The typical hedge fund fee structure is a management fee of 1% to 2% of assets plus an incentive fee equal to 20% of investment profits beyond a stipulated benchmark perfor- mance, annually. Incentive fees are effectively call options on the portfolio with a strike price equal to current portfolio value times 1 1 benchmark return. The manager gets the fee if the portfolio value rises sufficiently, but loses nothing if it falls. Figure 26.7 illus- trates the incentive fee for a fund with a 20% incentive fee and a hurdle rate equal to the money market rate, r f . The current value of the portfolio is denoted S 0 and the year-end value is S T . The incentive fee is equivalent to .20 call options on the portfolio with exercise price S 0 (1 1 r f ).
Example 26.4 Black-Scholes Valuation of Incentive Fees
Suppose the standard deviation of a hedge fund’s annual rate of return is 30% and the incentive fee is 20% of any investment return over the risk-free money market rate. If the portfolio currently has a net asset value of $100 per share, and the effective annual risk- free rate is 5% (or 4.88% expressed as a continuously compounded rate), then the implicit exercise price on the incentive fee is $105. The Black-Scholes value of a call option with S 0 5 100, X 5 105, s 5 .30, r 5 .0488, T 5 1 year is $11.92, just a shade below 12% of net asset value. Because the incentive fee is worth 20% of the call option, its value is just about 2.4% of net asset value. Together with a typical management fee of 2% of net asset value, the investor in the fund pays fees with a total value of 4.4%.
Figure 26.7 Incentive fees as a call option.
The current value of the portfolio is denoted S 0 and its year-end value is S T . The incentive fee is equivalent to .20 call options on the portfolio with exercise price S 0 (1 1 r f ).
S0(1 + rf) ST
Incentive Fee
Slope = .20
The major complication to this description of the typical compensation structure is the high water mark. If a fund experiences losses, it may not be able to charge an incentive fee unless and until it recovers to its previous higher value. With large losses, this may be dif- ficult. High water marks therefore give managers an incentive to shut down funds that have performed poorly, and likely are a cause of the high attrition rate for funds noted above.
One of the fastest-growing sectors in the hedge fund universe has been in funds of funds. These are hedge funds that invest in one or more other hedge funds. Funds of funds are also called feeder funds, because they feed assets from the
original investor to the ultimate hedge fund. They are marketed as providing investors the capability to diversify across funds, and also as providing the due diligence involved in screening funds for investment worthiness. In principle, this can be a valuable service because many hedge funds are opaque and feeder funds may have greater insight than typical outsiders.
However, when Bernard Madoff was arrested in December 2008 after admitting to a massive Ponzi scheme, many large feeder funds were found to be among his biggest clients, and their “due diligence” may have been, to put it mildly, lack- ing. At the head of the list was Fairfield Greenwich Advisors, with exposure reported at $7.5 billion, but several other feeder funds and asset management firms around the world were also on the hook for amounts greater than $1 billion, among them Tremont Group Holdings, Banco Santander (a Spanish bank, one of the largest in the euro area), Ascot Partners, and
On December 13, 2008, Bernard Madoff reportedly con- fessed to his two sons that he had for years been operat- ing a Ponzi scheme, one that had reached a staggering $60 billion. A Ponzi scheme is an investment fraud in which a manager collects funds from clients, claims to invest those funds on the clients’ behalf, reports extremely favorable investment returns, but in fact uses the funds for his own purposes. (The schemes are named after Charles Ponzi, whose success with this scheme in the early 1900s made him notorious throughout the United States.) Early investors who ask to redeem their investments are paid back with the funds coming in from new investors rather than with true earnings. The scheme can continue as long as new investors provide enough funds to cover the redemption requests of the earlier ones—and these inflows are attracted by the superior returns “earned” by early investors as well as their apparent ability to redeem funds as requested.
As a highly respected member of the Wall Street estab- lishment, Madoff was in a perfect position to perpetrate such a fraud. He was a pioneer in electronic trading and had served as chairman of the NASDAQ Stock Market.
Aside from its trading operations, Bernard L. Madoff Investment Securities LLC also acted as a money manager, and it claimed to achieve highly consistent annual returns, between 10% and 12% in good markets as well as bad.
Its strategy was supposedly based on option hedging strat- egies, but Madoff was never precise about his approach.
Still, his stature on Wall Street and the prestige of his client list seemed to testify to his legitimacy. Moreover, he played hard to attract new investors, and the appearance that one needed connections to join the fund only increased its appeal. The scheme seems to have operated for decades, but in the 2008 stock market downturn, several large cli- ents requested redemptions totaling around $7 billion.
With far less than $1 billion of assets left in the firm, the scheme collapsed.
