A Test for Mean-Variance Efficiency of a Given Portfolio ...
Discussion of Effort, Risk and Walkaway under High Water Mark Contracts by Indraneel Chakraborty and Sugata RayMahidol University, Bangkok Roy Kouwenberg Erasmus University Rotterdam Summary Theoretical model of hedge fund management and investment.
Incentive fees, with high water mark (HWM) Risk and effort chosen by the fund manager Investors capable of withdrawing funds (walk-away). Numerical solution of the model. Key results: As the fund value drops further below the HWM: Manager increases variance of returns Expected returns for investors decrease (lower effort/alpha) Investors more likely to withdraw funds Summary Calabration of model parameters using the CISDM hedge fund database. Empirical investigation using the CISDM database Effect of a funds required return to reach HWM on:
Risk taking (+) Expected returns () Probability of a fund dropping from the CISDM database (+) Numerical welfare analysis of modifying the fee contract, using the calibrated model. Discussion Overall, interesting work! Main comment: paper too long
67 pages 17 tables (!) 10 figures Result: focus and contribution become less clear Where lies the contribution: theory, empirical results, or calibration of the model (welfare analysis)? Suggestion: pick one or two areas to focus on. Discussion of theoretical model Some assumptions of the theoretical model: Manager can increase alpha through extra effort, but this is costly (utility loss)
Manager has no money in the fund No uncertainty about alpha; completely under control of manager No incentive alignment (no loss of reputation either). Assumption of a uniform portfolio return distribution Infinite period model: investor keeps a constant dollar amount of money in the fund (rebalancing) Investor anticipates the managers optimal effort and risk Numerical solutions only
Discussion of theoretical model The model assumes that the investor anticipates the managers optimal effort (alpha) and risk level at the beginning of the period. The investor will withdraw all money when the expected fund return is negative. Comparison to practice Investor have very little information about a hedge funds investment strategy and true alpha Investors face lock-up periods Hedge generate returns through beta exposure Who walks away: the manager or the investor?
Discussion of empirical analysis Some comments on empirical results: Brown, Goetzmann and Park (2001, p1870): we find little or no evidence that poor performers  increase volatility to meet their high water mark. Comparison? Relation between required return to reach HMW and future fund returns: adjust the returns for risk (volatility) and try to explain alpha (proxy for effort) Hedge funds report their returns to the database voluntarily: when a fund drops out of the database, we actually dont know why. => Paper interprets this as a walk-away by investors
Interpretation of empirical results Hedge funds compete for alpha: as more money flows into a strategy or anomaly, alphas will decrease and the high water mark (+hurdle rate) becomes more difficult to beat with same level of risk. Is the required return to reach the HWM in the papers empirical analysis perhaps a proxy for excessive fund flows and over-crowding of a strategy? Higher fund flows => lower future excess returns, higher risk taking, higher probability of dropping out? Control for fund flows?
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