Mutual Fund Mastery puzzles, solved step by step

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  1. 099An equity fund is 95% invested, with 5% in cash, and the stocks it holds have a portfolio beta of 1.2. What is its effective market exposure, and what should an investor expect if the market falls 10%?Risk, volatility and drawdownCoreRisk and complianceIndian AMCs

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    What is the fund's effective market exposure?

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    About 114% of the market, so a 10% fall would be expected to cost the fund about 11.4%. Effective exposure is the invested weight times the beta of what is held: 0.95 x 1.2 = 1.14. The 5% in cash looks cautious, but the stocks are more sensitive than the market, and that more than cancels the cash. A typical 10% fall in the index maps to about -11.4% for the fund, before stock-specific moves.

    Why can a fund with cash carry more market risk than the index?

    Two drivers on the same road: one drives only 95% of the distance but at 1.2 times the speed of traffic, the other drives all the way at traffic speed. The first covers more ground per hour despite stopping short. Market exposure is how much money is in stocks multiplied by how strongly those stocks move with the market, so a small cash buffer can be more than undone by holding high-beta stocks. Here 95% invested at a beta of 1.2 gives an exposure of 114%, more than a fully invested index fund.

    Less money in the market, more market riskIndexthe yardstick100%Invested weight5% held in cash95%Effective exposure95% x beta 1.2114%Another fundfully invested, beta 0.990%Market falls 10%: expected fund move about 1.14 x -10% = -11.4%, not the -9.5% the cash suggests
    A fund 95% invested in stocks with a beta of 1.2 has an effective exposure of 114%, more than the index, while a fully invested fund with a beta of 0.9 has only 90%, so the cash level alone says little about market risk.
    The relationship
    βfund=wequity×βstocks+wcash×0=0.95×1.2=1.14\beta_{fund} = w_{equity} \times \beta_{stocks} + w_{cash} \times 0 = 0.95 \times 1.2 = 1.14
    w_{equity}the share of the fund in stocks, 95%
    \beta_{stocks}the beta of the stock portfolio, 1.2
    w_{cash}the cash share, 5%, with a beta of zero
    What it says in wordsA fund's beta is the weighted average of the betas of what it holds, and cash has a beta of zero.

    What should the investor expect in a 10% fall, and how firm is that?

    About -11.4%, as a central estimate. The cash adds a sliver of interest, about 0.025% over a month at an assumed 6% a year, too small to change the answer. Beta is an average relationship, not a promise: in any one fall, the fund's own stocks can do better or worse than the beta implies, and betas measured from calm periods often rise in a sell-off. So -11.4% is the expected fund move, with a range around it that depends on how much of the fund's risk is stock-specific.

    For a risk desk the lesson is about which number to monitor. A fund manager who says 'we are defensive, we hold 5% cash' may be running more market risk than a fully invested peer. Report exposure as invested weight times beta, not cash level, when judging how a fund will behave in a fall. The fully invested fund with a beta of 0.9 in the figure has 90% exposure and would be expected to fall about 9% in the same move.

    Where candidates lose it

    The common answer is 95%, read straight from the cash level, which treats every stock as moving one for one with the market. It is the answer a fund's marketing would like you to give.

    The other slip is quoting 120% and forgetting the cash. Both numbers matter, and the answer is their product. Then add one sentence on beta being an estimate, so the expected fall is a centre, not a forecast.

    What the interviewer asks next

    • What cash level would bring this fund's effective exposure back to 100%?
    • The fund uses index futures worth 10% of assets on top. What is its exposure now?
    • Why might the measured beta of the stocks rise during a market fall?