is $500,000. Since $500,000 is less than 20 % of the entire $4 million profit, the fund manager is unable to fully catch up. Had the total profits exceeded $5 million, the catch-up of the fund manager would have been completed. With $5 million of profit, the GP would receive 50 % of the profits above $3 million, or $1 million (50 % of the $2 million profit in excess of the profit necessary to meet the hurdle rate for the LPs). The $1 million of catch-up equals 20 % of $5 million. Profits in excess of $5 million would then be split 20 % to the fund manager and 80 % to the limited partners.
3.5.8 Incentive Fee as an Option
Incentive fees are long call options to GPs, who receive the classic payout of a call option: If the assets of the fund rise, they receive an increasing payout, and if the assets of the fund remain constant or fall, they receive no incentive fee. The underlying asset is the fund's net asset value, and the time to expiration of the option is the time until the next incentive fee is calculated, at which time a new option is written for the next incentive fee. In the absence of a hurdle rate, the strike price of the call option is the net asset value of the fund at the start of the period or the end of the last period in which an incentive fee was paid, whichever is greater. The GPs pay for this call option by providing their management expertise.
A hurdle rate may be viewed as increasing the strike price of the incentive fee call option. A hurdle rate increases the amount by which the net asset value of the fund must rise before the fund manager receives an incentive fee. The higher the hurdle rate, the lower the value of the call option.
As a call option, incentive fees provide fund managers with a strong incentive to generate profits. The call option moves in-the-money when the net asset value of a fund rises to the point of providing a return in excess of any hurdle rate. The call option moves out-of-the-money when the net asset value of the fund falls below the point of providing a return in excess of any hurdle rate.
When the option is below or near its strike price, the incentive fees provide the fund manager with an incentive to increase the risk of the fund's assets. The effect of increased risk is to increase the value of the call option. If the risks generate profits, the fund manager can benefit through high incentive fees. If the risks generate losses, the effect on the fund manager is limited to receiving no incentive fee, ignoring clawbacks.
When the incentive fee call option is deep-in-the-money, the fund manager benefits less from an increase in the risk of the underlying assets. The consequences of net asset value changes to the fund manager are more symmetrical when the option is deep-in-the-money, meaning when large incentive fees are likely. Risk aversion may motivate the fund manager to lessen the risk of the underlying assets when the incentive fee option is deep-in-the-money.
It can be argued that the multifaceted incentives generated by the optionlike character of incentive fees are perverse. The LPs prefer fund managers to take risks based on market opportunities and the risk-return preferences of the LPs. However, incentive fees can motivate fund managers to base investment decisions on the resulting risks to their personal finances. In summary, incentive fees can cause decisions involving risk to be based on the degree to which an option is in-the-money, near-the-money, or out-of-the-money.
Review Questions
1. What is the general term denoting compound interest when the interest is not continuously compounded?
2. What is the primary challenge that causes difficulty in calculating the return performance of a forward contract or another position that requires no net investment? How is that challenge addressed?
3. Consider a position in a single forward contract. What distinguishes a fully collateralized position in this forward contract from a partially collateralized position?
4. An IRR is estimated for a fund based on an initial investment when the fund was created, several annual distributions, and an estimate of the fund's value prior to its termination. What type of IRR is this?
5. An investment has two solutions for its IRR. What can be said about the investment and the usefulness of the two solutions?
6. Two investments are being compared to ascertain which would add the most value to a portfolio. Both investments have simplified cash flow patterns of an initial cost followed by positive cash flows. Why might the IRRs of the investments provide an unreliable indication of which would add more value?
7. An analyst computes the IRR of one alternative to be 20 % and another to be 30 %. When the analyst combines the cash flows of the two alternatives into a single investment, must the IRR of the combination be greater than 20 % and less than 30 %?
8. Is an IRR a dollar-weighted return or a time-weighted return? Why?
9. In which scenario will a clawback clause lead to payments?
10. What is the difference between a hard hurdle rate and a soft hurdle rate?
CHAPTER 4
Statistical Foundations
This chapter provides foundational material regarding statistical methods for the study of alternative investments in general and for the subsequent material in this book in particular. The use of statistics in performing hypothesis tests is addressed in detail in Chapter 8.
4.1 Return Distributions
Risky assets experience unexpected value changes and therefore unexpected returns. If we assume that investors are rational, the more competitively traded an asset, the more these unexpected price changes may be random and unpredictable. Hence, asset prices and asset returns in competitively traded markets are typically modeled as random variables. Frequency and probability distributions therefore provide starting points for describing asset returns.
4.1.1 Ex Ante and Ex Post Return Distributions
Ex post returns are realized outcomes rather than anticipated outcomes. Future possible returns and their probabilities are referred to as expectational or ex ante returns. A crucial theme in understanding the analysis of alternative investments is to understand the differences and links between ex post and ex ante return data.
Often, predictions are formed partially or fully through analysis of ex post data. For example, the ex ante or future return distribution of a stock index such as the S&P 500 Index is often assumed to be well approximated by the ex post or historical return distribution. The direct use of past return behavior as a predictor of future potential return behavior requires two properties to be accurate. First, the return distribution must be stationary through time, meaning that the expected return and the dispersion of the underlying asset do not change. Second, the sample of past observations must be sufficiently large to be likely to form a reasonably accurate representation of the process. For example, equity returns were very high during the bull market decade of the 1990s and very low during the early years of the financial crisis (2007–08). Using either of these time periods in isolation would likely overstate or understate the realistic long-run equity market returns.
Taken together, the requirements for the past returns to be representative of the future returns raise a serious challenge. If the past observation period is long, the sample of historical returns will be large; however, it is likely that the oldest observations reflect different risks or other economic conditions than can be anticipated in the future. If the sample is limited to the most recent observations, the data may be more representative of future economic conditions, but the sample may be too small to draw accurate inferences from it.
For a traditional asset, such as the common stock of a large, publicly traded corporation, it may be somewhat
