Monte Carlo As a Hedge Fund Risk Forecasting Tool
Total Page：16
File Type：pdf, Size：1020Kb
F eat UR E Monte Carlo as a Hedge Fund Risk Forecasting Tool By Kenneth S. Phillips edge funds have gained The notion of uncorrelated, absolute popularity over the past “retur ns encompassing a broad range of asset Hseveral years, especially among institutional investors. Assets allocated classes and distinct strategies has enjoyed to alternative investment strategies, distinct from private equity or venture great acceptance among conservative inves- capital, have grown by several hundred tors seeking more predictable and consistent percent since the dot-com bubble burst in 2000 and now top US$2.5 trillion. retur ns with less volatility. The notion of uncorrelated, absolute returns encompassing a broad range ” of asset classes and distinct strategies has enjoyed great acceptance among conservative investors seeking more level of qualitative due diligence, may management objectives resulted in the predictable and consistent returns with or may not have provided warnings evaporation of nearly US$6.5 billion of less volatility. As a result, the industry and/or given investors adequate time to investor equity, virtually overnight. has begun to mature and investors now redeem their capital. Although the ar- Global Equity Market Neutral range from risk-averse fiduciaries to ag- ticle implicitly considers different forms (GEMN). Since 2003, GEMN had gressive high-net-worth individuals. of investment risk such as leverage managed a globally diversified, equity As the number of hedge funds and and derivatives, it focuses primarily on market neutral hedge fund. Employ- complex strategies has grown, so too quantitative return-based data that was ing various amounts of leverage while have the frequency and severity of publicly available rather than strategy- attracting several billion dollars of negative events—what statisticians refer or security-specific risk. For illustrative investor equity, the fund had developed to as “negative tail risk.” Five-sigma purposes this article does not target an excellent history of low-volatility, (5s) drawdowns, which many argue are any specific strategy and considers a) a uncorrelated, consistently positive re- unpredictable and rare, are occurring multi-strategy fund, b) a global equity turns. Despite the strategy’s investment with increasing frequency. During such market neutral fund, and c) a levered objectives and track record, however, at episodes the finger of blame almost credit/bond fund. maximum drawdown in August 2007 always points to the elusive concept of Multi-Strategy (MS). MS was this market neutral fund had lost ap- “liquidity”—that difficult-to-quantify perhaps the most notorious hedge fund proximately 35 percent of its value. elephant in the room that behaves well failure since Long Term Capital Man- Levered Credit/Bond (LCB). until it doesn’t. To be sure, liquidity (or agement in 1998. Formed in 2000 as a Backed by a major U.S. bank known for illiquidity) can be correlated closely low-volatility, relative-value/arbitrage its fixed-income trading expertise, LCB with falling prices and can be either fund, MS rode the wave of institutional was launched in 2003 and had never systemic or non-systemic—depending hedge fund popularity and grew to experienced a negative month until it on which argument suits your purpose more than US$9 billion before experi- lost 100 percent of its value around May at the time. But illiquidity doesn’t occur encing a 70-percent loss in September 2007, shortly after its first negative event. in a vacuum. When prices adjust, usu- 2006. The loss represented a remarkable All three of these incidents had sever- ally it’s for a reason, and an early signal failure of risk management that largely al things in common: a) each had “world often telegraphs the change. resulted from highly concentrated posi- class” management and sector expertise, This article examines three recent tions in what historically had been an b) each was a successful business with hedge fund failings and considers esoteric sector of the futures markets. notable institutional investors for clients, how quantitative analyses of historical This gigantic departure from the firm’s c) two were affiliated with internationally performance, combined with a realistic historical investment strategy and risk- acclaimed U.S. banks, d) all had impres- 20 Investments&Wealth MONITOR © 2008 Investment Management Consultants Association. Reprint with permission only. F eat UR E sive risk-management guidelines and TABLE 1: QUantitative HISTORICAL PERFORMANCE Data dedicated personnel, and e) all appeared MS GEMN LCB too large and sophisticated to fail. Sep 00–Mar 06 May 03–Jul 06 Oct 03–Mar 07 This article looks at the data avail- 1. Length of 67 months 39 months 42 months able to prospective investors before Track Record each negative event and considers how 2. Annualized it may have been misused, misunder- 16.58% 15.81% 11.72% stood, or simply inadequately managed. Return Was the potential magnitude