Hedge Fund Modelling and Analysis using MATLAB

CHAPTER 5 Performance Measurement

Hedge fund managers and CTAs can use leverage and take short positions (as opposed to traditional managers who cannot), and since their returns over time will be a direct function of leverage and their long-short portfolio mix, so the manager's performance should be measured on a cash basis (unleveraged) “relative” to the portfolio “risk” in order to offset the effects of leverage. The risk proxy measure used is generally based on the second moment of the distribution of returns, e.g. the “volatility” or some other measurable statistical estimate of the variation of the spread of returns associated with the manager. This chapter will look at the various performance measurements which can be used to analyse hedge fund returns in a risk-adjusted sense using the most common metrics applied in industry and academia.

5.1 THE INTUITION BEHIND RISK-ADJUSTED RETURNS

Consider two CTAs – Manager A and Manager B and assume both managers are operating in approximately the same style (e.g. diversified managed futures) and use similar underlying instruments for investment and trading purposes. Also assume that notional funding¹ is available for an investor who has $5 million to collateralise a managed account with their FCM of choice and is hoping one CTA will manage all or part of their capital through a Power Of Attorney (POA)² at 2% management fee and 20% incentive fee.³ Neglecting higher moments, the annualised first two moments (M1 = return and M2 ...