Mutual Fund Mastery puzzles, solved step by step

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  1. 042A fund that holds mostly mid caps says it beat the Nifty 50 by 4 percentage points over the year. A mid cap weighted index that matches its style beat the Nifty 50 by 5 points over the same year. Did the manager add value?Performance measurement and returnsWarm upFund research and ratingsIndian AMCs

    Try it first

    What was the manager's own contribution, against the right benchmark?

    Show the worked solution

    No. Against a benchmark that matches its style, the manager lagged by 1 point. The fund's 4-point lead over the Nifty 50 came from holding mid caps in a year when mid caps beat large caps by 5 points. A plain mid cap index would have delivered that 5 points with no stock picking. The manager's own choices, after costs, cost the investor 1 point. Beating the wrong benchmark hid an underperformance.

    Why is the Nifty 50 the wrong yardstick here?

    A runner who trains at altitude and races at sea level will post faster times; the stopwatch is right but the comparison flatters him. A benchmark should hold what the fund holds, so that the gap measures the manager's choices and not the market segment the fund happens to sit in. A mid cap heavy fund compared with a large cap index is mostly measuring whether mid caps beat large caps that year, which no manager controls once the mandate is set.

    Split the fund's lead into what the style gave and what the manager added12%Nifty 50the claimed yardstick+5Style effectmid cap tilt-1Managerstock choice, costs16%Fundwhat investors gotstyle index 17%Claimed: beat Nifty 50 by 4Manager's own: -1 point
    Starting from the Nifty 50's 12%, the mid cap style added 5 points to reach 17%, and the manager's own choices then took away 1 point, ending at the fund's 16%; the claimed 4-point lead is entirely style.

    How do you split the lead into style and skill?

    Insert the style benchmark between the two numbers. Fund minus broad index splits into style benchmark minus broad index, which is the style effect, plus fund minus style benchmark, which is what the manager added. Here that is 5 plus (minus 1), giving the claimed 4. Illustrating with a Nifty 50 return of 12%, the style index made 17% and the fund 16%.

    The relationship
    Rf−RN50⏟+4=Rstyle−RN50⏟+5+Rf−Rstyle⏟−1\underbrace{R_f - R_{N50}}_{+4} = \underbrace{R_{style} - R_{N50}}_{+5} + \underbrace{R_f - R_{style}}_{-1}
    R_fthe fund's return
    R_N50the Nifty 50's return
    R_stylethe return of a mid cap weighted index matching the fund's holdings
    What it says in wordsThe fund's lead over the broad index is the style's lead plus the manager's own lead over the style.

    Two fairness points. The fund's return is after its expenses and an index's is not, so part of the minus 1 is cost; a passive mid cap fund would also have trailed its index by its own cost. And one year is a small sample: the right test of skill is the gap to the style benchmark over a full cycle, measured consistently. Regulators in India require schemes to show a benchmark that reflects their category; confirm the current rules before relying on any particular index choice.

    Where candidates lose it

    The trap is accepting the 4 points as skill because the number is true. It is true and irrelevant: the question is what the manager added beyond the segment the fund sits in, and that needs the style benchmark.

    The second loss is the arithmetic sign. Candidates sometimes add the 5 and the 4, or subtract the wrong way. Write fund minus style benchmark, 4 minus 5, and the minus 1 is clear.

    What the interviewer asks next

    • In a year when mid caps lag large caps by 8 points and the fund trails the Nifty 50 by 6, what did the manager add?
    • How would you pick a fair benchmark for a fund that holds 60% large caps and 40% mid caps?
    • Why might a fund house prefer to show the Nifty 50 as its comparison?