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Abstract:
Over the years numerous portfolio performance measures have been proposed. In general they are designed to capture some particular enhancement that might result from active management. However, if a principal uses a measure to judge an agent, then the agent has an incentive to game the measure. Our paper shows that such gaming can have a substantial impact on a number of popular measures even in the presence of extremely high transactions costs. The question then arises as to whether or not there exists a measure that cannot be gamed? As this paper shows there are conditions under which such a measure exists and fully characterizes it. This manipulation-proof measure looks like the average of a power utility function, calculated over the return history. The case for using our alternative ranking metric is particularly compelling in the hedge fund industry, in which the use of derivatives is unconstrained and manager compensation itself induces a non-linear payoff and thus encourages gaming.

Abstract:
Incentive fees for money managers are frequently accompanied by high-water mark provisions that condition the payment of the performance fee upon exceeding the previously achieved maximum share value. In this paper, we show that hedge fund performance fees are valuable to money managers, and conversely, represent a claim on a significant proportion of investor wealth. The high-water mark provisions in these contracts limit the value of the performance fees. We provide a closed-form solution to the cost of the high-water mark contract under certain conditions. Our results provide a framework for valuation of a hedge fund management company.

Abstract:
Incentive or performance fees for money managers are frequently accompanied by high-water mark provisions which condition the payment of the performance fee upon exceeding the maximum achieved share value. In this paper, we show that hedge fund performance fees are valuable to money managers, and conversely represent a claim on a significant proportion of investor wealth. The high-water mark provisions in these contracts limit the value of the performance fees. We provide a closed-form solution to the high-water mark contract under certain conditions. This solution shows that managers have an incentive to take risks. Our results provide a framework for valuation of a hedge fund management company.

We conjecture that the existence of high-water mark compensation is due to decreasing returns to scale in the industry. Empirical evidence on the relationship between fund return and net money flows into and out of funds suggests that successful managers, and large fund managers are less willing to take new money than small fund managers.

Abstract:
Incentive options are held by managers and employees who
invariably hold undiversified portfolios with substantial
amounts invested in their own company's common stock. This lack of diversification makes the subjective value of incentive items such as options less than their market value. This paper derives a model for the marginal value of such options or other
incentive items. As such, it can be used to evaluate heterogeneous options which mature on different dates. It can also be used each time a new option is granted.

The identical model (with different parameters)can be used to determine three different values for each option, the market value, the subjective value and the objective values. The market value is the value the option would have if it were held by an unconstrained agent. The subjective value - the value of the holder - is less than the market value because the option is held in an undiversified portfolio and because it is exercised suboptimally from the market perspective. The objective value is the cost to the firm of issuing the option and lies between the market and subjective values. This value recognizes the suboptimal exercise but not the undiversified discount.

The model is no more difficult to use than is the Black- Scholes model. In fact, under the same conditions, it is simply the Black-Scholes model with modified parameters. The model can also be easily extended to handle vesting, employment termination, indexing, repricing and any number of other features found in incentive options.

Abstract:
This paper addresses the bias associated with parametric measurement of timing skill based on monthly timer returns when timers can make daily timing decisions. Simulations suggest that the classic Henriksson-Merton parametric measure of timing skill is weak and biased downward when applied to the monthly returns of a daily timer. The paper proposes an adjustment that mitigates this problem without the need to collect daily timer returns. Four tests of timing skill, carried out on a sample of 558
mutual funds, show that very few funds exhibit statistically significant timing skill. More encompassing, the adjusted-FF3 test (based on the specification that incorporates both the proposed adjustment and the Fama-French three-factor model) is the least biased measure of timing skill among the four--it provides for a sharper inference regarding timing skill and helps mitigate biases associated with the choice of investment style.

Abstract:
Cumulative Prospect Theory has gained a great deal of support as an alternative to Expected Utility Theory as it accounts for a number of anomalies in the observed behavior of economic agents. Expected Utility Theory uses a utility function and subjective or objective probabilities to compare risky prospects. Cumulative Prospect Theory alters both of these aspects. The concave utility function is replaced by a loss-averse utility function and probabilities are replaced by decision weights. The latter are determined with a weighting function applied to the cumulative probability of the outcomes. Several different probability weighting functions have been suggested. The two most popular are the original proposal of Tversky and Kahneman and the compound-invariant form proposed by Prelec. This note shows that the Tversky-Kahneman probability weighting function is not increasing for all parameter values and therefore can assign negative decision weights to some outcomes. This in turn implies that Cumulative Prospect Theory could make choices not consistent with first-order stochastic dominance.

