Performance Calculations 101 Monday, October 19, 2009 Public
Pension Financial Forum John D. Simpson, CIPM The Spaulding Group,
Inc. Slide 2 What well do today Well cover a few basic formulas
that are used to calculate rates of return and risk Nature is
pleased with simplicity Issac Newton, Principia We will try to make
this easy to comprehend But, we have a fair amount to cover and
limited time Feel free to ask questions Slide 3 Rates of Return:
Time-weighting vs. Money-weighting Time-weighted returns measure
the performance of the portfolio manager Money-weighted returns
measure the performance of the fund or portfolio Slide 4
Time-weighting Time-weighting eliminates or reduces the impact of
cash flows Because managers dont control the flows Two general
approaches: Approximations, which approximate the exact, true,
time-weighted rate of return Exact, true, time-weighted rate of
return Slide 5 Approximation methods well discuss Original Dietz
Modified Dietz Modified BAI (a.k.a. Modified IRR and Linked IRR)
Slide 6 What Are Cash Flows? Two types: External: impact the
portfolio Internal: impact securities, sectors Specifics: External:
contributions/withdrawals of cash and/or securities Internal:
buys/sells, interest/dividends, corporate actions Slide 7
Visualizing Flows Slide 8 The scenario we will use to demonstrate
the various formulas: Slide 9 Assumes constant rate of return on
the portfolio during the period Very easy method to calculate
Provides approximation to the true rate of return Returns can be
distorted when large flows occur Also, return doesnt take into
account market volatility, which further affects the accuracy
Weights each cash flow as if it occurred at the middle of the time
period Original Dietz Slide 10 Slide 11 Modified Dietz Method
Assumes constant rate of return on the portfolio during the period
Provides an improvement in the approximation of true time-weighted
rate of return, versus the Original Dietz formula Disadvantage
greatest when: (a) 1 or more large external cash flows; (b) cash
flows occur during periods of high market volatility Weights each
external cash flow by the amount of time it is held in the
portfolio Slide 12 Modified Dietz Method Slide 13 Slide 14
Determines internal rate of return for the period Takes into
account the exact timing of each external cash flow Market value at
beginning of period is treated as cash flow Disadvantage: Requires
iterative process solution difficult to calculate manually Modified
BAI (Modified IRR, Linked IRR) Slide 15 Modified BAI Method Slide
16 Slide 17 Value portfolio every time external flows occur
Advantage: calculates true time-weighted rate of return
Disadvantage: requires precise valuation of the portfolio on each
day of external cash flow True, exact TWRR Slide 18 Slide 19
Money-weighted returns Internal Rate of Return (IRR) Takes cash
flows into consideration Cash flows will impact the return Only
uses cash flows and the closing market value in calculation (dont
revalue during period) Produces the return that equates the present
value of all invested capital Slide 20 Its an iterative process We
solve for r, by trial-and error The general rule is to use the
Modified Dietz return as the first order approximation to the IRR
Solving for the IRR Slide 21 IRR Method Slide 22 Slide 23 Why did
the Modified BAI and IRR yield the same returns (2.63%)?
Calculation Question Slide 24 Contrasting IRR with time-weighting
IRR values portfolio at the beginning and end of the period TWRR
values at various times throughout the period Slide 25 Our
investment is a mutual fund Where two investors begin with 100
shares And both make two additional purchases during the year of
100 shares each But at different times And at different prices Well
use an example to compare TWRR and MWRR Slide 26 Our funds
end-of-month NAVs Slide 27 Believes Buy low/ Sell high Believes Buy
high/ Sell low Our investors purchases Slide 28 Paper gain of $600!
Paper loss of $600! The investments unrealized gains/losses Slide
29 The funds return (using an exact TWRR method): Whats our return?
Slide 30 How about our investors? But this investor lost $600 And
this investor made $600 Because time weighting eliminates the
effect of cash flows! Slide 31 Investor #1s IRR = -24.86% Investor
#2s IRR = +35.16% How about money-weighting? Slide 32 As a Plan
Sponsor Which returns make more sense to you? Which are more
meaningful? TWRR judges portfolio manager MWRR judges the portfolio
Slide 33 Multi-period rates of return We dont just want to report
returns for a month We want to link our returns to form quarterly,
annual, since inception, etc. returns How do we do this? Slide 34
The 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 1Q We geometrically link in
order to compound our returns Geometric linking Slide 35
Step-by-step process: 1.Convert the returns to a decimal 2.Add 1
3.Multiply these numbers 4.Subtract 1 5.Convert the number to a
percent Geometric linking Slide 36 Slide 37 Before we move to risk,
are there any questions? Slide 38 Risk measures Two categories
Formulas that measure risk Well look at standard deviation and
tracking error Formulas that adjust the return per unit of risk
Well look at Sharpe Ratio and Information Ratio Slide 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. Slide 40 Standard Deviation;
based on the Bell-shaped (normal) curve Slide 41 Standard Deviation
Formulas Note: This is represented in Excel as the STDEVP Function
Note: This is represented in Excel as the STDEV Function Slide 42
An example of standard deviation Slide 43 Tracking Error The
difference between the performance of the benchmark and the
replicating portfolio Measures active risk; the risk the manager
took relative to the benchmark Measured as annualized standard
deviation Standard deviation of excess returns Standard deviation
of the difference in historical returns of a portfolio and its
benchmark Slide 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. Slide 45 An
example of Tracking Error To annualize, multiply by square root of
12 Slide 46 The Sharpe Ratio Also known as Reward-to-Variability
Ratio Developed by Bill Sharpe Nobel Prize Winner Equity Risk
Premium (Return) / Standard Deviation (Risk) Slide 47 Sharpe Ratio
Formula Equity Risk Premium divided by standard deviation of
portfolio returns Slide 48 An example of Sharpe Ratio To annualize,
multiply by square root of 12 Slide 49 Information Ratio The
Information Ratio measures the excess return of an investment
manager divided by the amount of risk the manager takes relative to
the benchmark Its 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 Slide 50 Information Ratio IR serves as a measure of
the special information an active portfolio manager has Value Added
(excess return) / Tracking Error Typically annualize Slide 51
Information Ratio Active Return on the account Accounts Active Risk
Slide 52 An example of Information Ratio Slide 53 What have we
covered today Hopefully youll agree a lot in a short time Return
measures TWRR approximation measues Original Dietz Modified Dietz
Modified BAI TWRR exact measure True daily Geometric Linking Slide
54 What have we covered today Risk measures Measurements of risk
Standard deviation Tracking error Measurements of risk-adjusted
returns Sharpe ratio Information ratio Slide 55 Questions? John D.
Simpson [email protected] 1.310.500.9640
www.spauldinggrp.com
