Dollar-Weighted vs. Time-Weighted Returns

Dollar-Weighted Rate of Return

The dollar-weighted rate of return (DWRR) is the internal rate of return (IRR) of a fund, accounting for the timing and amounts of deposits and withdrawals. It solves: B_0*(1+i)^T + sum of C_t*(1+i)^(T-t) = B_T, where B_0 is the initial balance, B_T is the ending balance, and C_t are net contributions at time t. This can also be set up as a present value equation.

The simple interest approximation uses: i is approximately (B_T - B_0 - sum C_t) / (B_0*T + sum C_t*(T - t)). This approximation is frequently used on Exam FM when exact calculation is impractical.

Time-Weighted Rate of Return

The time-weighted rate of return (TWRR) eliminates the effect of cash flow timing by computing the geometric mean of sub-period returns. If the fund values are known at each contribution/withdrawal date, the TWRR is: (1+i)^T = product of (V_after_t / V_before_t) for each sub-period, where V_before includes the contribution and V_after is the fund value just before the next event.

The TWRR measures the fund manager's performance independent of investor behavior (deposits/withdrawals).

Comparison and When to Use Each

DWRR is appropriate for measuring an individual investor's return because it accounts for the timing of their investments. TWRR is appropriate for evaluating a fund manager because it removes the effect of investor-driven cash flows. When contributions are made before strong performance, DWRR > TWRR. When contributions precede poor performance, DWRR < TWRR. Exam FM tests both calculations and the conceptual difference.