF index had a monthly loss of 0.07%, whereas the ABS factors differed. The S&P500 had a positive monthly average return of 0.69%, the small – large cap spread had positive monthly average return of 1.03%, and the credit spread had a negative monthly average return of 0.0026%. This implies that the TassFoF index profited from its positive exposures to the S&P500, lost with its negative exposure to the small – large cap spread, and gained with its negative exposure to the credit spread. These results are the research benchmark for this study, by recreating the regression performed in Fung & Hsieh’s original work in 2004 for our interval.

For the convertible arbitrage strategy 4 significant variables were found and an of 0.74. A significantly positive α (the constant) was found. The S&P500 had a positive

significant coefficient, while small – large cap spread, the credit spread, and the PTFSCOM (primitive trend following strategy on commodities) had significant negative exposures. The positive α suggests an outperformance of the index after the exposures to the benchmark risk factors (ABS factors). The PTFSCOM had a negative monthly average return of 0.74%. Combined with the ABS returns from the previous paragraph this would imply that the index gained on its positive exposure toward the S&P500, lost on its negative exposure towards the small – large cap spread, gained on its negative exposure towards the credit spread, and gained on its negative exposure toward the PTFSCOM. The relatively high negative exposure

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towards the credit spread and its positive exposure to the market, is to be expected for a strategy whose primary strategy is to profit from pricing differences in the conversion factor of a security.

The dedicated short bias strategy was the overall worst performing strategy and only had two significant variables and an of 0.60. The α was significantly negative, meaning that after exposure to the market risk factor benchmarks it had an unexplained negative return and therefore underperforms its benchmarks. The only significant coefficient was the

PTFSBO (primitive trend following strategy bonds) which was positive. The PTFSBO had a negative monthly average return of 1.99%. This would infer that the dedicated short bias strategy index lost on its positive exposure to the PTFSBO. The positive exposure towards PTFSBO could be expected with the dedicated short bias strategy. To profit by betting on market swings in the bond market.

The emerging markets strategy had 4 significant variables with an of 0.71. The strategy had a monthly average return of 0.22%. It had a positive exposure to the S&P500, a negative exposure to the 10YTY (monthly change in the 10 year treasury yield), a negative exposure to the credit spread, and a negative exposure to the PTFSCOM. The 10YTY had a negative monthly average return of 0.01% and the returns from the other ABS factors are same as in the previous paragraphs. So this would suggest that the strategy index gained on its positive exposure to the S&P500, gained on its negative exposure to the 10YTY, and gained on its negative exposure to the PTFSCOM. Few things can be said about the expectations about the results for this category, knowing that the strategy usually invests in emerging markets, while none of the ABS factors embodies an emerging market index return. Perhaps the S&P500 is highly correlated with emerging markets index returns.

The equity market neutral strategy had two significant coefficients and an of 0.45. It had an average negative performance of 0.31% per month. The significant positive

exposures were to the 10YTY and to the PTFSCOM. This would imply that the index strategy lost on its exposure to 10YTY and on PTFSCOM. For this strategy this result is not

unexpected. Equity market neutral strategy tries to have a zero exposure with market indexes and attempt to profit from superior stock selections.

The event driven strategy had 4 significant variables and an of 0.67. The strategy had a monthly average return of 0.38%. It generated a positive significant α after exposures to the ABS factors benchmarks. Also it had a positive exposure to the S&P500, a negative exposure to the credit spread, and a negative exposure to the PTFSCOM. Inference would

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lead to believe that the exposures to these factors would cause positive gains for this strategy index. The event driven strategy tries to gain from potential mispricing of stocks.

The Fixed income arbitrage strategy had 4 significant coefficients and an of 0.68. The monthly average return for this strategy was 0.32%. It had a positive exposure towards the S&P500, a negative exposure to the small – large cap spread, a negative exposure to the 10YTY, and a negative exposure to the credit spread. All these exposures, except for the small – large cap, would suggest a positive effect on the return of the index. The fixed income strategy attempts to profit from potential securities mispricing, which trade on multiple markets. So, an exposure to the 10YTY and credit spread is to be expected.

