How to solve Portfolios — time-weighted and dollar-weighted rates of return questions on Exam FM?

Question

A fund is worth $10000$ at the start of the year. Immediately before a cash flow at time $t=0.25$, the fund is worth $10793$; the investor withdrew $2400.0$ at that time. At year end the fund is worth $8725$. Calculate the time-weighted rate of return for the year.

Accepted Answer

Formula
$1+TWR=\prod_j(1+r_j)$. For one cash flow $D$ at time $f$, the simple-interest approximation used here is $DWR\approx\dfrac{V_1-V_0-D}{V_0+D(1-f)}$.

Why this formula applies
Time-weighted return removes the effect of external cash-flow timing by chaining subperiod returns. Dollar-weighted return instead solves an equation of value that includes the actual cash-flow dates.

Substitution and calculation
$1 + \text{TWR} = \dfrac{V_b}{V_0} \cdot \dfrac{V_{end}}{V_b + D} = \dfrac{10793}{10000} \cdot \dfrac{8725}{10793+(-2400.0)}$, so $\text{TWR} = 0.12200$.

Answer
The answer is 0.1220, option (A).

How to Solve Portfolios — time-weighted and dollar-weighted rates of return Questions on Exam FM

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