Not everyone was fooled, and in retrospect, several red flags should have aroused suspicion. For example, some institutional investors shied away from the fund, objecting to its unusual opacity. Given the magnitude of the assets supposedly under management, the option hedging trades purportedly at the heart of Madoff’s investment strategy should have dominated options market trading volume, yet there was no evidence of their execution. Moreover, Madoff’s auditor, a small firm with only three employees (including only one active accountant!), seemed grossly inadequate to audit such a large and complex operation. In addition, Madoff’s fee structure was highly unusual. Rather than acting as a hedge fund that would charge a per- centage of assets plus incentive fees, he claimed to profit instead through trading commissions on the account—if true, this would have been a colossal price break to cli- ents. Finally, rather than placing assets under management with a custodial bank as most funds do, Madoff claimed to keep the funds in house, which meant that no one could independently verify their existence. In 2000, the SEC received a letter from an industry professional named Harry Markopolos concluding that “Madoff Securities is the world’s largest Ponzi scheme,” but Madoff continued to operate unimpeded.
Several questions remain unanswered. How much help did Madoff have from others? How much money was actu- ally lost? Much of the “lost” funds represented fictitious earnings on invested money, and some was returned to early investors. Where did the money go? Was it lost to bad trades, or was it skimmed off to support Madoff’s life style?
And why did the red flags and early warnings not prompt a more aggressive response from regulators?
WORDS FROM THE STREET
Access International Advisors. In the end, it appears that some funds had in effect become little more than marketing agents for Madoff. The nearby box presents further discussion of the Madoff affair.
The option-like nature of compensation can have a big impact on expected fees in funds of funds. This is because the fund of funds pays an incentive fee to each underlying fund that outperforms its benchmark, even if the aggregate performance of the fund of funds is poor. In this case, diversification can hurt you! 16
16 S. J. Brown, W. N. Goetzmann, and B. Liang, “Fees on Fees in Funds of Funds,” Journal of Investment Management 2 (2004), pp. 39–56.
Example 26.5 Incentive Fees in Funds of Funds
Suppose a fund of funds is established with $1 million invested in each of three hedge funds. For simplicity, we will ignore the asset-value-based portion of fees (the manage- ment fee) and focus only on the incentive fee. Suppose that the hurdle rate for the incentive
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1. Like mutual funds, hedge funds pool the assets of several clients and manage the pooled assets on their behalf. However, hedge funds differ from mutual funds with respect to disclosure, investor base, flexibility and predictability of investment orientation, regulation, and fee structure.
2. Directional funds take a stance on the performance of broad market sectors. Nondirectional funds establish market-neutral positions on relative mispricing. However, even these hedged positions still present idiosyncratic risk.
3. Statistical arbitrage is the use of quantitative systems to uncover many perceived misalignments in relative pricing and ensure profits by averaging over all of these small bets. It often uses data- mining methods to uncover past patterns that form the basis for the established investment positions.
4. Portable alpha is a strategy in which one invests in positive-alpha positions, then hedges the sys- tematic risk of that investment, and, finally, establishes market exposure where desired by using passive indexes or futures contracts.
5. Performance evaluation of hedge funds is complicated by survivorship bias, by the potential instability of risk attributes, by the existence of liquidity premiums, and by unreliable market valuations of infrequently traded assets. Performance evaluation is particularly difficult when the fund engages in option positions. Tail events make it hard to assess the true performance of posi- tions involving options without extremely long histories of returns.
SUMMARY
The idea behind funds of funds is to spread risk across several different funds. However, investors need to be aware that these funds of funds operate with considerable leverage, on top of the leverage of the primary funds in which they invest, which can make returns highly volatile. Moreover, if the various hedge funds in which these funds of funds invest have similar investment styles, the diversification benefits of spreading investments across several funds may be illusory—but the extra layer of steep management fees paid to the manager of the fund of funds certainly is not. 17
17 One small silver lining: while funds of funds pay incentive fees to each of the underlying funds, the incentive fees they charge their own investors tend to be lower, typically around 10% rather than 20%.
fee is a zero return, so each fund charges an incentive fee of 20% of total return. The fol- lowing table shows the performance of each underlying fund over a year, the gross rate of return, and the return realized by the fund of funds net of the incentive fee. Funds 1 and 2 have positive returns, and therefore earn an incentive fee, but Fund 3 has terrible perfor- mance, so its incentive fee is zero.
