Case 091Performance evaluation and manager selectionCore
A multi-manager programme blends three large cap managers equally, each with 5% tracking error and a 1.5% fee. What is the combined tracking error if their active returns correlate 0.8, and if they correlate minus 0.2? Is it worth its fees against a 0.2% index fund?
1The situation
Sammilan Multi-Manager Programme runs Rs 900 crore of large cap equity split equally across three active managers. Each manager has 5% tracking error against the index and charges 1.5% a year. A large cap index fund would cost 0.2%.
The programme's selling point is diversification across styles. Your analysis of past holdings suggests two possible worlds: the managers' active returns correlate about 0.8, because they chase similar stocks, or about minus 0.2, because their styles lean against each other.
2Your task
What is the combined tracking error in each world, what does the client actually pay for, and when is the programme worth its fees?
Quick check
Correlation minus 0.2 between the three managers. What is the combined tracking error?
Worked solution
Try it on paper, then open one step at a time.
30-second answerThe answer to give first
About 4.65% at a correlation of 0.8 and 2.24% at minus 0.2. In the first world the client pays three fees for roughly one manager's bets; in the second the bets cancel, so 1.3 points of extra fee buy only 2.24 points of active risk, and the programme must earn an information ratio of 0.58 just to match the index fund. Holding 45% in one manager and the rest in the index fund gives the same active risk for 0.78%.
Step 1How do three managers' risks combine?
Three friends each betting on a different football team in the same match: whatever happens, one of them wins and at least one loses, and the group as a whole barely moves. When managers' active bets lean against each other, much of the active risk cancels, and what remains looks more and more like the index. The formula for equal weights is the tracking error times the square root of (1 + 2 x correlation) / 3.
| TE | each manager's tracking error, 5% |
| n | number of equally weighted managers, 3 |
| rho | correlation between their active returns |
Step 2What does the client pay for in each world?
At 0.8 the three managers hold much the same bets. Tracking error of 4.65% is barely below one manager's 5%, so the client pays three fees for roughly one set of ideas. At minus 0.2 the opposite happens: the managers' overweights offset each other's underweights, and the fee, 1.3 points above the index fund, buys only 2.24 points of active risk. Per point of active risk that is 0.58% of fee against 0.26% for a single manager, more than twice as expensive.
Step 3When is the programme worth its fees?
Only if the combined portfolio's alpha before fees exceeds the 1.3 point fee gap. At a combined tracking error of 2.24%, that is an information ratio of 0.58, a bar few managers clear reliably, and one that would take about 12 years of results to confirm at conventional confidence. The same active risk is available more cheaply: 45% in one of the managers and 55% in the index fund also gives 2.24% tracking error, for a blended fee of 0.78%, a saving of about Rs 6.5 crore a year on Rs 900 crore.
| Structure | Tracking error | Fee | Information ratio needed to match index fund |
|---|---|---|---|
| One manager alone | 5.00% | 1.50% | 0.26 |
| Three managers, correlation 0.8 | 4.65% | 1.50% | 0.28 |
| Three managers, correlation -0.2 | 2.24% | 1.50% | 0.58 |
| 45% one manager + 55% index fund | 2.24% | 0.78% | 0.26 |
Say what diversification genuinely buys. If each manager has real, independent skill, combining them lowers the risk of relying on one person and smooths the ride. The limit is that fees scale with money while active risk scales with disagreement: a multi-manager programme earns its fee only when the managers differ in ideas, not in the direction of the same bets.
Where candidates lose it
The common loss is dividing 5% by three, or by the square root of three, without using the correlation at all. The correlation is the whole question, and it can move the answer from 4.65% to 2.24%.
The second is praising low tracking error as diversification. Low active risk at full active fees is an expensive index fund, and the interviewer wants to hear the fee set against the active risk it buys.
What the interviewer asks next
- What correlation between the managers makes the programme exactly as expensive per point of active risk as a single manager?
- How would you measure the correlation of active returns before hiring the managers?
- Would you rather cut one manager or negotiate the fees down, and why?
Company names and figures are illustrative.