 101 Concepts for the Level I Exam

Concept 3: Money-Weighted & Time Weighted Rate of Return Money-weighted rate of return

• The money-weighted rate of return is simply the IRR of a portfolio taking into account all cash inflows and outflows.
• If a manager controls the cash inflows and outflows of a portfolio, then use money-weighted return to measure performance.

An investor buys a stock for \$10 at time t=0. At the end of Year 1, he receives a dividend of \$1 and purchases another stock for \$12. At the end of Year 2, he receives a dividend of \$0.5 per share and sells both shares for \$13. Calculate the money-weighted return.

Solution:

 Year Outflow Inflow Net Cash Flow 0 \$10 to purchase the first share -10 1 \$12 to purchase the second share \$1 dividend received on first share -11 2 \$1.00 dividend (\$0.50 x 2 shares) received \$26 received from selling 2 shares @ \$13 per share +27

Enter the following in a calculator: CF0 = -10; CF1 = -11; CF2 = 27; CPT IRR = 18.28%. The money weighted return is 18.28%.

Time-weighted rate of return

• Time-weighted rate of return is the compound growth rate at which \$1 invested in a portfolio grows over a given measurement period.
• If a manager cannot control the cash inflows and outflows of a portfolio, then use time-weighted return to measure performance.

An investor buys a stock for \$10 at time t=0. At the end of Year 1, he receives a dividend of \$1 and purchases another stock for \$12. At the end of Year 2, he receives a dividend of \$0.5 per share and sells both shares for \$13. Calculate the time-weighted rate of return.

Solution:

1. Break the measurement period into two sub-periods based on the timing of the cash flows.
 Holding period 1 Beginning value = \$10 Dividends paid = \$1 Ending value = \$12 Holding period 2 Beginning value = \$24 (12 x 2) Dividends paid = \$1 (0.5 x 2) Ending value = \$26 (13 x 2)
1. Compute the HPY for each sub-period.

HPY1 = (12 – 10 +1)/10 = 30%

HPY2 = (26 – 24 + 1)/24 = 12.5%

1. Calculate the compounded annual rate by taking the geometric mean of the two sub-periods.

(1 + TWRR)2 = 1.30 x 1.125; TWRR = 20.93%

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