Fund 1 Fund 2 Fund 3 Fund of Funds
Start of year (millions) $1.00 $1.00 $1.00 $3.00
End of year (millions) $1.20 $1.40 $0.25 $2.85
Gross rate of return 20% 40% 275% 25%
Incentive fee (millions) $0.04 $0.08 $0.00 $0.12
End of year, net of fee $1.16 $1.32 $ .25 $2.73
Net rate of return 16% 32% 275% 29%
Even though the return on the aggregate portfolio of the fund of funds is negative 5%, it still pays incentive fees of $.12 for every $3 invested, which amounts to 4% of net asset value. As demonstrated in the last column, this reduces the rate of return earned by the fund of funds from 2 5% to 2 9%.
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6. Hedge funds typically charge investors both a management fee and an incentive fee equal to a percentage of profits beyond some threshold value. The incentive fee is akin to a call option on the portfolio. Funds of hedge funds pay the incentive fee to each underlying fund that beats its hurdle rate, even if the overall performance of the portfolio is poor.
Related Web sites for this chapter are available at www.
mhhe.com/bkm
hedge funds lock-up periods directional strategy nondirectional strategy market neutral pure plays
statistical arbitrage pairs trading data mining portable alpha alpha transfer
backfill bias survivorship bias incentive fee high water mark funds of funds
KEY TERMS
1. Would a market-neutral hedge fund be a good candidate for an investor’s entire retirement port- folio? If not, would there be a role for the hedge fund in the overall portfolio of such an investor?
2. How might the incentive fee of a hedge fund affect the manager’s proclivity to take on high-risk assets in the portfolio?
3. Why is it harder to assess the performance of a hedge fund portfolio manager than that of a typi- cal mutual fund manager?
4. Which of the following is most accurate in describing the problems of survivorship bias and backfill bias in the performance evaluation of hedge funds?
a. Survivorship bias and backfill bias both result in upwardly biased hedge fund index returns.
b. Survivorship bias and backfill bias both result in downwardly biased hedge fund index returns.
c. Survivorship bias results in upwardly biased hedge fund index returns, but backfill bias results in downwardly biased hedge fund index returns.
5. Which of the following would be the most appropriate benchmark to use for hedge fund evaluation?
a. A multifactor model.
b. The S&P 500.
c. The risk-free rate.
6. With respect to hedge fund investing, the net return to an investor in a fund of funds would be lower than that earned from an individual hedge fund because of:
a. Both the extra layer of fees and the higher liquidity offered.
b. No reason; fund of funds earn returns that are equal to those of individual hedge funds.
c. The extra layer of fees only.
7. Which of the following hedge fund types is most likely to have a return that is closest to risk-free?
a. A market-neutral hedge fund.
b. An event-driven hedge fund.
c. A long/short hedge fund.
8. Is statistical arbitrage true arbitrage? Explain.
9. A hedge fund with $1 billion of assets charges a management fee of 2% and an incentive fee of 20% of returns over a money market rate, which currently is 5%. Calculate total fees, both in dollars and as a percent of assets under management, for portfolio returns of:
a. 2 5%
b. 0 c. 5%
d. 10%
10. A hedge fund with net asset value of $62 per share currently has a high water mark of $66. Is the value of its incentive fee more or less than it would be if the high water mark were $67?
PROBLEM SETS
i. Basic
ii. Intermediate
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11. Reconsider the hedge fund in the previous problem. Suppose it is January 1, the standard devia- tion of the fund’s annual returns is 50%, and the risk-free rate is 4%. The fund has an incentive fee of 20%, but its current high water mark is $66, and net asset value is $62.
a. What is the value of the annual incentive fee according to the Black-Scholes formula?
b. What would the annual incentive fee be worth if the fund had no high water mark and it earned its incentive fee on its total return?
c. What would the annual incentive fee be worth if the fund had no high water mark and it earned its incentive fee on its return in excess of the risk-free rate? (Treat the risk-free rate as a continuously compounded value to maintain consistency with the Black-Scholes formula.) d. Recalculate the incentive fee value for part ( b ) now assuming that an increase in fund lever-
age increases volatility to 60%.
12. Go to the Online Learning Center at www.mhhe.com/bkm, link to Chapter 26, and find there a spreadsheet containing monthly values of the S&P 500 index. Suppose that in each month you had written an out-of-the-money put option on one unit of the index with an exercise price 5%
lower than the current value of the index.
a. What would have been the average value of your gross monthly payouts on the puts over the 10-year period October 1977–September 1987? The standard deviation?
b. Now extend your sample by 1 month to include October 1987, and recalculate the average payout and standard deviation of the put-writing strategy. What do you conclude about tail risk in naked put writing?
