Empirical Results - Banking - Lecture Slides, Slides of Banking and Finance

Download Empirical Results - Banking - Lecture Slides and more Slides Banking and Finance in PDF only on Docsity! 9 unique way of interpreting them qualitatively. The conventional way of interpreting these components is to think of them as uncorrelated factors (across components) each representing a source of systemic risk. Relating the ABS factors to these principal components thus help us identify the systematic risk factors common to funds in the same component. 3. Empirical results ABS factors better capture hedge fund return characteristics A simple way of assessing how ABS factors contribute to our understanding of hedge fund returns is to look at how well they explain hedge fund returns. Recall from Figure 1 that conventional asset class indices have low correlations to hedge fund returns. Another way of describing this observation is that a hedge fund style equation using conventional asset class indices will have low explanatory power when applied to hedge fund returns. Figure 2 illustrates how much improvement can be achieved when we replace the conventional asset class indices by ten ABS factors. Figure 2. Distribution of R²s Vs ABS Factors 0% 5% 10% 15% 20% 25% 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Fr eq ue nc y Hedge Funds This figure updates Figure 1 in two aspects. Firstly, it uses individual hedge fund data from the TASS database ending April 2001. Secondly, it uses ten ABS factors that are related to the main hedge fund styles we have analyzed thus far. There are four ABS factors for equity hedge funds: the S&P, Small Cap-Large Cap stocks, Value-Growth stocks, Emerging Market equities. There are 3 ABS factors for fixed income hedge funds: High Yield bonds minus 10Y Treasury, Convertible bonds minus 10Y Treasury, Mortgage bonds minus 10Y Treasury. There are also 3 ABS factors for trend-following strategies: lookback straddles on bonds, currencies, and commodities. Comparing Figures 1 and 2, we see that the rightward shift of the ‘black’ bars , which indicates that the ABS factors can explain hedge fund returns better than standard asset- class indices. Capturing the dynamic style allocation of hedge fund portfolios using ABS factors Docsity.com 10 While the results in Figure 2 can be repeated using different sampling techniques to demonstrate the robustness of the results, the approach is not designed to capturing the time varying style allocation of diversified hedge fund portfolios.7 The next example illustrates how a simple model with only a handful of ABS factors can capture most of the return variations of large hedge fund portfolios. To demonstrate the concept, we use the Hedge Fund Research’s (HFR for short) fund- of-hedge funds (FOF for short) index to proxy the typical performance of a diversified hedge fund portfolio. In terms of risk factors, we use two ABS factors for equity hedge funds (S&P, Small Cap minus Large Cap stocks), two for fixed income hedge funds (changes in the 10Y government bond yield, and changes in the Baa-10Y bond yields), and three for trend-following funds (lookback straddles on bonds, currencies, and commodities). These choices are meant to represent risk factors in the most likely hedge fund styles. We test for coefficient stability using one-period ahead recursive residuals. Under the null hypothesis of no parameter change, the recursive residuals are normal, with mean 0 and variance 1. The cumulative recursive residuals have mean 0 and variance T, where T is the number of periods over which the residuals are cumulated. The null of parameter constancy is rejected in March 2000. Thus we ran the HFR FOF regression in two samples: Jan 1994-Feb 2000, and Apr 2000-Dec 2002. Figure 3 graphs the actual and fitted monthly returns of the HFR FOF index. It shows that the small number of risk factors can reliably model the returns of large hedge fund portfolios. Figure 3. Actual vs Fitted HFR FOF Index -10% -8% -6% -4% -2% 0% 2% 4% 6% 8% Dec- 89 Dec- 90 Dec- 91 Dec- 92 Dec- 93 Dec- 94 Dec- 95 Dec- 96 Dec- 97 Dec- 98 Dec- 99 Dec- 00 Dec- 01 Dec- 02 M on th ly R et ur n Actual Fitted 7 A frequency plot of the explanatory power from a multiple regression across individual hedge funds is designed to capture the cross-sectional characteristics of the regression equation. Although it is possible to repeat the exercise over different sampling periods, the results remain specific to the reference sample period. It will not capture the process that governs the time variation of the multiple regression statistics. In addition, it is unlikely that such a process will work for all funds individually. A better starting point to analyze time varying behavior of the factor coefficients is to look at portfolios of hedge funds. Docsity.com 13 An immediate application of this concept is the refinement on the portability of hedge-fund alphas. It is commonly accepted that hedge fund returns are portable alphas given the low historical correlation between hedge fund returns and conventional asset class indices. What the above decomposition shows is that not all hedge fund alphas are born equal. Some are more portable than others and the ABS factors help us measure the ex-ante correlation between the systematic component of hedge fund style returns and conventional asset class indices. We can represent the portability of hedge fund alphas via the ABS equation as follows: Alternative alpha + Σ (βi * ABS factori ) Completely portable Partially portable depending on correlation of ABS factors and conventional asset class indices Application to Risk Management An important advantage of linking the systematic component of hedge fund returns to observable market prices via the ABS