Case 060Macro and multi-asset scenariosCore
A multi-asset fund faces four regimes, growth up or down and inflation up or down, with asset returns and a probability for each. Build risk-balanced weights and compare them with betting everything on the most likely regime.
1The situation
Chaturang All-Weather Portfolio wants an allocation that does not depend on calling the economy. The strategist has set out four regimes for the coming year with probabilities: growth up and inflation up 20%, growth up and inflation down 40%, growth down and inflation up 15%, growth down and inflation down 25%.
Illustrative one-year returns in each regime, in that order, are: equities +10%, +20%, -10%, -4%; nominal bonds +0%, +8%, -2%, +15%; inflation-linked bonds +11%, +4%, +9%, +5%; gold +18%, -2%, +15%, +5%.
2Your task
Build weights that balance risk across the four assets, and compare the result with putting everything in the asset that wins in the most likely regime.
Quick check
The most likely regime is growth up, inflation down. How often is a bet on that regime wrong?
Worked solution
Try it on paper, then open one step at a time.
30-second answerThe answer to give first
Weights inversely proportional to each asset's risk give about 12% equities, 22% nominal bonds, 49% inflation-linked bonds and 17% gold. That mix expects 6.6% against 7.5% for all equities, but its worst regime returns +5.3% against -10%, and its spread across regimes is 1.6 points against 11.9. Giving up 0.9 points of return removes almost all the regime risk.
Step 1Why not simply bet on the most likely regime?
Because the most likely outcome is still unlikely. Packing only for sunshine because sun is the single most likely forecast leaves you soaked on the other days. The favourite regime here has a 40% chance, so an all-equity bet on it is wrong 60% of the time, and in 40% of outcomes, both growth-down regimes, equities lose money. The expected return of all equities is 7.5%, but the range runs from +20% to -10%.
Step 2How do you build risk-balanced weights on paper?
Measure each asset's risk as the spread of its returns across the regimes, weighted by probability, then give each asset a weight proportional to one over that spread. The steadier the asset across regimes, the more of it you hold, so that each asset contributes a similar amount of risk rather than a similar amount of money. Equities swing by 11.9 points, gold by 8.2, nominal bonds by 6.2 and inflation-linked bonds by only 2.8. That gives the weights in the table. It is the simplest version of risk parityAn allocation that sizes positions so each contributes a similar share of total portfolio risk, instead of a similar share of capital.; a fuller version also accounts for how the assets move together.
| Asset | Expected | Spread across regimes | Risk-balanced weight |
|---|---|---|---|
| Equities | 7.50% | 11.95 | 12% |
| Nominal bonds | 6.65% | 6.18 | 22% |
| Inflation-linked bonds | 6.40% | 2.84 | 49% |
| Gold | 6.30% | 8.17 | 17% |
| Balanced portfolio | 6.57% | 1.56 | 100% |
Step 3What do you give up, and is it worth it?
About 0.9 points of expected return. In exchange, the worst regime goes from -10% to +5.3%, and the spread of outcomes shrinks from 11.9 points to 1.6. Per unit of regime risk, the balanced mix earns several times what equities do. That is why funds built this way often borrow modestly to lift the whole mix back towards equity-like returns: it is cheaper to lever a steady portfolio than to accept a volatile one. Say the cost of that honestly: borrowing adds its own risk, and the plan relies on bonds and gold behaving in future regimes as they do in the table.
Compare, too, the naive alternative of 25% in each asset. It expects 6.7% with a spread of 2.2 points and a worst regime of +3.0%: far better than all equities, but with equities and gold driving most of the swings it is less steady than the risk-balanced mix. The case for balance is not that it is never wrong, but that it does not need you to be right about which regime arrives. The limitation is the table itself: real regimes blur, probabilities are guesses, and in a sudden crisis most assets can fall together for a while.
Where candidates lose it
The common loss is putting everything in the asset that wins in the most likely regime and calling that a view. A 40% favourite is wrong 60% of the time, and the interviewer wants to hear that sentence.
The second is balancing money instead of risk: 25% in each asset looks balanced, but equities and gold then drive most of the swings, and the worst regime falls from +5.3% to +3.0%.
What the interviewer asks next
- How would you add correlation between the assets to these weights?
- The strategist raises the probability of stagflation to 35%. What changes?
- How much leverage would bring the balanced portfolio's expected return up to equities', and what new risk does that add?
Company names and figures are illustrative.
