A trust with a portfolio already 70% in Indian equities asks how to allocate a new Rs 100 crore mandate across an equity fund, a credit fund and a multi-strategy fund. Show how the answer changes when you judge the whole portfolio rather than the mandate alone.

Judged in Sarvodhan's portfolio, the multi-strategy fund adds the least risk per rupee and the equity fund by far the most. Putting all Rs 100 crore in the equity fund lifts portfolio volatility to 13.38%; a 40/60 split between credit and multi-strategy gives 10.82%. Judged alone, the credit fund looks safest. The split depends on the trust's return needs, but the equity fund mostly doubles the bet it already holds.

A family that already owns three shops on one street does not reduce its risk by buying a fourth shop on the same street, however well run. Risk is a property of everything the investor holds together, so a new fund must be judged by what it adds to the existing portfolio, not by its own volatility. Sarvodhan's Rs 500 crore already carries Rs 63 crore a year of volatility, 12.6%, all of it from Indian equities.

When one asset dominates the portfolio, a small addition's marginal riskHow much the portfolio volatility changes for one more rupee in a holding: roughly its volatility times its correlation with the existing portfolio. is roughly its volatility times its correlation with that asset. The equity fund adds 17.1% per rupee, the credit fund 1.8% and the multi-strategy fund 1.6%. The credit fund is the least volatile alone, 6% against 8%, but the multi-strategy fund's lower correlation more than makes up the difference.

Run the full calculation on Rs 600 crore. All Rs 100 crore in the equity fund takes volatility to Rs 80.3 crore a year, 13.38%, while 40 in credit and 60 in multi-strategy gives Rs 64.9 crore, 10.82%. The equity choice adds Rs 17.3 crore of volatility over leaving the money in cash; the diversifying split adds Rs 1.9 crore. An equal split sits in between at 11.66%, because a third in equities brings most of the extra risk with it.

Start from the trust's objective, because risk is only half the answer. If the trust needs growth and can bear equity swings, part of the money can go to equities, but through something that diversifies the existing holdings, not a fund 0.95 correlated with them. If the aim is to make the portfolio more resilient, the case is for credit and multi-strategy, with the weights set by how much return each is expected to earn per unit of added risk. The limitation: correlations of 0.2 and 0.3 are calm-market estimates, and in a sell-off both diversifiers tend to move closer to equities, so test the split at stressed correlations before committing.