1 / 55

Performance Calculations 101

Performance Calculations 101. Monday, October 19, 2009 Public Pension Financial Forum John D. Simpson, CIPM The Spaulding Group, Inc. What we’ll do today. We’ll cover a few basic formulas that are used to calculate rates of return and risk “Nature is pleased with simplicity”

boyd
Download Presentation

Performance Calculations 101

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Performance Calculations101 Monday, October 19, 2009 Public Pension Financial Forum John D. Simpson, CIPM The Spaulding Group, Inc.

  2. What we’ll do today • We’ll 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

  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

  4. Time-weighting • Time-weighting eliminates or reduces the impact of cash flows • Because managers don’t control the flows • Two general approaches: • Approximations, which approximate the exact, true, time-weighted rate of return • Exact, true, time-weighted rate of return

  5. Approximation methods we’ll discuss • Original Dietz • Modified Dietz • Modified BAI (a.k.a. Modified IRR and Linked IRR)

  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

  7. Visualizing Flows

  8. The scenario we will use to demonstrate the various formulas:

  9. Original Dietz • 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 doesn’t 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

  10. Original Dietz

  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

  12. Modified Dietz Method

  13. Modified Dietz Method

  14. Modified BAI(Modified IRR, Linked IRR) • 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

  15. Modified BAI Method

  16. Modified BAI Method

  17. True, exact TWRR • 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

  18. True, exact TWRR

  19. Money-weighted returnsInternal 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 (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 error • The general rule is to use the Modified Dietz return as the “first order approximation” to the IRR

  21. IRR Method

  22. IRR Method

  23. Calculation Question Why did the Modified BAI and IRR yield the same returns (2.63%)?

  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

  25. We’ll use an example to compare TWRR and MWRR • 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

  26. Our fund’s end-of-month NAVs

  27. Our investors’ purchases Believes Buy high/ Sell low Believes Buy low/ Sell high

  28. The investments’ unrealized gains/losses Paper gain of $600! Paper loss of $600!

  29. What’s our return? The fund’s return (using an exact TWRR method):

  30. How about our investors? But this investor lost $600 And this investor made $600 Because time weighting eliminates the effect of cash flows!

  31. How about money-weighting? • Investor #1’s IRR = -24.86% • Investor #2’s IRR = +35.16%

  32. As a Plan Sponsor … • Which returns make more sense to you? • Which are more meaningful? TWRR judges portfolio manager MWRR judges the portfolio

  33. Multi-period rates of return • We don’t 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?

  34. Geometric linking • 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

  35. Geometric linking Step-by-step process: • Convert the returns to a decimal • Add 1 • Multiply these numbers • Subtract 1 • Convert the number to a percent

  36. Geometric linking

  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 error • Formulas that adjust the return per unit of risk • We’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 Function Note: This is represented in Excel as the STDEV Function

  42. An example of standard deviation

  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

  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 RatioAlso known as Reward-to-Variability Ratio • Developed by Bill Sharpe – Nobel Prize Winner • Equity Risk Premium (Return) / Standard Deviation (Risk)

  47. Sharpe Ratio FormulaEquity 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 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 • It’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 Ratio • IR serves as a measure of the “special information” an active portfolio manager has • Value Added (excess return) / Tracking Error • Typically annualize

More Related