The global macro strategy has 3 significant variables and an of 0.30. This strategy had the highest average returns of 0.49% per month. It also generated the highest significant α, after its exposure to its risk factor benchmarks. Furthermore, it had a negative exposure to 10YTY and the credit spread. Implying that they are beneficial to the return of the index in question. Global macro strategy tries to realize return with betting on large trends. So, little can be said what global macro strategy hedge funds expect to be the next big trend.

The long short equity hedge strategy has 2 significant coefficients with an of 0.68. The monthly average returns were for this strategy 0.33%. It had a Significant positive exposure to the S&P500 and a negative significant exposure to the credit spread. Which possibly both would be beneficial for the return of the strategy index. Long short equity hedge strategy could have a net long or short exposure to the S&P500. So, this also falls within expectations.

The managed futures strategy has two only slightly significant coefficients and had the lowest of all the complete period strategy regressions performed, which was 0.21. The monthly average returns were 0.21% for this strategy. It had a positive exposure to the S&P500 and a negative exposure to the small – large cap spread, which would suggest that it would have positive and negative effect, respectively, on the returns on the index.

The multi strategy has the 5 significant variables and an the highest of 0.75. The monthly average returns for multi strategy was 0.40%. It had a positive α after the exposures to its benchmark risk factors. It had a positive exposure to the S&P500 and negative

exposures to the small – large cap, credit spread, and PTFSCOM. Inferring would lead to believe that all would have a positive influence on the return of the index except the small – large cap negative exposure. Not much can be said about what is to be expected for the exposures of the multi strategy category, only perhaps that it would have exposures in various ABS factors.

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In 8 of the 11 strategies the S&P500 ABS factor is significant and therefore suggesting that it is an valuable contribution to this model for multiple strategies. Also noticeable is that for the credit spread ABS factor there were 8 of 11 strategies largely significant, signifying its importance to the model for all strategies.

In table 4 the strategies are categorized by their into three categories. So representing the importance of the model per strategy.

Table 4. ranking

category Strategy

High ( Convertible arbitrage, emerging markets, event driven, fixed income arbitrage, long/short equity hedge, and multi strategy Middle TassFoF, dedicated short bias, and equity market neutral

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Standard error between parentheses

*Significant at the 10 percent level in a two-tailed test **Significant at the 5 percent level in a two-tailed test ***Significant at the 1 percent level in a two-tailed test

Table 5.

