Hedge Funds - Term Paper Example

Hedge Funds Key Questions This paper describes the analysis of information related to a few hedge funds using the Monte Carlo and Historical methods of simulation. The primary objective of this exercise is to provide useful inferences to a potential investor on the distribution on potential returns associated with hedge fund investments. The paper answers to key questions based on this scenario: How confident is the investor of not losing money within a five-year period? How confident is the user of realizing an excess return of 10% per annum? In other words, how confident is the investor in achieving an excess return of at least 50% during the five-year period? Summary of Data The data used for this exercise consists of monthly returns and Assets under Management (AUM) over a period of ten years (September 1999 – August 2009) for over 28 hedge funds. The information on these sample hedge funds was obtained from the EurekaHedge database which stores information on over 21,000 hedge funds. The sample hedge funds follow one of the following strategies typical of financial institutions operating in this domain: Long/Short Equities CTA/Managed Futures Multi-Strategy Arbitrage The table below details results of the results from the Monte Carlo and the Historical simulation methods using the sample data. Historical Monte Carlo         prob Not Losing prob Number of run > 50% Not losing Not Losing prob Number of run > 50% Drift SD Mean   98.90% 9814 13.05% 1,354 98.95% 9865 13.10% 1319 0.45% 1.59% 0.46% Arbitrage 86.56% 8600 53.01% 5,363 86.02% 8532 53.20% 5371 0.76% 5.63% 0.92% CTA/Managed Futures 87.53% 8729 58.98% 5,944 85.10% 8434 56.77% 5779 0.86% 6.65% 1.08% Multi-Strategy 86.98% 8611 55.45% 5,595 87.10% 8661 52.53% 5331 0.74% 5.19% 0.88% Long/Short Equities The above results show that the mean monthly returns (lowest to highest) for each fund class are 0.46% (Arbitrage), 0.88% (Long-Short Equities), 0.92% (CTA-Managed Futures) and 1.08% (Multi-Strategy). The dispersion (Standard Deviation - SD) of returns among these fund classes follows the same order suggesting that Arbitrage funds have the lowest mean and the lowest SD while Multi-Strategy funds exhibit the highest mean and highest SD. Summary of Approaches used The analysis uses both the Monte Carlo and the Historical simulation methods for answering the key questions listed previously. The Monte Carlo Simulation method depends on the formulation of an appropriate model that can suitably explain and analyze the monthly returns used as input for this analysis. To model the behaviour of these monthly returns, the concept of geometric Brownian Motion (BM) was specified (Rubinstein, 2008). The BM used in this context is a Markov Process which simply means that the monthly returns follow a random walk and exhibit behaviour consistent with the weak form of the EMH (Efficient Market Hypothesis) (Robert, 2004). This implies that the Monte Carlo method in this case utilizes the fact that movements in monthly returns are conditionally independent from such movements during previous periods. Under the Monte Carlo Method, a number of iterations for each test case was conducted to analyze the deterministic model configured using a sequence of random numbers generated as inputs. This simulation technique is especially useful when modelling non-linear, uncertain and complex parameters (Hammersley, 2005). On an average, the current simulations utilize between 5500 and 9000 iterations under any given test case. The Historical Simulation method, also known as back simulation, is part of the Value at Risk (VaR) approach which also utilizes a large number of iterations like the Monte Carlo method. As the name suggests, the Historical method depends on past information on monthly returns (unlike the Monte Carlo method that depends on random input) and simulates useful results through the construction of a CDF (Cumulative Distribution Function) of these monthly returns over time) (Dowd, 2009). Key Findings Monte Carlo Method On the question of the chances of earning more than 50%, the number of iterations in both methods was around 5500 with the exception of the Arbitrage class (where the number of iterations was around 1350). The results indicate that the probabilities of earning returns in excess of 50% over a 5-year period were 55% in the case of the CTA-Managed, Multi-Strategy and Long-Short Equity Classes. Based on the lower mean returns for the Arbitrage class, the probability of realizing excess returns in this category was only 13.10% suggesting that investors belonging to this trading strategy were not in a good position to realize their return targets. Although a higher SD is an indicator of enhanced risk, the Multi-strategy class with the highest SD was also found to possess the greatest probability of realizing returns in excess of 50%. The Monte Carlo Method was also used to analyze the probability of not losing any returns during a 5-year period and the number of iterations across all fund classes was significantly higher. The findings reflect the thumb rule that higher returns are associated with higher risk and greater vulnerability (or fluctuations). Although funds belonging to the Arbitrage class were not found appropriate for achieving excessive returns, this class was also found to be the most stable among the four classes and guaranteed a positive return during the 5-year period (probability of not losing in excess of 98%). The remaining fund classes also had high chances of not losing any money although their probabilities were comparatively lesser. The Multi-Strategy class with the highest risk was evidently the category with the lowest probability of guaranteeing no-loss returns to the Investor. Historical Method The simulations using the Historical method consisted of a similar number of iterations as the Monte Carlo method in the case of both questions. The historical trends show a higher probability of excessive returns