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  1. 097A fund makes 50% in year one on Rs 100 crore, then takes in Rs 400 crore of new money and loses 20% in year two. What are its time-weighted and money-weighted returns, and did its investors make money?Returns, compounding and feesHardFund of funds and allocatorsMulti-manager platforms

    Try it first

    The fund reports its two-year return. Which statement is right?

    Show the worked solution

    The time-weighted return is +20%; the money-weighted return is about -10.2% a year, and investors as a group lost Rs 60 crore. Rs 100 crore grows to Rs 150 crore, then Rs 400 crore arrives and the Rs 550 crore falls 20% to Rs 440 crore. Chaining 1.5 x 0.8 gives +20%, the manager's record. But Rs 500 crore went in and Rs 440 crore remains, because most of the money arrived just before the loss.

    What does each measure answer?

    Think of a restaurant that gets a glowing review after a good year, triples its tables, and then has a poor year. Its record over the two years looks fine, but most of the diners ate in the poor year. The time-weighted return measures the manager, chaining each period's return so the timing of money coming in or out does not count; the money-weighted return measures the investors, weighting each period by the money actually exposed to it.

    The 50% gain was earned on Rs 100 crore; the 20% loss hit Rs 550 crore100Start150End of year 1550After inflow440End of year 2+400 new+50%-20%Rs croreManager's recordtime-weighted1.5 x 0.8 = 1.20+20% over two yearsInvestors' resultmoney-weightedput in 500, hold 440lost Rs 60 croreabout -10.2% a year
    The fund earns 50% on Rs 100 crore, takes in Rs 400 crore, then loses 20% of Rs 550 crore, so the manager's time-weighted record is +20% while investors put in Rs 500 crore, hold Rs 440 crore, and earned about -10.2% a year.

    How do you compute the money-weighted return?

    Treat the investors' money as a set of cash flows and find the single annual rate that links them: Rs 100 crore in at the start, Rs 400 crore in after a year, Rs 440 crore out at the end. Solve 100(1 + r) squared + 400(1 + r) = 440; the root is 1 + r = 0.8983, so the money-weighted return is about -10.2% a year. It is negative because most of the money sat through the losing year: Rs 550 crore lost 20%, Rs 110 crore, while the good year earned only Rs 50 crore on Rs 100 crore.

    The relationship
    100(1+r)2+400(1+r)=440  ⇒  1+r=−4+33.62=0.898100(1+r)^2 + 400(1+r) = 440 \;\Rightarrow\; 1 + r = \frac{-4 + \sqrt{33.6}}{2} = 0.898
    100Rs crore invested at the start
    400Rs crore added after one year
    440Rs crore the investors hold at the end
    rthe money-weighted return, the internal rate of return on those flows
    What it says in wordsThe money-weighted return is the one rate that grows every rupee invested, from the day it arrived, into what the investors hold at the end.

    Which number should an allocator look at?

    Both, for different questions. To judge the manager's skill, use the time-weighted +20%, because the manager did not choose when investors arrived. To judge whether the fund was good for the people in it, or whether money chased performance, use the money-weighted figure. A wide gap between the two, as here, is a warning about hot money: investors piling in after a strong year and bearing the next year's loss on a much bigger base. Had all Rs 500 crore arrived at the start, both measures would agree and the investors would hold Rs 600 crore.

    Where candidates lose it

    The common loss is reporting +20% and saying the investors made money. The chained return deliberately ignores that most rupees arrived just before the loss, and the interviewer built the numbers so the two measures point in opposite directions.

    The second loss is averaging the two yearly returns, +50% and -20%, to get +15% a year. That is neither measure: the time-weighted annual figure is the square root of 1.2 minus 1, about 9.5% a year.

    What the interviewer asks next

    • What is the time-weighted return expressed as an annual rate?
    • The Rs 400 crore had arrived at the start of year one instead. What are both returns now?
    • Why do fund fact sheets report time-weighted returns?