of these 3. Annualized losses simply ignored by investors, Standard 5.93% 7.07% 2.83% Deviation which in every case included several 4. Sharpe prominent global risk-management 1.81 1.43 2.22 Ratio teams? Was the historical data not robust enough to reveal the risks? Or 5. Percent Profit- 79.10% 82.05% 97.62% did investors become lazy and/or com- able Months placent? The conclusion also considers 6. # of Profitable 53 32 41 how emotions may have influenced Months investor decisions when empirical data 7. Percent Nega- become opaque, and how notions of 20.90% 17.95% 2.38% trust and goodwill, based on past per- tive Months formance, may have influenced and/or 8. # of Negative 14 7 1 delayed investor decision making. Months Table 1 shows historical perfor- 9. Maximum mance data for each fund. This informa- –4.37% –3.48% –3.50% Drawdown tion was readily available from several industry sources, although MS and LCB stopped reporting when their funds investors still would not have dissuaded would have provided an investor with failed (an important survivor-bias con- most investors. Simply stated, absent a adequate information for effective sideration when evaluating hedge fund subjective dislike for the specific fund decision making. This article does not indexes and peer group comparisons). or strategy, all lights appeared green. meaningfully consider the full range of Before their problem periods, all three hedge fund related risks such as illiquid- Monte Carlo Forecasting funds boasted attractive risk–return ity due to initial investment lock-ups, characteristics, superior Sharpe ratios, Monte Carlo forecasting (stress testing) infrequent redemption rights and and generally appeared to be delivering techniques are among the best, though notice periods, or the use of “gates” to on promises of absolute returns. Each certainly not the only, statistical meth- halt or limit redemptions when a fund fund had a relatively long track record, ods for estimating risk and gain/loss is receiving lots of withdrawals. Hedge especially for such a young and rapidly probabilities. Integrating Monte Carlo fund investors can and should consider growing industry. with historical correlations results such risk factors before investing, or Before each failure, none of the in value-at-risk (VaR) data, but basic risk learning that a necessary or desired funds ever experienced a meaningful Monte Carlo forecasting without cor- redemption may be unavailable for loss (drawdown) and each had a favor- relations also provides a robust data several months. able batting average, i.e., the ratio of stream. Monte Carlo techniques can be The three best-known methods of winning months versus losing months. used to develop and actively manage Monte Carlo forecasting—GARCH, From a statistical perspective, an risk budgets and optimally size invest- normal, and bootstrap—provide different investment in any of these funds would ments. Other risk measures, such as ranges of best- and worst-case estimates have appeared prudent. More detailed the Omega ratio,1 also can be useful but by employing different variable-relax- qualitative due diligence, including may not place adequate emphasis on ation techniques. Each method is good office visits, meetings with manage- downside risk by assuming that positive at forecasting returns although GARCH, ment, review of risk guidelines, analyses and negative fat tails are uncorrelated.2 which provides the greatest relaxation of of due diligence questionnaires, and This article focuses on whether the variables, generally forecasts both higher conversations with prime brokers, audi- historical performance of a particular highs and lower lows. Said differently, tors, fund administrators, and existing fund and Monte Carlo forecasting although the 50th-percentile forecasts of March/April 2008 21 © 2008 Investment Management Consultants Association. Reprint with permission only. F eat UR E TABLE 2: MONTE CARLO DISTRIBUTIONS (FORECASTS) OF MAXIMUM DRAWDOWNS* Forecasted Loss Forecasted Loss Forecasted Loss Maximum Drawdown Confidence Levels ~ # Std Dev “MS” “GEMN” “LCB” 1/1,000 99.9% ~4–5 sigma (s) –12.51% –14.00% –9.37% 1/100 99% ~3 sigma (s) –6.19% –10.65% –6.88% 5/100 95% ~2 sigma (s) –4.59% –8.15% –6.88% 10/100 90% –4.20% –6.99% –4.22% 70/100 70% ~1 sigma (s) –2.78% –5.21% –3.50% * Monte Carlo forecasts are not readily translated into standard deviation statistics, thus we show an approximate standard deviation (sigma [s]). One standard deviation should capture 68 percent of observations, two standard deviations should capture 94 percent of observations, and three standard deviations should capture 99 percent of observations. The Monte Carlo simulations above go beyond three standard deviations, to 99.9 percent, estimated to be nearly five standard deviations. Of course, standard deviations measure the expected range of returns around the “mean” return; this article does not attempt to address the potential disconnects between Monte Carlo best- and worst-case forecasts and the use of standard deviation to model risk.