Return Measurement. Performance. Single period return Money weighted return Time weighted return Multi-period return Impact of fees Relative returns

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1 Performance Agenda

2 Return Measurement Performance Single period return Money weighted return Time weighted return Multi-period return Impact of fees Relative returns

3 Holding Period Returns Simplest way of computing returns r= mv end mv begin cfl mv begin mv = market value cfl = net cashflows - is outflow, + is inflow Formula is for cashflows at period end Different denominator for beginning Ignores time value of money Not accurate if cashflows in middle

4 Daily Returns Best case, we have daily information Use holding period formula for a single day Don't need to discount intra-day Can aggregate upward easily By-product of daily accounting cycle

5 Adjusted Equity Prices Now adjusted equity prices make sense An adjusted equity price series treats all cashflows as if they are reinvested, so we can neglect cash flows in any return calculation. It allows us to take the adjusted price at any two points and compute the return between them with no extra effort!

6 Not always available Daily Returns Real Estate Private Equity/Venture Capital Natural Resources (farmland) Other Illiquid investments

7 Fees/Costs As often as trades can occur fees occur For ETFs and Mutual funds Subtracted daily Legally obligated to document them For Hedge funds Subtracted monthly (obscured) These folks try to hide their fees

8 Fees/Costs Trading costs directly passed through Management fees Performance fees Versus a bogey (benchmark, threshold) Usually have a highwater mark

9 Time Weighted Return (TWR) Independent of amounts invested Geometric linkage across periods Compounds like interest Example January return 2% February return 3% Calendar Return to date (1+2%)*(1+3%) - 1 = 5.06%

10 Time Weighted Return (TWR) Standard form or return to report Fund Manager doesn't control flows Hard for investor to predict flows So we ignore them! CFA Institute GIPS Standards Requires TWR reporting Allows apples to apples comparisons between fund managers

11 Modified Dietz Method Generalization of Holding Period Return Approximation For time periods with mid-period cashflows r= (mv end mv begin cfl ) (mv begin + w i cfl i ) ; w i =(T t i )/T Denominator includes time weighted cashflows

12 Returns Answers what question? How much would I have made if I was totally invested for the entire period. What if period is greater than 1 day? What if I wasn't totally invested? What if cashflows occurred in the period? How to account for time value of cashflows

13 No daily information? To properly account for mid-period cashflows we need a better method. Use Internal Rate of Return (IRR) Takes into account timing of cashflows Sensitive to the time period used Does not need MV around cashflow Requires iterative solver Excel has a function to compute irr Financial calculator will also do this

14 IRR Example Date Cashflow Description 1/1/2010 $100,000,000 Initial MV 3/15/2010 $5,000,000 Cashflow in 6/30/2010 ($108,000,000) Ending MV IRR for this example is 6% (Annualized) Using excel XIRR function

15 Money Weighted Return We call IRR - Money Weighted Returns It takes into account Amount invested Size of cashflows Time value of money is implicitly included End to end IRR will give different result than linked IRRs (usually)

16 Money Weighted Return Behavioral economists like this When we analyze flows into mutual funds Most investors underperform TWR Buy high and sell low Money chasing prior period returns Under performance can be significant!

17 Problems with IRR IRR assumes cost of capital at all times is same Gives multiple answers for projects with interim out flows. Assumes Reinvestment rate is same for all flows.

18 Modified IRR Solves some of the problems with IRR MIRR= n FV of Positive Flows at Reinvestment rate 1 PV of negative flows at Cost of capital Date Name Value Rate PV/FV 01/01/2010 Initial Investment /01/2011 Capital Call % /01/2012 Capital Call % /01/2013 Distribution % /01/2014 Investment Sold FV = 15,240,000 ; PV = 12,675,520 MIRR = 4.71% IRR = 4.26%

19 Modified IRR Solves some of the problems with IRR MIRR= n FV Example of Positive Flows at Reinvestment rate 1 PV of negative flows at Cost of capital Date Name Value Rate PV/FV 01/01/2010 Initial Investment /01/2011 Capital Call % /01/2012 Capital Call % /01/2013 Distribution % /01/2014 Investment Sold

20 Performance Risk Adjusted Performance Treynor's composite Sharpe Ratio Jensen's alpha Information Ratio Tracking error

21 Treynor's Composite Based on CAPM Shows location vs SML T p = r p r f p Uses average statistics over period Implicitly only systemic risk Allows ranking investors

22 Sharpe Ratio Excess return divided by portfolio risk SR= r p r f p Measures risk adjusted performance Uses average statistics over period Considers all risk, not just systemic risk Most commonly used measure

23 Jensen's Alpha Measures excess returns adjusted for risk Derived from CAPM = r p r f r m r f p Based on only systemic risk Takes into account changes in risk free rate Skilled manager has positive alpha Residual should be 0

24 Tracking Error Standard deviation of return relative to the benchmark σ err = (Var (σ p σ b )) Denominator of Information Ratio Measures how closely one tracks the benchmark Is symmetric, fund manager is penalized for consistently outperforming the benchmark More of a risk measure than performance

25 Information Ratio Relative measure of performance Measures performance vs benchmark IR= (r p r b ) σ = α err σ err Numerator is excess return (over benchmark) Denominator is residual risk (idiosyncratic)

26 Benchmark selection Hurdle rate Benchmark index Performance

27 Performance What is Benchmark used for? Computing tracking error Computing information ratio Computing Beta and alpha Poor benchmark leads to Low beta High alpha High tracking error

28 Benchmarks Compensation may be tied to relative performance Wrong benchmark might be easy to beat Don't want to pay for beta

29 Benchmarks We like benchmarks to be investable More for asset allocation than performance This means we can buy or sell the index We can hedge our investments

30 Investment Style For example, in equity 2 axis Growth, Blend, Value Large Cap, Blend, Small Cap Hedge funds Strategies convertible arb, etc Morningstar mutual fund analysis

31 Investment Style Is not perfect Useful when no transparency Backward looking Both style indexes and investor Investor style can change

32 Return Based Style Analysis Developed by Sharpe Uses optimization Assumes alpha/residual is constant Finds best fit Computes factor betas Different from Least Squares Assumes random residual Minimizes residual/alpha squared

33 Performance Attribution GIPS standards CFA Institute Standard Primarily around presentation What needs to be included/not included Used by asset managers Allows apples to apples comparisons

34 Attribution Process of determining where out or under performance comes from

35 Index Case Study Two Small-Cap Domestic benchmarks S&P 600 Russell 2000 Measurable performance difference between them Even within sector indices are different

36 Index Case Study Monthly return analysis shows Predictable rebalancing hurts Fama-French model shows Russell 2000 has more small cap exposure S&P 600 has more value exposure