Monte Carlo As a Hedge Fund Risk Forecasting Tool

F eat u r 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-

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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

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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. In the world of hedge fund analyses, it is more common to model worst-case scenarios (maximum drawdown) in absolute terms rather than in terms of distributions around the mean. Hedge fund performance tends to be evaluated ultimately on an absolute rather than relative return basis.

all three techniques are generally similar, 9.37 percent versus actual losses of 70 Simply noting that past performance the best- and worst-case scenarios will percent, 35 percent, and 100 percent, is not indicative of the future is anti-cli- differ greatly. Although we generally have respectively. In other words, events matic, useless, and needlessly fatalistic; experienced good risk-management re- forecasted to occur once every 1,000 investment managers and consultants sults with Monte Carlo, these three funds months (or every 83.3 years) occurred must dig deeper and find ways to better lost substantially more than forecasted within 49 months, on average, of the anticipate and prepare for these events. at the 99.9-percent (1/1,000) confidence launch date of each fund—despite Building well-diversified hedge fund level using bootstrap methodology. alleged management quality and risk- portfolios with a stress-tested, forecast Table 2 reveals the worst-case maxi- management disciplines. 1/1,000 (99.9-percent) likelihood of mum drawdowns forecasted using the Absent a negative predisposition to- each fund losing a significant amount bootstrap method of Monte Carlo over ward these funds and/or their strategies, may provide initial comfort, but only the periods shown in table 1. We pur- little statistical data warned a prospec- until you are reminded that this 1/1,000 posely used these periods because they tive investor of the risks or magnitude of knock-out risk exists with each of historically were “typical” for each fund; future loss. My firm, for example, never your underlying investments. Naïve the majority of investors would have has favored the mortgage loan space diversification into an equally weighted made initial investment decisions based and, as a result, had little interest in the portfolio of 40 underlying funds results on these return patterns. The months LCB mortgage fund, irrespective of its in average allocations of 2.5 percent per immediately subsequent to these attractive track record. Our firm’s deci- investment, which surely would limit periods would have provided a different sion to avoid the space was not based the damage from any one bad invest- Monte Carlo view of each fund’s risk- on expectations of loss or any quarrel ment. But this structure still results in a and-return profile due to each fund’s with management. Other investors may statistical 40/1,000 (i.e., 1/25) monthly increased volatility, potentially offering not have favored super-large funds such probability of experiencing a similar prospective investors different (i.e., as MS or the leveraged equity market event because you now have 40 invest- greater) risk scenarios. This article fo- neutral sector. Either way, I’ve seen no ments that each have a 1/1,000 chance cuses only on the data reasonably avail- study that meaningfully claims to have of blowing up. Increasing the size of able to prospective or existing investors forecasted the large losses these funds your individual allocations can lower before the negative events, exclusive of experienced. The resulting damage from this probability, although the direct those bad months when the problems these investments is like what RCG damage incurred by one bad investment were becoming statistically apparent. Principal Ron Surz and his former col- would be proportionally greater. The actual drawdown of each fund league Frank Myer (Glenwood Funds) The answer, we believe, is to identify was meaningfully greater than the refer to as “airplane risk”: You know signals that may correlate with fund Monte Carlo forecast at the 99.9- the risk is there, but nothing specific implosions and to move aggressively percent confidence level. In each case, stops you from boarding the plane. And, to protect assets when they occur. losses were characterized as rare, 5+s much like a passenger on a problem Bernoulli odds ratio estimation, which events. The maximum bootstrap-fore- flight, an investor can do little in a attempts to explain why a coin flipper casted drawdowns for MS, GEMN, and hedge fund crisis because of limited and might flip “heads” five times in a row LCB were 12.5 percent, 14 percent, and lengthy redemption policies. with only a 50–50 chance on each toss,

