TROUBLESHOOTING NEGATIVE TWR AND INVESTMENT GAIN, OR VICE VERSA

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1 TROUBLESHOOTING NEGATIVE TWR AND INVESTMENT GAIN, OR VICE VERSA It is possible to have a negative Time Weighted Rate of Return (TWR) with an Investment Gain or a positive TWR and an Investment Loss, especially when there is volatility in the market. The TWR calculation is a percentage based on the size of the portfolio, whereas the Investment Gain calculation is an absolute number not impacted by the size of the portfolio. For example, a $1,000 Investment Gain on a $5,000 portfolio has a TWR of 20% while a $1,000 Investment Gain on a $50,000 portfolio has a 2% TWR. The portfolios have the same Investment Gain, but the percentage gained in each of these portfolios is different because of the size of the portfolios. Online This document focuses on the Time Weighted Return (TWR) and does not explain the Internal Rate of Return (IRR) calculation found on some PortfolioCenter Presentations and Reports. See The Difference between TWR and IRR at schwabpt.com/pdflibrary/open.asp?id= for more information about the differences between these calculations. THE CALCULATIONS The TWR calculation has two parts: 1. Calculate sub-period returns or intervals during the period. [(Ending Value / Beginning Value) -1 ] x Link the sub-period returns/intervals to produce the overall TWR for the period. [(1 +r1) x (1 + r2) x (1 + rn) x 100 = TWR To get the final TWR number, link the sub-period returns using the linking formula, as shown below: The Investment Gain calculation, on the other hand, is a combination of elements from the performance report: Capital Appreciation + Income + Total Expenses + Change in Accrued Using simplified examples, this document demonstrates four examples of TWR and Investment Gain misalignment: EXAMPLE DESCRIPTION PAGE 1 Investment Gain, negative TWR and a substantial withdrawal from the portfolio (negative net contributions). 2 Investment Loss, positive TWR and a substantial withdrawal from the portfolio (negative net contributions). 3 Investment Gain, negative TWR and a substantial deposit to the portfolio (positive net contributions). 4 Investment Loss, positive TWR and a substantial deposit to the portfolio (positive net contributions) DocumentID: SPT Last Updated: July 2, 2012

2 EXAMPLE #1 INVESTMENT GAIN, BUT NEGATIVE TWR (SUBSTANTIAL WITHDRAWAL) WITHDRAWAL: INVESTMENT GAIN $10, $11, $7, $3, (6.50)% $ This portfolio had a substantial withdrawal from the portfolio on 2/15/2007, but this condition arises because the return before the withdrawal was different from the return after the withdrawal. Let s look at the calculations: STEP 1: CALCULATE THE RETURN BEFORE THE WITHDRAWAL (12/31/2006 2/14/2007) First, let us calculate the return before the withdrawal. The withdrawal took place on 2/15/2007, so we calculate the return from 12/31/2006 to 2/14/2007. The value of the portfolio on 2/14/2007 was $11,000.00, giving us a $1, gain for the first half of the quarter. The TWR is: Thus, the Investment Gain for the period of 12/31/2006 through 2/14/2007 is $1, and the TWR is 10%. STEP 2: CALCULATE THE RETURN AFTER THE WITHDRAWAL (2/15/2007 3/31/2007) Next, we account for the return after the withdrawal of $7, on 2/15/2007. The beginning value on 2/15/2007 is now $4, ($11, $7, = $4,000.00). The ending value of this portfolio on is $3,400.00, giving us a $ loss for the last half of the quarter. The TWR through is: Thus, the Investment Loss for the period of 2/15/2007 through3/31/2007 is $ and the TWR is (15.00)%. STEP 3: LINK THE INFORMATION FROM BOTH PERIODS: Next, we link the information from each period. First, let us look at the Investment Gain or Loss: The Investment Gain in the first half of the quarter, $1, is greater than the Investment Loss in the second half of the quarter $(600.00) producing a net Investment Gain of $ [( ) x (1-0.15) 1 ] x 100 = (6.5)% The percent loss for the period is greater than the TWR gain for the period, therefore creating an overall Troubleshooting Negative TWR and Investment Gain, or Vice Versa Page 2 of 5

3 EXAMPLE #2 INVESTMENT LOSS, BUT POSITIVE TWR (SUBSTANTIAL WITHDRAWAL) WITHDRAWAL: INVESTMENT GAIN $10, $9, $7, $2, % $(400.00) This portfolio had a substantial withdrawal from the portfolio on 2/15/2007, but this condition arises because the return before the withdrawal was different from the return after the withdrawal. Let s look at the calculations: STEP 1: CALCULATE THE RETURN BEFORE THE WITHDRAWAL (12/31/2006 2/14/2007) First, let us calculate the return before the withdrawal. The withdrawal took place on 2/15/2007, so we calculate the return from 12/31/2006 to 2/14/2007. The value of the portfolio on 2/14/2007 was $9,000.00, giving us a $1, loss for the first half of the quarter. The TWR is: Thus, the Investment Loss for the period of 12/31/2006 through 2/14/2007 is $(1,000.00) and the TWR is (10.00)%. STEP 2: CALCULATE THE RETURN AFTER THE WITHDRAWAL (2/15/2007 3/31/2007) Next, we account for the return after the withdrawal of $7, on 2/15/2007. The beginning value on 2/15/2007 is now $2, ($9, $7, = $2,000.00). The ending value of this portfolio on 3/31/2007 is $2,600.00, giving us a $ gain for the last half of the quarter. The TWR is: Thus, the Investment Gain for the period of 2/15/2007 through 3/31/2007 is $ and the TWR is 30.00% Next, we link the information from each period. First, let us look at the Investment Gain or loss: The Investment Loss in the first half of the quarter, $(1,000.00), is greater than the Investment Gain in the second half of the quarter, $600.00, producing a net Investment Loss of $(400.00). [(1-0.10) x ( ) 1 ] x 100 = 17% The percent gain for the period is greater than the percent loss for the period, therefore creating an overall Troubleshooting Negative TWR and Investment Gain, or Vice Versa Page 3 of 5

