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Lesson 5 of 10 · 13 min

Money-weighted return

The money-weighted return is the IRR of the investor's own cash flows: what the investor actually earned, given when and how much money went in and out.

In short

Arithmetic and geometric means ignore how much money was invested when. The money-weighted return (MWR) does not.
MWR = internal rate of return (IRR): the rate that makes the present value of all cash flows zero.
From the investor's view, deposits are outflows (−); withdrawals, cash income and the ending value are inflows (+).
Periods with more money invested get more weight, so the MWR leans toward their returns.
It is investor-specific: two investors in the same fund can have different MWRs.

Why the timing of money matters

A −50% year hurts far more if most of your money was in the fund that year than if you held only a small stake. Arithmetic and geometric means cannot see this: they weight each period's return equally, whatever the amount invested.

The money-weighted return fixes this by weighting each period by the money at work in it. It measures what the investor personally earned on the amounts actually invested.

It is computed exactly like the internal rate of return of a project or the yield to maturity of a bond.

Setting up the cash flows

Take the investor's perspective. Money paid into the portfolio is an outflow (negative). Money taken out, such as withdrawals or dividends received in cash, is an inflow (positive). The portfolio's value at the end is treated as if it were withdrawn: a final inflow.

Put every flow on a timeline with t = 0 as the start, and net the flows at each date. If you receive a dividend of 2 and buy another share for 90 on the same date, the net flow is −88.

Reinvested dividends are not cash flows to the investor: the money never leaves the portfolio. Only cash crossing the line between investor and portfolio counts.

Then solve for the rate that sets the present value of all flows to zero. With more than two dates there is no neat formula; use the calculator's cash-flow worksheet, a spreadsheet's IRR function, or trial and error.

Tom's flows in GBP from his own side: purchases point down, cash received points up. At t = 1 the dividend and the second purchase are netted into one flow of −88. The IRR of these three flows is 10.15%.

Quick checks and period length

To see whether the MWR beats a hurdle rate, discount the flows at the hurdle. For the usual pattern of money in first and money out later, a positive present value means the MWR is above the hurdle and a negative one means it is below. No need to solve the IRR exactly.

If the timeline uses sub-periods (quarters, four-month blocks), the IRR you get is a per-period rate. Annualise it by compounding, $(1+\text{IRR}_{\text{period}})^{c} - 1$ , where c is the number of sub-periods in a year. Multiplying by c is only a rough shortcut.

For the foundation's flows (−50, −20, +15, +70), PV falls as the rate rises. It is still positive at the 6% hurdle, so the curve must cross zero further right: the MWR is above 6% (exactly 7.94%).

What the MWR tells you, and what it does not

The MWR answers 'what return did I earn on my money?'. It reflects the investor's timing: adding money before strong periods raises it; adding before weak periods lowers it.

That same feature makes it a poor tool for comparing managers or funds. The client, not the manager, usually decides when money comes in or goes out. Two investors in the same fund with different deposit dates will report different MWRs.

MWR is the investor's report card, including their own timing decisions. The manager's report card is the time-weighted return in the next lesson.

Formulas

Money-weighted return (IRR): $\sum_{t=0}^{T} \dfrac{CF_t}{(1+\text{IRR})^{t}} = 0$
$CF_t$ = net cash flow at time t from the investor's view (deposits negative; withdrawals, cash income and ending value positive).
Annualising a sub-period IRR: $\text{MWR}_{\text{annual}} = (1+\text{IRR}_{\text{period}})^{c} - 1$
c = number of sub-periods per year (4 for quarters, 3 for four-month blocks).

Worked examples

Example 1 A simple two-year MWR

Sofia invests CHF 10,000 at t = 0 and adds CHF 5,000 at t = 1. At t = 2 the account is worth CHF 16,800. What is her money-weighted return?

Example 2 Dividends and a second purchase

At t = 0 Tom buys one share at GBP 80. At t = 1 the share pays a GBP 2 dividend (taken in cash) and he buys a second share at GBP 90. At t = 2 each share pays GBP 2 and he sells both at GBP 95. What is his MWR, and why does it differ from the average of the yearly returns?

Example 3 Testing against a hurdle

A foundation's account (EUR millions): t = 0 deposit 50; t = 1 deposit 20; t = 2 withdrawal 15; t = 3 ending value 70. The board requires 6% a year. Did the money-weighted return exceed 6%?

On the exam

Expect an IRR calculation with deposits and withdrawals (sign errors are the trap) and concept items on why two investors in one fund can have different MWRs.

Sign errors: deposits are negative; withdrawals and the ending value are positive from the investor's view.
Forgetting to net flows that fall on the same date, such as a dividend received and a new purchase.
Treating a reinvested dividend as a cash flow.
Multiplying a sub-period IRR by the number of periods instead of compounding it.

Check yourself

Q1An investor deposits USD 1,000 at t = 0 and USD 500 at t = 1. The account is worth USD 1,700 at t = 2. The money-weighted return is closest to:
Q2When computing an investor's money-weighted return, a withdrawal from the portfolio is entered as:
Q3Two investors held the same fund over the same five years but report different money-weighted returns. The most likely reason is that they:
Q4An account's money-weighted return computed on quarterly cash flows is 2.1% per quarter. The annualised money-weighted return is closest to:
Q5An investor deposited money first and withdrew it later. Discounting the cash flows at 8% gives a present value of −1,250. The money-weighted return is most likely:

0/5Check yourself

Answer the 5 questions: +10 XP for each one you get right first time.

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