Time-weighted returns: unraveling the mystery of investment performance calculations.Providing clients with fair and meaningful reporting of investment performance is among the primary objectives of investment management services. Often underestimated by CPAs who offer, or are considering offering such services, the process of calculating and presenting investment performance often can be problematic and, in some respects, "counter-intuitive." This article focuses on an important, yet often misunderstood mis·un·der·stood v. Past tense and past participle of misunderstand. adj. 1. Incorrectly understood or interpreted. 2. , aspect of the investment reporting process--calculating and presenting time-weighted returns time-weighted return A rate-of-return measure of portfolio performance that gives equal weight to each period included in the study regardless of any differences in amounts invested in each period. for clients. CALCULATING INVESTMENT RETURNS In its simplest form, the total return on an investment is its ending value, plus any distributions, less its beginning value, divided by the beginning value. In the absence of cash flows, the formula is [R.sub.TR] = (MVE MVE Murray Valley Encephalitis MVE Market Value of Equity MVE Midwest Vocal Express (barbershop chorus) MVE Mid Valley Engineering (Modesto, CA) MVE Modulo Variable Expansion - MVB MVB Multivesicular Body MVB Magdeburger Verkehrsbetriebe MVB Multifunction Vehicle Bus MVB Multimedia Viewer Book MVB Multifunctional Vehicle Bus MVB Moisture Vapor Barrier MVB Multivibrator MVB Minimum Variance Beamformer MVB MicroVax Business )/MVB Where RTR RTR Ready To Run RTR Rundfunk & Telekom Regulierungs Gmbh RTR Rotor RTR Radio e Televisiun Rumantscha (Romansh Radio and Television, Switzerland) RTR Response Time Reporter RTR Ready To Race RTR Ready to Roll is total return. MVE is market value--ending. MVB is market value-beginning. Exhibit 1, page 88, shows a sample calculation. Exhibit 1: Sample Total Return Calculation Chuck invests $100 in Growco, a mutual fund, on April 1. Exactly one year later, he sells his entire position for $113. Chuck's total return on Growco is 13%, calculated as follows: ($113-$100)/$100 = 13%. Unfortunately, investment calculations are rarely as straightforward as this single-period return. Generally, the rate of return on an investment involves an irregular HEIR, IRREGULAR. In Louisiana, irregular heirs are those who are neither testamentary nor legal, and who have been established by law to take the succession. See Civ. Code of Lo. art. 874. period of time, additional cash contributions, and withdrawals and distributions--all of which the above calculation ignored. A more common method of calculating returns during multiperiod time intervals is internal rate of return or dollar-weighted return. This enables an investment adviser to solve for an investment's return by discounting cash inflows and outflows over a given period of time. The formula for dollar-weighted return is Initial investment= [CF.sub.1]/(1+r)+[CF.sub.2]/[(1+r).sup.2]+...+[CF.sub.n]/[(1+r).sup.n] Where [CF.sub.(1 to n)] represents the cash flow at each time interval. r represents the return solved by the equation. (Investments are shown as negative cash flows, while distributions and the final payment are shown as positive cash flows.) Exhibit 2, page 88, shows a sample calculation. [Exhibit 2 ILLUSTRATION OMITTED] Exhibit 2 compares the experiences of two investors--Barry and Samantha--who both invest in the same mutual fund. Dollar-weighted returns reward Samantha's larger investment during the fund's successful first two years. Even though both Barry and Samantha invest in the same mutual fund over the same time period, their opinions of the fund manager's ability--based on their very different ending account balances--may differ. Accordingly, the principal limitation of this investor-centered means of measuring performance is that dollar-weighted returns do not isolate isolate /iso·late/ (i´sah-lat) 1. to separate from others. 2. a group of individuals prevented by geographic, genetic, ecologic, social, or artificial barriers from interbreeding with others of their kind. a fund's performance from an investor's timing, luck or lack thereof. Although the ending account balance may be of ultimate importance to an investor, dollar-weighted returns do not adequately reflect a fund manager's performance. TIME-WEIGHTED RETURNS Acknowledging the need for consistency in reporting investment returns separate from investors' actions, the investment community uses a standard performance measure--the time-weighted return--which essentially is a calculation of the investment return generated by a manager over specific time periods that are geometrically ge·o·met·ric also ge·o·met·ri·cal adj. 1. a. Of or relating to geometry and its methods and principles. b. Increasing or decreasing in a geometric progression. 2. linked or compounded. This isolates a manager's specific performance from investor timing and the direction of cash flows. Time-weighted returns allow for a consistent measure of a manager's performance relative to other managers and to alternative investments and indices. Ideally, the daily linking of time intervals--the practice of the mutual fund industry--provides the most accurate performance calculations. One commonly used formula for calculating time-weighted returns when daily valuations are not available is the "modified Dietz" method. Return = (MVE-MVB-F)/(MVB + FW). Where MVE is market value-ending. MVB is market value-beginning. F is net cash inflows (outflows are negative). FW is the net cash inflows weighted by the days invested. Exhibit 3, on this page, shows how this calculation works. Exhibit 3: Sample Modified Dietz Method Modified Dietz Method A method of evaluating a portfolio's return based upon a time weighted analysis. Notes: The Modified Dietz Method is more accurate way to measure the return on your portfolio than a simple geometric return method. Calculation Phyllis invests $100 in Safeco, a mutual fund, on August 1. On August 10, she adds $25 to her investment. On August 31, the market value of her shares is $150. Her time-weighted return is 21.4%, calculated as follows: ($150-$100-$25)/($100+$25*21/31) = 21.4%. The modified Dietz method assumes an investment earns a constant rate of return