4 EXAMPLE #3 INVESTMENT GAIN, BUT NEGATIVE TWR (SUBSTANTIAL DEPOSIT) DEPOSIT: INVESTMENT GAIN $10, $6, $7, $18, (16.92%) $1, This portfolio had a substantial deposit to the portfolio on 2/15/2007, but this condition arises because the return before the deposit was different from the return after the deposit. Let s look at the calculations: STEP 1: CALCULATE THE RETURN BEFORE THE DEPOSIT (12/31/2006 2/14/2007) First, let us calculate the return before the deposit. The deposit took place on 2/15/2007, so we calculate the return from 12/31/2006 to 2/14/2007. The value of the portfolio on 2/14/2007 was $6,000.00, giving us a $4, loss for the first half of the quarter. The TWR is: Thus, the Investment Loss for the period of 12/31/2006 through 2/14/2007 is $(4,000.00) and the TWR is (40.00)%. STEP 2: CALCULATE THE RETURN AFTER THE DEPOSIT (2/15/2007 3/31/2007) Next, we account for the return after the deposit of $7, on 2/15/2007. The beginning value on 2/15/2007 is now $13, ($6, $7, = $13,000.00). The ending value of this portfolio on 3/31/2007 is $18,000.00, giving us a $5, gain for the last half of the quarter. The TWR is: Thus, the Investment Gain for the period of 2/15/2007 through 3/31/2007 is $5, and the TWR is 38.46% Next, we link the information from each period. First, let us look at the Investment Gain or Loss: The Investment Loss in the first half of the quarter, $(4,000.00), is less than the Investment Gain in the second half of the quarter, $5,000.00, producing a net Investment Gain of $1, [(1-0.40) x ( ) 1 ] x 100 = (16.92)% The percent loss for the period is greater than the percent gain for the period, therefore creating an overall Troubleshooting Negative TWR and Investment Gain, or Vice Versa Page 4 of 5

5 EXAMPLE #4 INVESTMENT LOSS, BUT POSITIVE TWR (SUBSTANTIAL DEPOSIT) DEPOSIT: INVESTMENT GAIN $10, $13, $7, $16, % $(1,000.00) This portfolio had a substantial deposit to the portfolio on 2/15/2007, but this condition arises because the return before the deposit was different from the return after the deposit. Let s look at the calculations: STEP 1: CALCULATE THE RETURN BEFORE THE DEPOSIT (12/31/2006 2/14/2007) First, let us calculate the return before the deposit. The deposit took place on 2/15/2007, so we calculate the return from 12/31/2006 to 2/14/2007. The value of the portfolio on 2/14/2007 was $13,000.00, giving us a $3, gain for the first half of the quarter. The TWR is: Thus, the Investment Gain for the period of 12/31/2006 through 2/14/2007 is $3, and the TWR is 30.00%. STEP 2: CALCULATE THE RETURN AFTER THE DEPOSIT (2/15/2007 3/31/2007) Next, we account for the return after the deposit of $7, on 2/15/2007. The beginning value on 2/15/2007 is now $20, ($13, $7, = $20,000.00). The ending value of this portfolio on 3/31/00 is $16,000.00, giving us a $(4,000.00) loss for the last half of the quarter. The TWR is: Thus, the Investment Loss for the period of 2/15/2007 through 3/31/2007 is $(4,000.00) and the TWR is (20.00%). Next, we link the information from each period. First, let s look at the Investment Gain or loss: The Investment Gain in the first half of the quarter, $3,000.00, is less than the Investment Loss in the second half of the quarter, $4,000.00, producing a net Investment Loss of $(1,000.00). [( ) x (1 -.20) 1 ] x 100 = 4.00% The percent gain for the period is greater than the percent loss for the period, therefore creating an overall percent gain for the quarter. PortfolioCenter is a product of Schwab Performance Technologies ( SPT ). SPT is a subsidiary of The Charles Schwab Corporation separate from its affiliate Charles Schwab & Co., Inc. ( CS&Co ). CS&Co is a registered broker-dealer that provides brokerage services, while SPT licenses software and provides related technology products and services Schwab Performance Technologies ( SPT ). All rights reserved. Troubleshooting Negative TWR and Investment Gain, or Vice Versa Page 5 of 5