Case 081Strategic and tactical allocationCore
A trust running a 60/40 portfolio has Rs 10 crore more to invest. Gold, mid caps, corporate bonds or international equity: which addition raises the portfolio's Sharpe ratio most?
1The situation
Devrai Educational Trust runs Rs 200 crore at 60% Indian equity and 40% bonds. On the trust's assumptions the equity earns 12.5% with 18% volatility, the bonds 7.25% with 5% volatility, with a correlation of 0.2. That gives the portfolio an expected 10.4% with 11.37% volatility. Cash earns 6.5%.
A donor gives Rs 10 crore. The committee will put all of it in one new holding. The candidates, each with its correlation to the existing portfolio:
Gold: 8% return, 15% volatility, correlation minus 0.1. Mid caps: 14%, 24%, 0.85. Corporate bonds: 8.2%, 4%, 0.3. International equity: 11%, 17%, 0.55.
2Your task
Which addition lifts the portfolio's Sharpe ratio most, and why is the answer not the asset with the highest return or the highest Sharpe ratio of its own?
Quick check
Which addition do you expect to lift the portfolio's Sharpe ratio most?
Worked solution
Try it on paper, then open one step at a time.
30-second answerThe answer to give first
Gold lifts the Sharpe ratio most, from 0.343 to 0.351, even though it has the lowest expected return. An addition helps when its excess return beats its correlation times its volatility times the portfolio's Sharpe ratio. Gold's negative correlation sets a hurdle below zero, which it clears by 2.01 points. Mid caps, the highest-return option, clear their hurdle by only 0.50, because they mostly repeat the equity risk the trust already holds.
Step 1Why is the highest-return asset not the answer?
A cricket side with five strong batsmen does not improve most by adding a sixth batsman; it improves by adding a bowler. What an asset adds depends on what the portfolio already holds, not on how good the asset looks alone. Mid caps earn 14%, but with a correlation of 0.85 they rise and fall with the equity the trust owns. Their risk arrives almost in full, and it arrives at the same time as the risk already there.
Step 2What is the test that decides it?
Compare each candidate's excess return with a hurdle set by the portfolio. A small addition raises the Sharpe ratio when its excess return is above its correlation with the portfolio, times its volatility, times the portfolio's own Sharpe ratio. Correlation times volatility is the risk the portfolio actually feels from the asset; multiplying by 0.343 converts that risk into the return it must earn to pay its way. The trust's Sharpe ratio is (10.4 - 6.5) / 11.37 = 0.343.
| E[R_i] - r_f | the candidate's expected return above cash |
| rho_i,p sigma_i | its correlation with the portfolio times its volatility |
| (E[R_p] - r_f)/sigma_p | the portfolio's Sharpe ratio, here 0.343 |
Step 3Do the full numbers agree with the shortcut?
Check it by adding Rs 10 crore of each, a 4.76% weight, and recomputing return and risk with the correlations. Gold takes the Sharpe ratio to 0.3512, corporate bonds to 0.3486, international equity to 0.3478 and mid caps to only 0.3446. The order matches the gap above the line. Gold lowers expected return slightly, to 10.29%, but cuts volatility to 10.78%, and that trade is what the ratio rewards.
| Candidate | Return | Excess over cash | Hurdle: rho x vol x Sharpe | Gap | New Sharpe |
|---|---|---|---|---|---|
| Gold | 8.0% | 1.5 | -0.10 x 15% x 0.343 = -0.51 | +2.01 | 0.3512 |
| Mid caps | 14.0% | 7.5 | +0.85 x 24% x 0.343 = 7.00 | +0.50 | 0.3446 |
| Corporate bonds | 8.2% | 1.7 | +0.30 x 4% x 0.343 = 0.41 | +1.29 | 0.3486 |
| International equity | 11.0% | 4.5 | +0.55 x 17% x 0.343 = 3.21 | +1.29 | 0.3478 |
State the limits before the committee does. The answer rests on a correlation of minus 0.1 for gold that can change sign in a crisis, and on expected returns that are estimates. The test is also marginal: it holds for a small addition, and a large gold weight would lower the Sharpe ratio again. A strong close is to name the answer, give the reason in one line, and say which assumption you would stress first.
Where candidates lose it
The common loss is picking mid caps for the return, or corporate bonds because their own Sharpe ratio of 0.43 is the best on the list. Both judge the asset alone, when the question is about the portfolio it joins.
The second is dismissing gold because 8% is barely above cash. Its value is in the correlation, and candidates who never compute the hurdle never see that its bar is below zero.
What the interviewer asks next
- What correlation would gold need before it stopped improving the portfolio?
- How much gold would maximise the trust's Sharpe ratio, roughly, and why does the benefit fade?
- The committee cares about the worst year, not the Sharpe ratio. Does the answer change?
Asked at Northern Trust, Asset Management, Chicago, 2025 (Wall Street Oasis): If you had to allocate an asset today, where would you put it?
Company names and figures are illustrative.