Abstract:
Cumulative Prospect Theory (CPT) has been used in a wide variety of economic models as an alternative to Expected Utility Theory (EUT). It is used to account for a number of anomalies in the observed behavior of economic agents. Like EUT, CPT uses a utility or value function to rate any given outcome. In CPT, however, the utility function is loss averse SS-shaped) rather than risk averse (concave). The other difference between the two theories is the use of decision weights rather than probabilities in computing the expectation.

This note provides a caution on the use of a popular form of decision weights - those proposed by Tversky and Kahneman (1992) in their introduction of the theory. In particular, the weights generated by their proposed probability weighting function can be negative for some parameter values. This could lead to evaluations that chose first-order stochastically dominated gambles rather than the dominating one.

The parameter values that can cause such problems are small relative to estimated values. Nevertheless, failure to recognize this problem may prevent the proofs of some theorems or allow the proof of some theorems which would be invalid with properly restricted probability weights.

Tversky-Kahneman, Probability Weighting, Cumulative Prospect Theory, economic models, Expected Utility Theory

Abstract:
It is now well known that the Sharpe ratio and other related reward-to-risk measures may be manipulated with option-like strategies. In this paper we derive the general conditions for achieving the maximum expected Sharpe ratio. We derive static rules for achieving the maximum Sharpe ratio with two or more options, as well as a continuum of derivative contracts. The optimal strategy rules for increasing the Sharpe ratio. Our results have implications for performance measurement in any setting in which managers may use derivative contracts. In a performance measurement setting, we suggest that the distribution of high Sharpe ratio managers should be compared with that of the optimal Sharpe ratio strategy. This has particular application in the hedge fund industry where use of derivatives is unconstrained and manager compensation itself induces a non-linear payoff. The shape of the optimal Sharpe ratio leads to further conjectures. Expected returns being held constant, high Sharpe ratio strategies are, by definition, strategies that generate regular modest profits punctunated by occasional crashes. Our evidence suggests that the 'peso problem' may be ubiquitous in any investment management industry that rewards high Sharpe ratio managers.

Abstract:
Incentive fees for money managers are frequently accompanied by high water mark provisions which condition the payment of the incentive upon exceeding the maximum achieved share value. In this paper, we show that these high water mark contracts are valuable to money managers, and conversely represent a claim on a significant proportion of investor wealth. We provide a closed-form solution to the high water mark contract under certain conditions. This solution shows that managers have an incentive to take risks. We conjecture that the existence of high water mark compensation is due to decreasing returns to scale in the industry. Empirical evidence on the relationship between fund return and net money flows into and out of funds suggests that successful managers, and large fund managers are less willing to take new money than small fund managers.

Abstract:
The assumption that bondholders follow either a buy-and-hold or a continuous realization trading policy, rather than the optimal trading policy,is at variance with reality and, as we demonstrate, may seriously bias the estimation of the yield curve and the implied tax bracket of the marginal investor. Tax considerations which govern a bondholder`s optimal trading policy include the following: realization of capital losses, short term if possible; deferment of the realization of capital gains, especially if they are short term; changing the holding period status from long term to short term by sale of the bond and repurchase, so that future capital losses may be realized short term; and raising the basis through sale of the bond and repurchase in order to deduct from ordinary income the amortized premium. Because of the interaction of these factors, no simple characterization of the optimal trading policy is possible. We can say, however, that it differs substantially from the buy-and-hold policy irrespective of whether the bondholder is a bank, a bond dealer, or an individual. We obtain these strong results even when we allow for transactions costs and explicitly consider numerous IRS regulations designed to curtail tax avoidance.

Abstract:
Numerous measures have been proposed to gauge the performance of active management. Unfortunately, these measures can be gamed. Our article shows that gaming can have a substantial impact on popular measures even in the presence of high transactions costs. Our article shows there are conditions under which a manipulation-proof measure exists and fully characterizes it. This measure looks like the average of a power utility function, calculated over the return history. The case for using our alternative ranking metric is particularly compelling for hedge funds whose use of derivatives is unconstrained and whose managers' compensation itself induces a nonlinear payoff.

G11, G23, G24

Abstract:
This article presents a simple, unified approach for valuing a variety of financial assets using digital contracts. Three types of digitals are used: a digital option paying either one dollar or nothing, a digital share paying nothing or converting into one share of the underlying asset, and a first-touch digital paying one dollar the first time that the price of the underlying stock moves into some specified region. It is shown how the values of these three types of digitals can be determined for a wide variety of payoff events and how they can be combined to price complex contracts.

Abstract:
In frictionless markets having no arbitrage, the asymptotic zero-coupon rate never falls. The same is true of the long forward rate. The long par-coupon rate can rise and fall due to forward rate movements at short maturities. This paper relates the three types of interest rate and formalizes and proves the impossibility results for falling asymptotic rates. These results can be tested in a parametric term structure specification that is rich enough to identify a time series of long rates. The results show that it is not possible to specify arbitrarily the long forward or zero-coupon rate process.