Case 092Investment and portfolio riskCore
A fund of funds must drop one of two managers: one returned 14% with 20% volatility and a 32% drawdown, the other 11% with 10% volatility and a 12% drawdown. Compare them on risk-adjusted measures and decide which to keep.
1The situation
Tamravel Fund of Funds has to cut one of two long-short equity managers to make room for a new strategy. Over the same five years, Manager A returned 14% a year with 20% annual volatility and a worst peak-to-trough fall, its maximum drawdown, of 32%. Manager B returned 11% a year with 10% volatility and a maximum drawdown of 12%.
Use a risk-free rate of 6%. The investment committee chair likes Manager A because it made more money. Both charge the same fees, and both have similar correlation with the rest of the portfolio.
2Your task
Compare the two on the Sharpe ratio and on return per unit of drawdown, and say which you keep and why.
Quick check
Which manager has the higher Sharpe ratio?
Worked solution
Try it on paper, then open one step at a time.
30-second answerThe answer to give first
Keep Manager B: its Sharpe ratio is 0.50 against 0.40, and it earns 0.92 of return per unit of drawdown against 0.44. A's extra 3 points of return came with twice the volatility and nearly three times the drawdown. Held at twice the size, B would earn about 16% at the same 20% volatility as A. The limits: five years is a short record, and a drawdown is one observed path, not a measured probability.
Step 1Why is the higher return not the answer?
Because the return came with a different amount of risk. Two drivers who reach the city in the same time are not equally good if one drove at double the speed limit. The Sharpe ratioReturn above the risk-free rate, divided by volatility: how much extra return an investment earned for each unit of ups and downs. puts both on the same footing: A earns 8 points over the risk-free rate with 20% volatility, 0.40; B earns 5 points with 10%, 0.50. Per unit of risk taken, B is a quarter better.
Step 2What does the drawdown add that volatility does not?
Volatility averages the ups and downs; the maximum drawdown shows the worst stretch an investor actually lived through. A fell 32% from a peak before recovering, which needs a 47% gain to get back; B's worst fall was 12%. Return over drawdown is 0.44 for A and 0.92 for B, and on excess return the gap is similar, 0.25 against 0.42. Investors in a fund of funds redeem after drawdowns, not after bad Sharpe ratios, so the drawdown measure is the one that decides whether the money is still there to recover.
Step 3Could B match A's return?
Yes, and that is the argument that settles it. Hold B at twice the weight, funded at the risk-free rate, and it returns 2 times 11 less 6, about 16%, at 20% volatility, the same risk as A for 2 more points of return. Its drawdown would scale to roughly 24%, still better than A's 32%. In practice a fund of funds gets the same effect by giving B a larger allocation within the portfolio's risk budget rather than by borrowing.
| Measure | Manager A | Manager B | B at twice the weight |
|---|---|---|---|
| Return | 14.0% | 11.0% | 16.0% |
| Volatility | 20.0% | 10.0% | 20.0% |
| Maximum drawdown | 32.0% | 12.0% | about 24% |
| Sharpe ratio | 0.40 | 0.50 | 0.50 |
| Return / drawdown | 0.44 | 0.92 | 0.67 |
Close with what could overturn the decision. Five years of monthly data is a small sample, and a Sharpe gap of 0.10 is within the noise of such a record. Check whether B's smooth returns come from hard-to-value positions, which can understate volatility, and whether A's drawdown came from a style that has since changed. If both checks come back clean, the numbers favour keeping B and giving it more of the risk budget.
Where candidates lose it
The frequent miss is forgetting to subtract the risk-free rate, which gives Sharpe ratios of 0.70 and 1.10 and exaggerates B's advantage. The ranking survives here, but interviewers mark the formula.
The second is treating B's lower return as a reason to drop it. Return and risk can be scaled together; what cannot be scaled is the return earned per unit of risk.
What the interviewer asks next
- Manager A's returns have a correlation of minus 0.2 with the rest of the portfolio and B's plus 0.6. Does the answer change?
- How would you test whether B's low volatility comes from stale prices?
- Why might the Sortino ratio rank these two differently from the Sharpe ratio?
Company names and figures are illustrative.