Institutional Investor's Alpha Magazine - December 2008 / January 2009 - (Page 36)

Gaming the System sequence of returns need not correspond to the track record of an actual manager; it sufﬁces that the record look as if it could have been generated by a manager with real talent. The technique for achieving this, which we call piggybacking, is simple and almost costless to implement. It is not the same as replication or cloning, which are strategies designed to reproduce the statistical properties — that is, the sources of returns and the corresponding risks — of a given hedge fund or class of funds. The point of piggybacking is to reproduce a speciﬁc sequence of returns with a high degree of probability. In this way the fund manager earns the performance or incentive fees associated with these returns and attracts new money into his fund just as if he were a star manager. Let’s say you want to deliver a performance record like that in Figure 1. Managers with similar records are lionized and attract large amounts of money. In fact, it is surprisingly easy to duplicate this performance using the piggybacking strategy as long as investors can’t see your positions, and as long as you are willing to accept a small annual probability that your fund could go bust. FIGURE 1: CUMULATIVE TOTAL RETURN FOR HYPOTHETICAL HEDGE FUND VS. S&P 500 INDEX 4.0 3.5 Hedge Fund 3.0 Total Value 2.5 2.0 1.5 S&P 500 1.0 0.5 0.0 1 998 1999 2000 2001 2002 2003 2004 2005 2006 2007 January 1998 – December 2007 FIGURE 2: CUMULATIVE TOTAL RETURN FOR PIGGYBACKING VS. RISK-FREE BOND YIELDING 4 PERCENT* 4.0 3.5 Piggybacking 3.0 Total Value 2.5 2.0 1.5 Risk-Free Bond 1.0 0.5 0.0 1 998 1999 2000 2001 2002 2003 2004 2005 2006 2007 January 1998 – December 2007 *The size of the piggybacked return is varied from year to year, the average being 10 percent. Source: Foster and Young. Here’s how to do it: At the start of the year, invest all your funds in the S&P 500. Once a year take a short position in a bundle of asset-or-nothing puts on the S&P 500 that have a nearby expiration date. (An asset-or-nothing put pays out one share of the index if and only if the closing price is less than the strike price on the expiration date. You can create such a derivative by combining a plain-vanilla European put with a cash-or-nothing put, both of which are routinely traded on exchanges.) Let α be the target amount by which you plan to inﬂate your total return over the next 12 months — the amount of fake alpha. For example, to achieve the result in Figure 1, you would take α = 0.07, which will generate an annual return that is 7 percent higher than the return on the S&P 500. Once you have established the target value of α, choose the strike price so that the options are exercised with probability α/(1 + α). In our present example, the strike price would be chosen so that the probability of exercise is approximately 0.07/1.07 = 0.065, or 6.5 percent. Now go short the maximum number of puts you can cover. The idea is to go for broke: If the puts are exercised, the fund will be cleaned out; but if they are not exercised, you will increase the number of shares in the fund by the factor (1 + α).1 In the latter case you just sit back and wait until the end of the year (or any 12-month period), at which time you report that the fund grew by a factor of (1 + α) times the total return on the S&P 500 in that year. (During the entire time you have been fully invested in the S&P 500, which you used as collateral on your options position.) To the investors it looks as if you generated excess returns, and you collect a substantial performance fee. In reality you took a gamble and got lucky. There is always the chance your fund will go bust, but this is not much of a deterrent. The reason is that piggybacking generates sizable values of alpha without much risk. As we have just seen, for example, you can generate alpha of 7 percent a year, and the risk of crashing is only 6.5 percent a year. Of course, someone’s suspicions might be aroused by the fact that the fund is returning exactly 7 percentage points more than the S&P 500 year in and year out. However, this can be avoided by varying the target amount of fake alpha from one year to the next. In some years you might inﬂate the index’s total return by 5 percent, in other years by 9 percent, and so forth. The same basic method can be used to re-create any target sequence of returns that you choose. Using the piggybacking strategy, you can generate M times the return on the S&P 500 (or any other market portfolio) with a probability of at least 1/M over any range of time you choose. For example, you can deliver twice the total cumulative return on the S&P 500 over ﬁve years, or ten years, or any other target period, and the chances are one in two that your fund will not crash before then. You can deliver three times the return on the S&P 500 over any target period and the chances are one in three the fund will not crash, and so forth. Naturally, the more you pump up returns by these methods, the higher the probability that the fund will crash. As 36 • INSTITUTIONAL INVESTOR’S ALPHA • DECEMBER 2008/JANUARY 2009

Table of Contents Feed for the Digital Edition of Institutional Investor's Alpha Magazine - December 2008

Institutional Investor's Alpha Magazine - December 2008 Contents Letter from the Editor Longs & Shorts Inside the Trade Pension Corner The Good Guys Interview: Stanley Fink Cover Story: The New Regulatory Reality United States: The Usual Suspects Europe: Flirting with Unity Asia-Pacific: What Asian Contagion? In Theory In Focus Strategies Research Center Alpha Bytes Unhedged Commentary

Institutional Investor's Alpha Magazine - December 2008

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