Mutual Fund Mastery puzzles, solved step by step

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  1. 011A Rs 500 crore equity fund has a daily volatility of 1.2%. What is its one-day 95% value at risk, what is its ten-day VaR by the square-root-of-time rule, and what does VaR not tell you?Risk, volatility and drawdownCoreBlackRockNew York · 2026

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    Pick the one-day 95% VaR before you work it.

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    One-day 95% VaR is about Rs 9.9 crore, and ten-day VaR about Rs 31 crore. On 19 days out of 20 the fund should lose less than 1.645 times 1.2%, which is 1.97% or Rs 9.87 crore. Scaling by the square root of 10 gives Rs 31.2 crore. What VaR does not say is how much is lost on the one bad day in 20.

    What does a 95% one-day VaR actually promise?

    Think of a flood marker on a riverbank that says the water passes this line in one year out of twenty. It tells you where the bad years start. It says nothing about whether the water stops a foot above the line or ten feet above it. VaR is a threshold: on 95% of days the loss should stay below it, and on the other 5% it is exceeded by an amount VaR does not measure. For a normal distributionthe bell-shaped curve where most outcomes sit near the average and extreme ones are rare in a fixed, symmetric way, the 5% left tail starts 1.645 standard deviations below the average.

    The working is three multiplications. Daily standard deviation 1.2%, times 1.645, is 1.974%. On Rs 500 crore that is Rs 9.87 crore. The quiet assumption is that the average daily return is about zero, which is reasonable over one day for an equity fund.

    VaR marks where the bad days begin, not how bad they getVaR line: -1.97%a loss of Rs 9.9 crore5% of daysland herehow far? VaR is silent-4%-2%0+2%+4%Daily return of the fundOne day, 95%Rs 9.9 croreTen days, x root 10Rs 31.2 croreAssumes normal, independentdays and an unchanged book
    The one-day 95% VaR of the Rs 500 crore fund sits at a loss of 1.97%, or Rs 9.9 crore, and the shaded 5% of days beyond that line can lose any amount, which VaR does not report.

    Why does ten days scale by the square root of ten and not by ten?

    Because daily moves partly cancel. If each day is independent, variances add, so ten days carry ten times the variance and the square root of ten, about 3.16, times the standard deviation. Ten-day VaR is Rs 9.87 crore times 3.162, about Rs 31.2 crore, not Rs 99 crore, because a bad day is often followed by a better one. Multiplying by ten would assume every one of the ten days is a 5% tail day, which almost never happens.

    The relationship
    VaRh=z0.95 σ1h V=1.645×1.2%×10×500≈Rs 31.2 crore\text{VaR}_{h} = z_{0.95}\,\sigma_{1}\sqrt{h}\,V = 1.645 \times 1.2\% \times \sqrt{10} \times 500 \approx \text{Rs } 31.2 \text{ crore}
    z_{0.95}the one-tailed 95% point of the normal curve, 1.645
    \sigma_1the daily volatility, 1.2%
    hthe horizon in days, 10
    Vthe fund's value, Rs 500 crore
    What it says in wordsCut the bell curve at its 5% left tail, scale the daily spread up by the square root of the days, and apply it to the fund's value.

    Now the limitation, which is what the interviewer is waiting for. VaR is silent on the size of the tail. On a normal curve the average loss on those worst 5% of days, the expected shortfallthe average loss on the days that are worse than the VaR line, is about Rs 12.4 crore, but real daily returns have fatter tails than the normal, so the true figure can be larger. The square-root rule also assumes independent days and an unchanged portfolio; in a falling market, losses cluster and correlations rise, and both assumptions break when VaR is needed most.

    Where candidates lose it

    The common slip is using 1.96 or 2 standard deviations, the two-sided 95% band from statistics class. VaR asks only about losses, so it uses one tail and 1.645. The other slip is multiplying by ten for ten days, which overstates the ten-day figure by a factor of about three.

    The bigger loss is treating VaR as the worst case. Saying the fund's worst possible day is a Rs 9.9 crore loss tells the interviewer you have the definition backwards: it is the loss exceeded one day in twenty, and the question asks what it does not tell you so that you will say so.

    What the interviewer asks next

    • What is the one-day 99% VaR for the same fund?
    • Why might a risk team prefer expected shortfall to VaR?
    • How would you check, after a year, whether the VaR model was any good?

    Asked at BlackRock, Restructuring, New York, 2026 (Wall Street Oasis): Techincal and behavioral (VAR, market views, stock valuation) why blackrock, python experience?