13. Suppose a hedge fund follows the following strategy. Each month it holds $100 million of an S&P 500 index fund and writes out-of-the-money put options on $100 million of the index with exercise price 5% lower than the current value of the index. Suppose the premium it receives for writing each put is $.25 million, roughly in line with the actual value of the puts.
a. Calculate the Sharpe ratio the fund would have realized in the period October 1982– September 1987. Compare its Sharpe ratio to that of the S&P 500. Use the data from the previous prob- lem, available at the Online Learning Center, and assume the monthly risk-free interest rate over this period was .7%.
b. Now calculate the Sharpe ratio the fund would have realized if we extend the sample period by 1 month to include October 1987. What do you conclude about performance evaluation and tail risk for funds pursuing option-like strategies?
14. The following is part of the computer output from a regression of monthly returns on Water- works stock against the S&P 500 index. A hedge fund manager believes that Waterworks is underpriced, with an alpha of 2% over the coming month.
Beta R-square
Standard Deviation of Residuals .75 .65 .06 (i.e., 6% monthly)
a. If he holds a $2 million portfolio of Waterworks stock, and wishes to hedge market exposure for the next month using 1-month maturity S&P 500 futures contracts, how many contracts should he enter? Should he buy or sell contracts? The S&P 500 currently is at 1,000 and the contract multiplier is $250.
b. What is the standard deviation of the monthly return of the hedged portfolio?
c. Assuming that monthly returns are approximately normally distributed, what is the prob- ability that this market-neutral strategy will lose money over the next month? Assume the risk-free rate is .5% per month.
15. Return to the previous problem.
a. Suppose you hold an equally weighted portfolio of 100 stocks with the same alpha, beta, and residual standard deviation as Waterworks. Assume the residual returns (the e terms in Equations 26.1 and 26.2 ) on each of these stocks are independent of each other. What is the residual standard deviation of the portfolio?
e X c e l
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e X c e l
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iii. Challenge
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b. Recalculate the probability of a loss on a market-neutral strategy involving equally weighted, market-hedged positions in the 100 stocks over the next month.
16. Return again to Problem 14. Now suppose that the manager misestimates the beta of Water- works stock, believing it to be .50 instead of .75. The standard deviation of the monthly market rate of return is 5%.
a. What is the standard deviation of the (now improperly) hedged portfolio?
b. What is the probability of incurring a loss over the next month if the monthly market return has an expected value of 1% and a standard deviation of 5%? Compare your answer to the probability you found in Problem 14.
c. What would be the probability of a loss using the data in Problem 15 if the manager simi- larly misestimated beta as .50 instead of .75? Compare your answer to the probability you found in Problem 14.
d. Why does the misestimation of beta matter so much more for the 100-stock portfolio than it does for the 1-stock portfolio?
17. Here are data on three hedge funds. Each fund charges its investors an incentive fee of 20% of total returns. Suppose initially that a fund of funds (FF) manager buys equal amounts of each of these funds, and also charges its investors a 20% incentive fee. For simplicity, assume also that management fees other than incentive fees are zero for all funds.
Hedge Fund 1
Hedge Fund 2
Hedge Fund 3 Start of year value (millions) $100 $100 $100
Gross portfolio rate of return 20% 10% 30%
a. Compute the rate of return after incentive fees to an investor in the fund of funds.
b. Suppose that instead of buying shares in each of the three hedge funds, a stand-alone (SA) hedge fund purchases the same portfolio as the three underlying funds. The total value and composition of the SA fund is therefore identical to the one that would result from aggregating the three hedge funds. Consider an investor in the SA fund. After paying 20% incentive fees, what would be the value of the investor’s portfolio at the end of the year?
c. Confirm that the investor’s rate of return in SA is higher than in FF by an amount equal to the extra layer of fees charged by the fund of funds.
d. Now suppose that the return on the portfolio held by hedge fund 3 were 2 30% rather than 1 30%. Recalculate your answers to parts ( a ) and ( b ). Will either FF or SA charge an incentive fee in this scenario? Why then does the investor in FF still do worse than the investor in SA?
E-INVEST- MENTS EXERCISES
Hedge Fund Styles and Results
Log on to www.hedgeindex.com, a site run by Credit Suisse/Tremont, which maintains the TASS Hedge Funds Data Base of the performance of more than 2,000 hedge funds, and produces indexes of investment performance for several hedge fund classes. Click the Downloads tab (free registration is required for access to this part of the Web site). From the Downloads page, you can access historical rates of return on each of the hedge fund subclasses (e.g., market neutral, event-driven, dedicated short bias, and so on). Download 5 years of monthly returns for each subclass and download returns on the S&P 500 for the same period from finance.yahoo.com. Calculate the beta of the equity-market-neutral and dedicated short bias funds. Do the results seem reasonable in terms of the orientation of these funds? Next, look at the year-by-year performance of each hedge fund class. How does the variability of performance results in different years compare to that of the S&P 500?