Case 094Strategic and tactical allocationHard
A provident fund trust must allocate Rs 800 crore across six funds to earn 9.5% a year with no more than a 12% loss in a bad year at 95% confidence. Find an allocation that meets both targets, then test it.
1The situation
Ghatprabha Employees' Provident Trust has Rs 800 crore to allocate across six funds. The trustees want 9.5% a year and no more than a 12% loss in a bad year, defined as the worst year in twenty, return minus 1.645 volatilities on a normal model. No fund may exceed 40%, and weights move in 5% steps.
Assumptions: large cap index fund 10.5% return, 20% volatility; mid cap active fund 12.5%, 27%; short duration debt 6.8%, 1.5%; gilt fund 7.0%, 6%; gold ETF 7.0%, 16%; global equity fund of funds 9.5% after its extra fee layer, 18%. Large and mid caps correlate 0.85, each correlates about 0.6 with the global fund, gold is close to uncorrelated with equity, and the two debt funds correlate 0.6.
2Your task
Find an allocation that meets both targets, say how much room there is, and test it against a severe year.
Quick check
At a 9.5% expected return, what is the most volatility the loss limit allows?
Worked solution
Try it on paper, then open one step at a time.
30-second answerThe answer to give first
A mix with about 55% in equity funds, leaning on mid caps, meets both targets: 9.51% expected return and a worst year in twenty of -11.0%. But only 494 of the 27,237 mixes tested pass both tests, so the answer sits at the corner of a thin feasible zone. A severe equity crash takes the same mix down 21.1%, about Rs 169 crore. Tell the trustees the two targets are compatible only on a normal model, and ask which one gives.
Step 1What do the two targets mean together?
Planning a road trip that must arrive by a set time and never exceed a speed limit: each rule alone is easy; together they allow only a narrow range of routes. At 9.5% expected return, the loss limit allows volatility of at most (9.5 + 12) / 1.645 = 13.07%, and the funds that earn more than 9.5% on their own are all more volatile than that. So the job is to find mixes that borrow return from equity and borrow calm from debt and gold, in just the right proportions.
Step 2How much room is there?
Try every mix in 5% steps with no fund above 40%: 27,237 of them. 5,511 reach 9.5%, but only 494 of those also pass the loss test. The highest return any mix can reach is 11.1%, so the target sits near the top of what these funds can deliver, and every mix that gets there is carrying close to the maximum risk the trustees allow.
| Fund | Return | Volatility | Weight | Rs crore | Stress year |
|---|---|---|---|---|---|
| Large cap index | 10.5% | 20% | 10% | 80 | -40% |
| Mid cap active | 12.5% | 27% | 35% | 280 | -50% |
| Short duration debt | 6.8% | 2% | 10% | 80 | +7% |
| Gilt | 7.0% | 6% | 30% | 240 | +8% |
| Gold ETF | 7.0% | 16% | 5% | 40 | +15% |
| Global equity fund of funds | 9.5% | 18% | 10% | 80 | -35% |
| Portfolio | 9.51% | 12.49% | 100% | 800 | -21.1% |
Step 3Which mix, and why that one?
Among the mixes that pass, take the least volatile, because it leaves the most room for the assumptions to be wrong. It holds 10% large cap, 35% mid cap, 10% short debt, 30% gilt, 5% gold and 10% in the global fund. The heavy mid cap weight is not a view on mid caps; it is the cheapest source of the extra return the target demands. Whether a provident fund may hold that much equity, and of what kind, depends on the investment pattern prescribed for such trusts, which must be confirmed before any of this goes to the trustees.
Step 4Does it survive a severe year?
Test it with a stress, not the model that built it. If large caps fall 40%, mid caps 50% and the global fund 35%, while gold rises 15% and gilts 8%, the mix loses 21.1%, Rs 169 crore, nearly twice the limit. The normal model calls a year like that close to impossible; equity markets have produced several in living memory. The allocation meets the targets on paper and breaks them in exactly the year the limit exists for.
Close with the choice for the trustees rather than a single answer: keep 9.5% and accept that a crash year could cost around a fifth of the fund, or keep the 12% limit as a hard stress limit and lower the return target to what a stress-tested mix can earn. Either is defensible; pretending both hold is not.
Where candidates lose it
The common loss is finding one mix that passes both numbers and presenting it as the answer. The interviewer wants to hear how thin the feasible zone is and what the answer leans on, here mid caps and a normal model of losses.
The second is skipping the test. A risk target checked only with the model that produced the allocation has not been tested at all; one stress scenario shows the limit is breached in the year that matters.
What the interviewer asks next
- What return target would a mix need if the 12% limit had to hold in the stress year?
- How would you set the loss limit for a provident fund whose members retire in a known pattern?
- Why might a fund of funds be a poor way to buy global equity for this trust?
Asked at MSCI, Risk Management, Remote, 2013 (Wall Street Oasis): How would you allocate an investment mandate of $100 million among a portfolio of funds?
Company names and figures are illustrative.