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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