factors is the ability to simulate the risk of hedge fund strategies over long economic cycles. Consider the following example: During the second quarter of 1997, one can establish the following ABS equation for fixed- income arbitrage hedge funds: (HER) Fixed-Income Arbitrage Hedge Fund Index Returns= 0.96%-5.37*(Change in credit spread) Define the credit-spread variable in the same way as in the four-factor model of hedge fund portfolio (Baa yield –ten year Treasury. We can see from this equation that a +/- 1% change in credit spread will impact the monthly return of fixed-income arbitrage funds by –4.41%/+6.33%. From the risk management perspective, it is important to know the likelihood of a 1% adverse move in credit spread. Figure 5 plots the movement of the credit-spread variable over the ten-year period from July 1987 to July 1997. The maximum range over this ten-year period is 1.1%. One may conclude from this that a 1% adverse move is a low probability event. However, if one extends the plot in figure 5a to the beginning of 1970, a different picture emerges. Here, a 1% adverse move in the credit- spread variable is a much more likely event. The point here is that the ability to extend stress tests over a wider range of economic cycles using the ABS factors helps to refine one’s assessment of risk during extreme markets. Over the period June 30th to October 16th, credit spread widened by 110bp. A highly leveraged fund using fixed-income arbitrage strategies, like Long-Term Capital Management (LTCM), would have experienced substantial loss over that period.9 9 Prior to the fall of 1998, LTCM’s returns were easily 4 times more volatile than the HFR fixed-income arbitrage index. Using this as a crude approximation, the credit spread expansion during the July to October period in 1998 would have cost LTCM in the region of –15.3%. The actual loss of LTCM over this period was –44.8%. Thus this single variable would have accounted for approximately one-third of LTCM’s losses. Docsity.com 14 Figure 5. Moody's Baa - 10Y Treasury Spread: Jul 1987 to Jul 1997 0.0% 0.5% 1.0% 1.5% 2.0% 2.5% Jul-87 Jan-88 Jul-88 Jan-89 Jul-89 Jan-90 Jul-90 Jan-91 Jul-91 Jan-92 Jul-92 Jan-93 Jul-93 Jan-94 Jul-94 Jan-95 Jul-95 Jan-96 Jul-96 Jan-97 Jul-97 C re di t S pr ea d Figure 5a. Moody's Baa - 10Y Treasury Spread: Jan 1970 to Jul 1997 0.0% 0.5% 1.0% 1.5% 2.0% 2.5% 3.0% 3.5% 4.0% 4.5% Jan-70 Jan-72 Jan-74 Jan-76 Jan-78 Jan-80 Jan-82 Jan-84 Jan-86 Jan-88 Jan-90 Jan-92 Jan-94 Jan-96 C re di t S pr ea d Just as ABS factors can be applied to refine investor’s stress test estimates, it can also be used to identify diversifying styles during stressful markets. Fung and Hsieh (1997) noted the inverse performance characteristics of trend-following funds to global equity markets. Subsequently, this empirical regularity was modeled and verified in Fung and Hsieh (2002). Table 2 provides out- of-sample (in the sense that these are data points not used in the construction of the model) comparisons of the Fung and Hsieh (2001) model to Zurich/MAR trend following index during large down moves of the S&P 500 index. Docsity.com 15 This table is extracted from Fung and Hsieh (2002). It shows how the trend-following factor can be used to generate large positive returns during periods of large equity market declines. The periods marked with an asterisk represent out-of-sample forecasts of our original model (Review of Financial Studies, 2001). During all large equity market declines, trend-followers (as proxy by the Zurich Trend Followers Index) did well delivering large positive returns (consistent with the ABS Factor returns except for one period in 2000 where the ABS factor incorrectly predicted a negative performance for trend-following funds). The same pattern persisted into 2002, where during the period April to September 2002, the S&P 500 index declined by 31.9%, the trend- following ABS Factor predicted a return of 11.1% versus a return of 28.2% from the Zurich Trend Followers index.10 These results illustrate how the trend-following ABS factor can be used to provide large, positive returns during periods when conventional equity markets are under stress. 5. Concluding remarks Overall, ABS factors help us to decompose hedge fund returns into systematic and idiosyncratic components. This in turn helps investors differentiate between diversifying versus correlated hedge fund styles in an ex-ante setting. Ex-post, ABS factors help investors identify alphas adjusted for systematic style risks. ABS factors help enhance the integration of hedge funds into the conventional asset allocation process in a consistent manner. By linking hedge fund returns to market prices, ABS factors help to overcome the data limitation of hedge fund returns in conducting stress tests. In time, more ABS factors will be identified as the body of research on this approach grows. The following list of ABS factors extracted from Figure 4 illustrates how far we have come over the last three years. 10 There is often a scale difference between the trend-following ABS factor’s return versus the actual trend- following funds. This is due to the fact that no financial leverage is assumed in the construction of the ABS factor. T a b le 2 . R e t u r n s D u r in g E x t r e m e D e c lin e s in t h e S t o c k M a r k e t P e r io d s o f Z u r ic h T r e n d A s s e t - B a s e d L a r g e D e c lin e S & P 5 0 0 F o llo w e r s S t y le F a c t o r S e p - N o v o f 1 9 8 7 - 2 9 .6 % 1 1 .7 % 1 2 .9 % J u n - O c t 1 9 9 0 - 1 4 .7 % 2 3 .5 % 2 8 .5 % J u l- A u g o f 1 9 9 8 * - 1 5 .4 % 9 .4 % 5 .6 % S e p - N o v 2 0 0 0 * - 1 3 .1 % 6 .5 % - 5 .0 % F e b - M a r 2 0 0 1 * - 1 4 .9 % 9 .3 % 3 .6 % A u g - S e p 2 0 0 1 * - 1 3 .8 % 9 .2 % 3 .9 % Docsity.com