Regression on investment category indixes from 2008 through 2013

α S&P500 R2-S&P500 10YTY Baa-10YTY PTFSBO PTFSFX PTFSCOM F-Test

TassFoF -0.0013 (0,0013) 0.2242 (0,0703)** -0.1291 (0.0537)** 0.1336 (0.5798) -2.2036 (0.5252)*** -0.0045 (0.0103) -0.0087 (0.0085) -0.0063 (0.0100) 12.46 0.5768 Convertible Arbitrage 0.0032 (0.0019)* 0.03013 (0.1016)** -0.2162 (0.0776)** -1.2447 (0.8384) -6.5996 (0.7594)*** -0.0048 (0.0149) -0.0077 (0.0123) -0.0371 (0.0144)** 26.38 0.7426 Dedicated Short Bias -0.0064 (0.0037)* -0.1612 (0.2024) -0.2370 (0.1545) -0.5866 (1.6691) 0.6720 (1.5119) 0.0640 (0.0296)** 0.0048 (0.0244) -0.0192 (0.0288) 13.52 0.5966 Emerging Markets 0.0000 (0.0022) 0.3958 (0.1187)*** -0.1495 (0.0906) -1.7564 (0.9786)* -4.9524 (0.8865)*** -0.0196 (0.0174) 0.0011 (0.0143) -0.0314 (0.0169)* 22.26 0.7088 Equity Market Neutral -0.0048 (0.0048) 0.1400 (0.2601) 0.1739 (0.1985) 5.9812 (2.1451)** 0.2222 (1.9431) -0.0495 (0.0380) 0.0307 (0.0313) 0.0657 (0.0371)* 7.49 0.4503 Event Driven 0.0029 (0.0015)* 0.2339 (0.0843)** -0.0899 (0.0644) 0.9319 (0.6957) -2.6304 (0.6302)*** -0.0193 (0.0123) 0.0125 (0.0102) -0.0230 (0.0120)* 18.48 0.6690 Fixed Income Arbitrage 0.0019 (0.0018) 0.2493 (0.0957)** -0.1457 (0.0731)** -2.0388 (0.7895)** -5.0014 (0.7152)*** -0.0094 (0.0140) -0.0150 (0.0115) -0.0127 (0.0136) 19.30 0.6786 Global Macro 0.0042 (0.0019)** 0.1650 (0.1032) -0.1174 (0.0788) -2.8271 (0.8511)*** -2.4661 (0.7710)** -0.0103 (0.0151) -0.0016 (0.0124) 0.0024 (0.0147) 3.88 0.2980 Long/Short Equity Hedge 0.0017 (0.0019) 0.3509 (0.1027)*** -0.1059 (0.0783) 0.4170 (0.8465) -2.7205 (0.7668)*** -0.0125 (0.0150) 0.0063 (0.0124) -0.0238 (0.0146) 19.87 0.6848 Managed Futures 0.0026 (0.0035) 0.3219 (0.1925)* -0.2593 (0.1469)* -2.4307 (1.5875) 0.1235 (1.4380) -0.0121 (0.0282) 0.0177 (0.0232) 0.0370 (0.0274) 2.40 0.2076 Multi Strategy 0.0033 (0.0013)** 0.2817 (0.0683)*** -0.1630 (0.0521)** 0.3358 (0.5628) -3.4628 (0.5098)*** -0.014 (0.0100) 0.0021 (0.0082) -0.0195 (0.0097)** 27.60 0.7512

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22 5.2 Regression for 2 intervals

In this section the results are discussed about the regressions performed for the complete period compared to the regressions for the two intervals of the complete period (i.e., period 1: from 2008 through 2010; and period 2: from 2011 through 2013). The regressions done for the two intervals can be found in the appendix in table 8 and table 9.

The results have been summarized in table 6 and in table 7 the parameters for the

complete, first, and second period are summarized. This table gives a good overview whether the variables are the same or differ for the periods.

Noticeable is that the model that had a high predictive power for some strategies in the complete and first period, had a relative lower in the second period. This is the case with TassFoF (1), convertible arbitrage (2), fixed income arbitrage(7). The coefficients in table 7 also illustrate this drop in for the second period. For some strategies the reverse is also true. Strategies that performed poorly in the complete and first period, surprisingly had a relative high for the second period. This is the case with dedicated short bias (3), Global macro (8), and managed futures (10). It is not clear why this phenomena occurs. The strategies that maintain their high are emerging markets (4), event driven (6) long short equity hedge (9) and multi strategy (11).

Table 6. results

On the horizontal axis 1 is TassFoF, 2 is convertible arbitrage, 3 is dedicated short bias, 4 is emerging markets, 5 is equity market neutral, 6 is event driven, 7 is fixed income arbitrage, 8 is global macro, 9 is long/short equity hedge, 10 is managed futures, and 11 is multi strategy. On the vertical axis are the ’s, c is for the complete period, 1 is for the period from 2008 through 2010, and 2 is the period from 2011 through 2013.