for the Multi-Strategy class than the Monte Carlo method while the Arbitrage class demonstrated very little chance of guaranteeing any sizeable excessive returns over a 5-year period. Thus, the Multi-Strategy method was the most promising class to provide excessive returns while the Arbitrage class had the least chance of assuring annual returns in excess of 10% to the investor. While the Historical method demonstrated that the best chance of not losing any money lay with the Arbitrage method, a surprising outcome in contrast to the results from the Monte Carlo method was the identification of the CTA-Managed Futures class as the most risky category in this context. From the two methods, it appears that the investor has the least chance of not losing any money by investing in the two highest yielding fund classes (namely the Multi-Strategy and CTA-Managed Futures classes). Possible Limitations The Monte Carlo method is primarily based on randomly generated values and cannot overcome the assumptions made while constructing the underlying model. Further, the Monte Carlo method is a purely statistical approach and not an analytic method and cannot provide deep insights into the findings as the analytic methods (Jackel, 2009). Another limitation with the Monte Carlo method is that the usual assumptions associated with this approach include the presence of normal distributions and the correlation coefficients have a value of zero. Both these assumptions do not hold in financial markets (Rubinstein, 2008). It is therefore important to understand these assumptions that can lead to inconsistent and unrealistic results through the analysis. Gallati (2003) says that the Historical method suffers from the primary limitation that past information on risk factors is not a precise indicator of trends in the future. This method is also incapable of answering various ‘what-if’ scenarios that the Monte Carlo method is capable of given its extensive dependence on random values (Olson, 2008). The Historical method also has the deficiency of imposing various restrictions on the simulation as it wrongly assumes that the monthly returns are independent and distributed in an identical manner (Marrison, 2009). According to McLeish (2005), it is well known that monthly returns are not entirely independent and display dependent behaviour like ‘volatility clustering’. Moreover, the historical method assigns equal weights to all monthly returns within the entire sample period. Such an assumption is inconsistent with the decreasing predictability of the monthly return data as it lies further away from the current timestamp (Best, 2008). Recommendations Given the wide universe of hedge funds, it is recommended that any further simulation exercises incorporate more hedge funds than the current sample size of 28. This will provide a comprehensive overview of the performance of fund categories in broader detail and minimize the chances of errors in estimation. It is also recommended to analyze every candidate hedge fund for reporting efficiency and ensure that only those funds which disclose both positive and negative information on performance are included in the analysis. This requirement arises from the concept known as ‘Survivorship bias’ which is a known problem among indexes that cover hedge or mutual funds. Robert (2004) says that such funds do not have any legal obligation or investor covenants to disclose the entire information pertaining to their performance. Thus, funds are at liberty to choose between the information to report to the outside world and the information to withhold. This provision tends to motivate funds from potentially concealing information that reveals poor performance or inconsistent internal controls. As such, most indexes including the EurekaHedge database may have the deficiency of containing only positive information (or at least a majority of the information may only reflect positive performance) as reported by the constituent hedge funds. Thus, it is recommended that the study incorporate filtering mechanisms that can identify and segregate funds based on the kind of information that they disclose and only consider those that reveal their entire performance data for the analysis. Conclusion The preceding sections describe the results of the Monte Carlo and Historical simulation methods performed on four categories of hedge funds using data on monthly returns over a ten-year period. The analysis has revealed that the Multi-Strategy class has the highest chance of ensuring returns in excess of 50% while the Arbitrage class showed little promise of achieving this target. Likewise, the Monte Carlo method showed the Multi-Strategy class as having the least chance of not losing any money while the Historical method showed that this was the case with CTA-Managed Futures. In either case, the Arbitrage class had the highest probability of ensuring a positive return despite having the least average return among all fund classes. It is recommended that the investor choose an intermediary class, most notably the Long-Short Equities, for further investment as it has an acceptable level in guaranteeing excessive returns and a medium level of probability in assuring a positive return. References 1. Best (2008), Implementing value at risk. New York: McGraw Hill. 2. Dowd (2009), An introduction to market risk measurement. London: Routledge. 3. Hammersley (2005), Monte Carlo methods. Boston: Taylor & Francis. 4. Hill.Gallati (2003), Risk management and capital adequacy. London: Routledge. 5. Jackel (2009), Monte Carlo methods in finance. New York: Wiley. 6. Marrison (2009), The fundamentals of risk measurement. New York: McGraw 7. McLeish (2005), Monte Carlo simulation and finance. New York: John Wiley. 8. Olson (2008), Enterprise risk management. World Scientific. 9. Robert (2004), Monte Carlo statistical methods. New York: Springer. 10. Rubinstein (2008), Simulation and the Monte Carlo method. Chicago: Wiley. Read More