over a selected period, eliminating the need to know the exact valuation on the date of each cash flow. Intuitively, this return might be thought of as a weighted average of achieving a 25% return (earning $25 on $100 invested) for one-third of the period under analysis and a 20% return (earning $25 on $125 invested) for two-thirds of the period. Calculating Barry's and Samantha's investments in Riskco using time-weighted returns provides an interesting insight, as shown in exhibit 4, page 89. The time-weighted return for Riskco is the same for both Barry and Samantha. (After all, both investors were part of the same pool of commingled funds Commingled Fund A type of mutual fund consisting of assets from several accounts that are blended together. Sometimes called a "pooled fund." Notes: They are "commingled" to reduce the costs of managing them separately. ). In addition, Samantha's returns are identical to her dollar-weighted return, since there were no additional cash flows after her initial investment. Barry did experience a very real economic loss over the period the fund reported a positive rate of return. However, the difference between these two calculations rests squarely square·ly adv. 1. Mathematics At right angles: sawed the beam squarely. 2. In a square shape. 3. on Barry's timing of his investments--crushing his belief in the infallibility infallibility (ĭnfăl'əbĭl`ətē), in Christian thought, exemption from the possibility of error, bestowed on the church as a teaching authority, as a gift of the Holy Spirit. of dollar-cost averaging dollar-cost averaging Investment of a fixed amount of money at regular intervals, usually each month. This process results in the purchase of extra shares during market downturns and fewer shares during market upturns. , at least over the short term. In the process, Barry learned the meaning of still another expression--getting "whipsawed Whipsawed Buying stocks just before prices fall and selling stocks just before prices rise in a volatile market, often as the result of misleading signals. " by the markets. CHOICE OF TIME INTERVALS When providing investment advisory services advisory services advisory services provided to the public, in their capacity as owners and managers of animals, are an important part of veterinary science. They may be provided by government bureaux, by commercial companies who deal in pharmaceuticals or animals or animal , CPAs should consider following the guidelines guidelines, n.pl a set of standards, criteria, or specifications to be used or followed in the performance of certain tasks. of the Association for Investment Management and Research (AIMR AIMR See Association for Investment Management and Research (AIMR). ), a self-governing organization recognized as the investment community's resource for the fair and accurate reporting of investment performance. The AIMR, performance presentation standards established the voluntary standards investment professionals and organizations follow to promote uniformity and comparability among investment performance presentations. The AIMR Performance Presentation Standards Handbook--1997 is an invaluable resource for investment advisers. The shorter the time between valuations, the more accurate the measurement. AIMR, encourages geometrically linked daily portfolio valuations. Generally, monthly performance calculations are adequate for most purposes, with quarterly intervals being the absolute minimum. The AIMR standard is as follows: "Performance must be valued at least quarterly, and periodic returns must be geometrically linked." AIMR also recommends that if portfolios are not valued daily, they should be valued "whenever cash flows and market action combine to materially distort performance." CPAs should consider several factors when selecting time intervals, including the nature and magnitude of investor cash flows, the marginal accuracy gained by using shorter time intervals, the availability of investment data and the methodology used to perform the calculations. THE NEED FOR TIME-WEIGHTED PERFORMANCE A modest investment that has performed quite well over the past several years may experience a disastrous run immediately after a large additional investment, leaving a client with a very real aggregate economic loss and a biased perception of the manager's performance. Although the client's own timing created the loss, many are slow to acknowledge their contribution. For investors to rely on historical performance as a factor in future investment decisions, they need the objectivity and consistency of time-weighted performance reporting.
Exhibit 4: Time-Weighted Return for Barry and Samantha
Barry
Year 1 ($150-$100)/ $100=50%
Year 2 ($350-$150-$100)/($150+$100)= 40%
Year 3 ($270-$350-$100)/($350+$100)= (40%)
Time-weighted
return: (1+.5)x(1+.4)X(1-.4)=(1+.26)=8.0% annualized
Samantha
Year 1 ($450-$300)/$300=50%
Year 2 ($630-$450)/$450=40%
Year 3 ($378-$630)/$630=(40%)
Time-weighted
return: (1+.5)X(1+.4)X(1-.4)=(1+.26)=8.0% annualized
Investment Outlook Advisory Board Robert A. Clarfeld, CPA/PFS, CFP 1. CFP - Constraint Functional Programming. 2. CFP - Communicating Functional Processes. 3. CFP - Call For Papers (for a conference). , Editor Steven I. Levey, CPA/PFS Eric A. Norberg, CPA/PFS, CFP Phyllis J. Bernstein, CPA (Computer Press Association, Landing, NJ) An earlier membership organization founded in 1983 that promoted excellence in computer journalism. Its annual awards honored outstanding examples in print, broadcast and electronic media. The CPA disbanded in 2000. Susan A. Frohlich, CPA ROBERT A. CLARFELD, CPA/PFS, CFP, is president of Clarfeld & Co., PC, a New York City New York City: see New York, city. New York City City (pop., 2000: 8,008,278), southeastern New York, at the mouth of the Hudson River. The largest city in the U.S. CPA financial planning Financial planning Evaluating the investing and financing options available to a firm. Planning includes attempting to make optimal decisions, projecting the consequences of these decisions for the firm in the form of a financial plan, and then comparing future performance against firm. He is a member of the American institute of CPAs personal financial planning executive committee and chairman of its investment services task force. |
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