1 2 3 4 5 6 7 8 9 10 11

0.58 0.74 0.60 0.71 0.45 0.67 0.68 0.30 0.68 0.21 0.75 0.70 0.84 0.53 0.80 0.57 0.72 0.76 0.35 0.70 0.26 0.81 0.37 0.42 0.82 0.61 0.66 0.70 0.47 0.51 0.81 0.54 0.68

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Furthermore, what is counter intuitive is the relative high for dedicated short bias, which is 0.53, but has zero significant variables. The same goes for equity market neutral, while having a relative high and few significant coefficients. This brings doubt to the validity of the model for the dedicated short bias category and equity market neutral.

Table 7 also illustrates that the strategies that maintained their high ’s (i.e., emerging markets (4), event driven (6) long short equity hedge (9) and multi strategy (11)) also greatly kept their composure with which variables were significant.

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Table 7. Summary of regressions

This table contains a summary of the parameters per regression (c is for the complete period, 1 is for the period from 2008 through 2010, and 2 is the period from 2011 through 2013). On the horizontal axis 1 is TassFoF, 2 is convertible arbitrage, 3 is dedicated short bias, 4 is emerging markets, 5 is equity market neutral, 6 is event driven, 7 is fixed income arbitrage, 8 is global macro, 9 is long/short equity hedge, 10 is managed futures, and 11 is multi strategy.

1 2 3 4 5 6 7 8 9 10 11 0 0 0 +* 0 0 -* 0 0 0 0 0 0 0 0 +* +* 0 0 0 +*** +** 0 +** 0 0 0 0 +* 0 +** 0 +*** +** +*** 0 +** +*** 0 0 0 -* +*** +*** 0 0 0 +*** +** +** 0 +** +* +** 0 0 +** +*** +*** +** +* 0 +*** +*** +*** +*** -** -** 0 -** -*** 0 0 0 -* 0 +** 0 0 0 0 0 -** 0 -** 0 -** 0 0 0 0 -* 0 -* 0 -** -** -*** 0 0 0 0 0 -* 0 0 0 0 -* 0 -* +** +* 0 0 0 0 -** -** -* -*** -* -*** 0 0 0 0 0 -*** 0 0 0 -*** -*** 0 -*** -*** 0 0 0 0 -*** -*** -* 0 0 0 -*** -*** -*** -*** -*** 0 -** 0 0 -*** -** -** 0 0 0 -*** -*** -** 0 0 0 0 0 0 +** 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +** 0 0 0 0 0 0 0 0 +** 0 0 +** 0 0 +*** 0 0 0 0 0 0 0 -* 0 0 0 0 -* 0 0 0 0 0 -* 0 -* 0 0 -* 0 0 0 0 0 0 0 +** 0 -** 0 0

0 : not a significant coefficient +: a positive significant coefficient - : a negative significant coefficient

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6. Conclusion

In this study the performance of different hedge funds strategies were analyzed and if the seven factor model from Fung & Hsieh (2004) is useful in the analysis of these different strategies. The model that was used, was originally designed for the fund of funds category. It used asset-based style factors as dependent variables. So, in this study a benchmark of the original paper was recreated for the FoF category for this period. Therefore, the returns per investment strategy were regressed upon the ABS factors.

To answer the first part of the research question, how hedge funds have performed from 2008 through 2013, the α’s per regression are observed. If there is a positive α it means that the strategy index return has outperformed its exposure to the risk factor benchmarks (ABS factors). For the complete period there were found 5 significant α’s of which 1 was negative. This was for convertible arbitrage, dedicated short bias (which was negative), event driven, global macro, and multi strategy. For period 1 there were only found 2 α’s. These were for the event driven strategy and the long/short equity hedge strategy. For the second period there were 3 highly significant positive α’s found, namely, fixed income arbitrage, global macro, and multi strategy.

For the second part of the research question, i.e., if the seven factor model is useful per investment category? The ’s of the performed regressions are compared to one another and the benchmark (recreated of the original paper of Fung & Hsieh (2004) for the fund of funds category for the period in this study). Also the composition of the significant variables was taken into account.

