Case 082Portfolio construction and optimisationCore

A welfare board puts 70% in an index core and 30% in active satellites. What are the portfolio's expected net alpha and tracking error, and what must the satellites earn to justify themselves?

The situation

Pranhita Workers Welfare Board has Rs 500 crore of equity. It holds 70% in an index fund core costing 0.10% a year and 30% across active satellite managers costing 1.50% on average.

The board's consultant expects the satellites together to beat the index by 2.5% a year before fees, with 6% tracking error. The core tracks the index closely enough to treat its tracking error as zero.

Your task

What net alpha and tracking error should the board expect for the whole portfolio, where do the fees go, and what gross alpha must the satellites deliver to be worth having?

Quick check

Roughly what net alpha should the whole portfolio expect?

Worked solution

Try it on paper, then open one step at a time.

30-second answerThe answer to give first

About 0.23% a year of net alpha, roughly Rs 1.15 crore, with 1.8% tracking error. The satellites earn 1.0% after fees on 30% of the money, and the core's fee costs 0.07%. The satellites absorb 87% of all fees on 30% of the assets, so they must beat the index by at least 1.4% before fees just to match an all-index portfolio. On the consultant's numbers they clear that in about 57% of years.

Step 1Why build a portfolio this way at all?

Think of a household that buys staples at the wholesale market and spends on a few dishes at a good restaurant. The staples are cheap and dependable; the restaurant is where the money goes and where the pleasure is meant to come from. A core-satelliteA structure that holds most of a portfolio in low-cost index funds and a smaller part with active managers who are expected to beat the index. portfolio buys the market cheaply and spends its fee budget only where it expects to be paid back. It keeps the board close to the index, which trustees usually want, while leaving room for skill.

Step 2What do the numbers add up to?

Alpha lives only in the satellites, so weight it. Net alpha is 30% x (2.5% - 1.5%) - 70% x 0.1% = 0.23% a year, about Rs 1.15 crore on Rs 500 crore. Tracking error also comes only from the satellites: 30% of 6% is 1.8%, because the core adds almost none. That gives an information ratio for the whole portfolio of 0.13, net alpha over tracking error.

Fees concentrate where alpha is sought: the satellites must pay their own wayIndex core70%, Rs 350 crorefee 0.10%, alpha sought: nonetracking error about 0%Satellites30%, Rs 150 crorefee 1.50%, alpha 2.50%tracking error 6%Where the Rs 2.60 crore of annual fees goesSatellites: Rs 2.25 crore, 87% of fees on 30% of assetsCore: Rs 0.35 croreNet alpha = 30% x (2.50 - 1.50) - 70% x 0.10 = 0.23% a yearTracking error = 30% x 6% = 1.8%. Satellites must beat 1.4% gross just to break even.
Pranhita's satellites hold 30% of the money but take 87% of the Rs 2.60 crore fee bill, so the whole portfolio's expected net alpha is only 0.23% a year with 1.8% tracking error, and the satellites must beat the index by 1.4% before fees to break even.
Step 3What must the satellites earn to be worth it?

Compare with the simple alternative, all Rs 500 crore in the index core. Every rupee moved to a satellite swaps a 0.1% fee for a 1.5% fee, so the satellites must earn more than 1.4% of gross alpha before the structure beats an all-index portfolio. The consultant's 2.5% clears that by 1.1 points, but with 6% tracking error the satellites fall short in any single year about 43% of the time.

Satellite gross alphaSatellite netPortfolio net alphaRs crore a year
0.0%-1.5%-0.52%-2.60
1.0%-0.5%-0.22%-1.10
1.4%-0.1%-0.10%-0.50
2.5%+1.0%+0.23%+1.15
3.5%+2.0%+0.53%+2.65
At the consultant's 2.5% the portfolio nets 0.23%; at 1.0% it loses 0.22% a year; and at 1.4% it merely matches an all-index portfolio's cost of 0.10%.
Step 4What would you tell the board?

That the structure is sound but the case for the satellites rests on one estimate. If the satellites deliver 1.0% instead of 2.5%, the portfolio earns -0.22% a year, worse than the plain index fund. Ask for evidence that each satellite manager's alpha is repeatable, cap the satellite fee, and review each one against its 1.4% hurdle, not against zero. Say the limit: 0.23% a year is small against 1.8% of tracking error, so years of results will not prove or disprove skill quickly.

Where candidates lose it

The usual loss is quoting 30% of 2.5%, 0.75%, as the portfolio's alpha, which forgets that the fee comes off the alpha, and that the core costs something too.

The second is judging the satellites against zero. The fair comparison is the index fund they replaced, so their bar is the fee difference, 1.4%, not nothing.

What the interviewer asks next

  • What satellite weight maximises the portfolio's information ratio on these assumptions?
  • Would you rather have one satellite at 6% tracking error or three uncorrelated ones at 6% each?
  • The board wants tracking error under 1.5%. What changes?

Company names and figures are illustrative.