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also may explain why a hedge fund investor might, or might not, have had Had the early volatility all been negative, investments in all three of these funds. “it’s likely that investors would have redeemed The information below doesn’t offer any proprietary secrets for avoiding these quickly. Positive beta is the addictive drug of hazards, but it does consider how a more rigorous and disciplined quantita- our industry; it requires tremendous discipline tive approach based upon Monte Carlo to cut winning positions. forecasting may have helped investors mitigate or totally avoid losses from ” these (or other) funds. Multi-Strategy. In 2004 MS in- ately and considered full redemption. the fund had experienced annualized formed investors of a change that would Unfortunately for many investors, MS’s returns of 11.7 percent with an annual- result in allocating a portion of the redemption terms were annual with ized standard deviation of 2.8 percent, fund to trading energy futures. A key 90-days notice or a 4-percent penalty. resulting in a Sharpe ratio of 2.20. The member of the original energy team left Many investors submitted redemptions quantitative historical data provided no the firm shortly thereafter and a new before September 2006, but few fully clue to a problem. head of energy trading was appointed. appreciated the risks and therefore were Conclusion Monthly letters revealed increasing unwilling to pay the 4 percent. allocations to this sector, although the Global Equity Market Neutral. Each of the funds we’ve considered had actual extent of the capital commit- The GEMN fund returned 18.4 percent superior management and an attractive ment may not ever have been clearly in 2004 and 20.2 percent in 2005. track record. Although two of the three or fully revealed. In September 2005, a During 2006 the fund was down 1.1 funds had experienced 3s events before full year before the fund failed, MS had percent following losses of 3.5 per- blowing up, much of that volatility had a positive return of 6.2 percent, nearly cent and 6.7 percent in October and been upside volatility. Investors were twice the return of any prior month November. The 6.7-percent Novem- making money, so much of that risk was except August 2005 (the prior month), ber loss was nearly twice the largest ignored. Had the early volatility all been which was up 4.4 percent. Monte Carlo prior monthly loss and approached a negative, it’s likely that investors would analyses suggest, in hindsight, that this 3s event. Increasing volatility led to a have redeemed quickly. Positive beta positive return was nearly a 3s event, positive 5.74-percent return in January is the addictive drug of our industry; it but it largely was ignored because it 2007, but a 6.6-percent loss in July 2007 was a positive variance, leading most revealed that volatility still was increas- Selecting example investors to think they were either lucky ing and that 3s events were becoming funds for this article: or smart. Monthly returns and volatility more frequent. In September the fund increased, and in April 2006 the fund melted down with a 5+s event—well 2007 was a year of extremes. posted a +13.1-percent return. How- beyond the 99.9-percent Monte Carlo In the hedge fund world more ever May 2006, the following month, forecasts. This fund had favorable re- directly than anywhere else, large brought the first serious negative loss; demption terms: monthly liquidity with losses for one investor equate the fund was down 10.5 percent. It 30-days notice. By acting quickly on to large gains for another. Many quickly became obvious that the large the empirical data showing increasing funds had extreme results; John monthly gains had correlated with an volatility rather than delaying and dis- Paulson’s funds, which were short increasing probability of loss. Four cussing with management, an investor in the subprime mortgage space, months later, MS lost nearly 70 percent would have had ample time to redeem. boasted returns of between 100 in a single month. Instead most investors chose to speak percent and 500 percent for the With the benefit of hindsight, we with management and received verbal year. Many other funds expe- know that the September 2005 return assurances that problems were “under rienced their largest losses and of 6.2 percent was a preview of coming control,” and then got caught in the several failed. The three funds attractions, a 3s event that represented fund’s collapse. selected for this article were substantial and inadequately disclosed Levered Credit/Bond. LCB is selected randomly; indeed, this style drift. Any investor bound by more of a conundrum; it had never past year provided no shortage of strict risk-budget guidelines should experienced a down month before subject matter in this area. have reduced his position immedi- its negative event. Since its inception

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requires tremendous discipline to cut call. Given the liquidity constraints received his education at Colorado winning positions. of hedge funds, a redemption notice State University. Contact him at A call-to-action sounds whenever (which often can be withdrawn) is the [email protected]. returns land outside the predictive bands only prudent weapon against a rogue Endnotes of Monte Carlo risk budgets. Whether manager or a faulty hedging scheme. Of the volatility is positive or negative, we course, management discussions that 1 See Ana Cascon and William F. Shadwick, believe it is time to resize and/or redeem assure investors that “everything is under “New Statistical Tools from Omega Func- positions. The Omega ratio tends to for- control” are normal and customary (the tions,” London: The Finance Development give positive volatility; we believe that in Stockholm Syndrome)—few managers Centre (August 6, 2005). Available at http:// practice this is an error and may lead to ever admit to being out of control or vol- www.allaboutalpha.com/doc_bin/newstatis- bad results. Indeed, monthly returns that untarily share problems with investors. ticsomegafnsfinal.pdf. are 2s or 3s outside the expected range It’s the data that supports the conclusion 2 Mean-variance optimization, while com- are signals of style drift and increasing that investors could have avoided both mon with traditional investment strategies, risk and/or illiquidity. Leverage only the MS and GEMN meltdowns by using is not as useful with hedge funds because exacerbates the situation, and if equity Monte Carlo forecasting and strict risk- hedge fund returns are not normally dis- ratios decline and margin calls are made, budgeting guidelines. tributed. Although a diversified portfolio of the combination can be disastrous. hedge funds initially can benefit from pas- When returns begin to fall outside the Kenneth S. Phillips is chief invest- sive mean-variance optimization, we have Monte Carlo forecasted range of expec- ment officer of RCG Capital Advi- come to believe that hedge fund investors tations, don’t call the portfolio manager sors, LLC in Boulder, CO, an invest- should be more concerned with fund-specif- and/or the fund’s marketing personnel. ment management firm specializing ic risk and should take an active role toward Push the redemption button first, then in alternative investments. He risk budgeting.

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