Emerging markets, event driven, long/short equity hedge, and multi strategy have consequently high ’s, while greatly maintaining their exposures for different periods. This would lead to believe that the model would be useful in the analysis of these indexes.

Fund of funds, convertible arbitrage, and fixed income arbitrage had high ’s for the complete and first period, but had much lower ’s for the second period. The fund of funds category was the benchmark for this study. So, it is not clear why this occurred. It is possible that the models could be useful for these strategies, but it is ambiguous.

Dedicated short bias and equity market neutral had relatively high ’s, while having few significant variables. Also for a strategy which tries to maintain a net exposure of zero (equity market neutral) to the market it would be unlikely to find many significant variables. Therefore, these strategies probably have less usefulness by applying the seven factor model.

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Finally, the global macro and managed futures strategies have the lowest ’s found in all the regressions and few significant variables. Leading to believe that the model is unfit for the analysis of these strategies.

Further research could find more relevant variables per specific investment strategy, for example, an emerging markets index.

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27

Appendix

Table 8. Regression on investment category indexes from January 2008 to December 2010.

Table 7. Regression on investment category indexes from January 2011 to December 2013.

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Table 8.

Regression on investment category indexes from January 2008 to December 2010

TassFoF -0.0005 (0.0021) 0.2801 (0.0965)*** -0.1837 (0.0747)** 0.5212 (0.8421) -2.2545 (0.6762)*** -0.0020 (0.0178) -0.0170 (0.0134) 0.0056 (0.0179) 9.51 0.7038 Convertible Arbitrage 0.0046 (0.0032) 0.4370 (0.1489)*** -0.3458 (0.1153)*** -2.5638 (1.3000)* -7.3959 (1.0439)*** -0.0465 (0.0275) 0.0026 (0.0207) -0.0541 (0.0277)* 21.45 0.8428 Dedicated Short Bias -0.0083 (0.0073) -0.01805 (0.3391) -0.1754 (0.2627) -1.0153 (2.9607) 0.9577 (2.3774) 0.04611 (0.0627) 0.0340 (0.0472) -0.0784 (0.0631) 4.56 0.5329 Emerging Markets 0.0028 (0.0035) 0.5825 (0.1644)*** -0.3161 (0.1273)** -1.2467 (1.4351) -4.7943 (1.1524)*** -0.0083 (0.0304) -0.0231 (0.0229) -0.0157 (0.0306) 16.07 0.8007 Equity Market Neutral -0.0154 (0.0093) -0.2556 (0.4316) 0.5261 (0.3343) 6.7962 (3.7680)* 0.2096 (3.0257) -0.1154 (0.0798) 0.0583 (0.0600) 0.0683 (0.0803) 5.36 0.5728 Event Driven 0.0045 (0.0025)* 0.3354 (0.1176)** -0.1887 (0.0911)** 0.9754 (1.0269) -2.6262 (0.8246)*** -0.0134 (0.0218) -0.0043 (0.0164) 0.0016 (0.0219) 10.45 0.7232 Fixed Income Arbitrage 0.0008 (0.0034) 0.2728 (0.1583)* -0.1663 (0.1226) -2.8848 (1.3824)** -5.4029 (1.1100)*** -0.0484 (0.0293) -0.0115 (0.0220) -0.0185 (0.0295) 12.53 0.7580 Global Macro 0.0063 (0.0037) 0.2278 (0.1733) -0.1780 (0.1342) -2.6423 (1.5129)* -2.2880 (1.2148)* -0.0116 (0.0320) -0.0239 (0.0241) 0.0203 (0.0322) 2.18 0.3526 Long/Short Equity Hedge 0.0037 (0.0034) 0.4715 (0.1567)*** -0.2316 (0.1213)* 0.8196 (1.3677) -2.7798 (1.0983)** 0.0085 (0.0290) -0.0175 (0.0218) 0.0055 (0.0292) 9.43 0.7022 Managed Futures 0.0105 (0.0058)* 0.3100 (0.2672) -0.2325 (0.2070) 0.8198 (2.3329) 1.8333 (1.8733) 0.0607 (0.0494) -0.0593 (0.0372) 0.1079 (0.0497)** 1.44 0.2643 Multi Strategy 0.0022 (0.0023) 0.3391 (0.1044)*** -0.2240 (0.0809)*** 0.2868 (0.9118) -3.7788 (0.7322)*** -0.0293 (0.0193) 0.0044 (0.0145) -0.0195 (0.0194) 17.39 0.8130

