Presentation on theme: "Performance Calculations 101"— Presentation transcript:
1 Performance Calculations 101 Monday, October 19, 2009Public Pension Financial ForumJohn D. Simpson, CIPMThe Spaulding Group, Inc.
2 What we’ll do todayWe’ll cover a few basic formulas that are used to calculate rates of return and risk“Nature is pleased with simplicity”Issac Newton, PrincipiaWe will try to make this easy to comprehendBut, we have a fair amount to cover and limited timeFeel free to ask questions
3 Rates of Return: Time-weighting vs. Money-weighting Time-weighted returns measure the performance of the portfolio managerMoney-weighted returns measure the performance of the fund or portfolio
4 Time-weightingTime-weighting eliminates or reduces the impact of cash flowsBecause managers don’t control the flowsTwo general approaches:Approximations, which approximate the exact, true, time-weighted rate of returnExact, true, time-weighted rate of return
5 Approximation methods we’ll discuss Original DietzModified DietzModified BAI(a.k.a. Modified IRR and Linked IRR)
6 What Are Cash Flows? Two types: Specifics: External: impact the portfolioInternal: impact securities, sectorsSpecifics:External: contributions/withdrawals of cash and/or securitiesInternal: buys/sells, interest/dividends, corporate actions
8 The scenario we will use to demonstrate the various formulas:
9 Original DietzAssumes constant rate of return on the portfolio during the periodVery easy method to calculateProvides approximation to the true rate of returnReturns can be distorted when large flows occurAlso, return doesn’t take into account market volatility, which further affects the accuracyWeights each cash flow as if it occurred at the middle of the time period
11 Modified Dietz MethodAssumes constant rate of return on the portfolio during the periodProvides an improvement in the approximation of true time-weighted rate of return, versus the Original Dietz formulaDisadvantage greatest when: (a) 1 or more large external cash flows; (b) cash flows occur during periods of high market volatilityWeights each external cash flow by the amount of time it is held in the portfolio
14 Modified BAI (Modified IRR, Linked IRR) Determines internal rate of return for the periodTakes into account the exact timing of each external cash flowMarket value at beginning of period is treated as cash flowDisadvantage: Requires iterative process solution – difficult to calculate manually
17 True, exact TWRR Value portfolio every time external flows occur Advantage: calculates true time-weighted rate of returnDisadvantage: requires precise valuation of the portfolio on each day of external cash flow
19 Money-weighted returns Internal Rate of Return (IRR) Takes cash flows into considerationCash flows will impact the returnOnly uses cash flows and the closing market value in calculation (don’t revalue during period)Produces the return that equates the present value of all invested capital
20 Solving for the IRR It’s an iterative process We solve for r, by trial-and errorThe general rule is to use the Modified Dietz return as the “first order approximation” to the IRR
23 Calculation QuestionWhy did the Modified BAI and IRR yield the same returns (2.63%)?ANSWER: Because both the Modified BAI and IRR use the same formula: the IRR. The difference is that with Modified BAI, we calculate the return for subperiods (e.g., months) and then geometrically link them; however, for the IRR, we do not link subperiod returns … we calculate the IRR across the entire period (e.g., if we were calculating a return for a year, we’d geometrically link the 12 monthly Modified BAI returns but we’d only calculate a single IRR, valuing the portfolio only at the start and the end of the year!
24 Contrasting IRR with time-weighting IRR values portfolio at the beginning and end of the periodTWRR values at various times throughout the period
25 We’ll use an example to compare TWRR and MWRR Our investment is a mutual fundWhere two investors begin with 100 sharesAnd both make two additional purchases during the year of 100 shares eachBut at different timesAnd at different prices
30 How about our investors? But this investor lost $600And this investor made $600Because time weighting eliminates the effect of cash flows!
31 How about money-weighting? Investor #1’s IRR = %Investor #2’s IRR = %
32 As a Plan Sponsor … Which returns make more sense to you? Which are more meaningful?TWRR judges portfolio managerMWRR judges the portfolio
33 Multi-period rates of return We don’t just want to report returns for a monthWe want to link our returns to form quarterly, annual, since inception, etc. returnsHow do we do this?
34 Geometric linkingThe process used to link sub-period returns to create returns for extended periods:e.g., We want to take January, February, and March returns to create a return for 1QWe geometrically link in order to compound our returns
35 Geometric linking Step-by-step process: Convert the returns to a decimalAdd 1Multiply these numbersSubtract 1Convert the number to a percent
37 Before we move to risk, are there any questions?
38 Risk measures Two categories Formulas that measure risk We’ll look at standard deviation and tracking errorFormulas that adjust the return per unit of riskWe’ll look at Sharpe Ratio and Information Ratio
39 Standard Deviation Measures volatility of returns over time The most common and most criticized measure to describe the risk of a security or portfolio.Used not only in finance, but also statistics, sciences, and social sciences.Provides a precise measure of the amount of variation in any group of numbers.
40 Standard Deviation; based on the Bell-shaped (normal) curve
41 Standard Deviation Formulas Note: This is represented in Excel as the STDEVP FunctionNote: This is represented in Excel as the STDEV Function
43 Tracking ErrorThe difference between the performance of the benchmark and the replicating portfolioMeasures active risk; the risk the manager took relative to the benchmarkMeasured as annualized standard deviationStandard deviation of excess returnsStandard deviation of the difference in historical returns of a portfolio and its benchmark
44 Tracking Formula: Volatility of Past Returns vs. Benchmark Tracking error measures how closely the portfolio follows the index and is measured as the standard deviation of the difference between the portfolio and index returns.
45 An example of Tracking Error To annualize, multiply by square root of 12
46 The Sharpe Ratio Also known as Reward-to-Variability Ratio Developed by Bill Sharpe –Nobel Prize WinnerEquity Risk Premium (Return) / Standard Deviation (Risk)
47 Sharpe Ratio Formula Equity Risk Premium divided by standard deviation of portfolio returns
48 An example of Sharpe Ratio To annualize, multiply by square root of 12
49 Information RatioThe Information Ratio measures the excess return of an investment manager divided by the amount of risk the manager takes relative to the benchmarkIt’s the Excess Return (Active Return) divided by the Tracking Error (Active Risk)IR is a variation of the Sharpe Ratio, where the Return is the Excess Return and the Risk is the Excess or Active Risk
50 Information RatioIR serves as a measure of the “special information” an active portfolio manager hasValue Added (excess return) / Tracking ErrorTypically annualize
51 Information RatioActive Returnon the accountAccount’sActive Risk
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