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Table 9.

Regression on investment category indexes from January 2011 to December 2013

TassFoF -0.0020 (0.0020) 0.2046 (0.1275) -0.0418 (0.0889) -1.5224 (1.1750) -2.3217 (1.5681) 0.0004 (0.0153) 0.0004 (0.0137) -0.0071 (0.0135) 2.36 0.3712 Convertible Arbitrage 0.0027 (0.0017) 0.1118 (0.1087) -0.0393 (0.0758) 0.4524 (1.0013) -2.0259 (1.3363) 0.0016 (0.0130) -0.0019 (0.0117) -0.0154 (0.0115) 2.98 0.4270 Dedicated Short Bias -0.0027 (0.0035) -0.4008 (0.2253)* -0.2836 (0.1571)* 3.1555 (2.0758) 4.3578 (2.7703) 0.0336 (0.0270) -0.0093 (0.0242) -0.0007 (0.0239) 18.60 0.8230 Emerging Markets -0.0003 (0.0030) 0.2547 (0.1941) 0.0866 (0.1353) -3.5271 (1.7882)* -4.7089 (2.3865)* -0.0246 (0.0233) 0.0349 (0.0208) -0.0178 (0.0206) 6.34 0.6130 Equity Market Neutral 0.0016 (0.0017) 0.3633 (0.1101)*** -0.0682 (0.0767) 0.1493 (1.0145) -0.1122 (1.3539) -0.0086 (0.0132) 0.0252 (0.0118)** 0.0026 (0.0117) 7.81 0.6612 Event Driven 0.0021 (0.0022) 0.1554 (0.1398) 0.0475 (0.0975) -0.3480 (1.2886) -4.7261 (1.7198)*** -0.0075 (0.0168) 0.0238 (0.0150) -0.0276 (0.0148)* 9.36 0.7006 Fixed Income Arbitrage 0.0043 (0.0009)*** 0.1370 (0.0552)** -0.0853 (0.0385)** -0.9220 (0.5082)* -0.8831 (0.6783) -0.0089 (0.0066) 0.0025 (0.0059) -0.0102 (0.0059)* 3.56 0.4709 Global Macro 0.0035 (0.0016)** 0.2144 (0.1047)** -0.0547 (0.0730) -3.9434 (0.9652)*** -1.7788 (1.2881) -0.0069 (0.0126) 0.0307 (0.0112)** 0.0050 (0.0111) 4.15 0.5093 Long/Short Equity Hedge 0.0006 (0.0020) 0.3393 (0.1299)** 0.0508 (0.0906) -1.3824 (1.1967) -3.9098 (1.5971)** -0.0120 (0.0155) 0.0292 (0.0139)** -0.0187 (0.0138) 17.53 0.8142 Managed Futures -0.0034 (0.0042) 0.8664 (0.2693)*** -0.4574 (0.1878)** -7.5905 (2.4816)*** -1.8131 (3.3119) -0.0213 (0.0323) 0.0840 (0.0289)*** 0.0155 (0.0286) 4.79 0.5451 Multi Strategy 0.0044 (0.0013)*** 0.1767 (0.0862)** -0.0135 (0.0601) -1.2752 (0.7945) -2.7762 (1.0604)** -0.0070 (0.0103) 0.0116 (0.0093) -0.0153 (0.0091) 8.34 0.6759

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