A Concentrated Position, a Redemption Queue and a Beta Target
A long-only equity fund runs $850m against an equity benchmark. Its largest holding is 9.5% of the fund versus 3.0% in the benchmark; the stock has a 38% volatility, the benchmark 16%, and the correlation between them is 0.55. Current tracking error is 5.2% against a 6.0% hard limit. The stock's 20-day average daily volume is $6m. The portfolio manager wants to add 200bp to the position, arguing that the thesis has strengthened. Meanwhile the client service team expects redemptions of about 7% of AUM over the coming quarter. The fund's measured beta to the benchmark is 1.08, and the PM asks whether shorting index futures at 5,400 with a $50 multiplier would let him keep the position and neutralise the market risk. The fund's stated liquidity policy assumes no more than 20% of ADV in any one name.
1. Assess the liquidity of the position today and after the proposed addition, and relate it to the expected redemptions.
Read the worked answer
Current position = 9.5% × 850 = $80.75m. At 20% of $6m ADV, i.e. $1.2m per day, that is 67 trading days - roughly three months, and that assumes the tape stays as liquid as today. In a drawdown both ADV and the acceptable participation rate fall, so 67 days is a best case.
With the addition of 200bp ($17.0m) the position becomes $97.75m, or 81 trading days.
Redemptions of 7% × 850 = $59.5m. Met solely from this name at $1.2m a day, that would take 50 trading days - far longer than a typical notice period, and it would be close to 74% of the entire position. In other words the fund's liquidity profile is already mismatched before any addition.
Judgement: the incremental $17m pushes the exit horizon to nearly four months and increases the share of the book that cannot be sold quickly. If the add is approved it should be conditional: a cash or liquidity buffer sized to the redemption risk, funding from the liquid sleeve, a documented exception to the 20%-of-ADV guideline, and a stress test of redemptions at 15–20% rather than 7%. Alternatively, express the stronger thesis by trimming other names and holding weight constant, or by using a smaller add of 50–100bp that keeps the exit under the policy horizon.
2. Estimate the position's contribution to tracking error today and after the proposed 200bp addition, and test the stability of that estimate.
Read the worked answer
Active weight = 9.5% − 3.0% = 6.5%. Residual (benchmark-uncorrelated) volatility = 38% × √(1 − 0.55²) = 38% × 0.835 = 31.7%. Contribution to active risk = 6.5% × 31.7% = 2.06%.
Share of risk: 2.06/5.20 = 40% of the fund's total tracking error from a single name; in variance terms 2.06²/5.20² = 16%.
After the add, active weight = 8.5%, contribution = 8.5% × 31.7% = 2.69%. New tracking error = √(2.69² + (5.20² − 2.06²)) = √(7.24 + 22.79) = 5.48%.
That is inside the 6.0% limit, but it consumes over 70% of the remaining risk budget (0.52pp left) and increases single-name concentration of risk from 40% to 49%.
Stability test: if the stock's volatility rises to 50% with the same correlation, residual volatility becomes 41.8% and the contribution 3.55%, giving tracking error √(12.6 + 22.79) = 5.95% - effectively at the limit. The estimate is fragile precisely when it matters: in a selloff idiosyncratic volatility rises, and correlation to the benchmark usually falls, both of which push residual risk, and therefore tracking error, higher. A 200bp add is not a marginal decision; it is a bet on the stability of a risk input.
3. Evaluate the futures hedge proposal: calculate the required contracts and explain what it does and does not achieve.
Read the worked answer
Contracts = (1.08 − 1.00) × 850m / (5,400 × 50) = 68m / 270,000 = 252 contracts short.
What it achieves. It brings the fund's market beta to approximately 1.00, reducing the fund's sensitivity to a broad market fall. That may be exactly what the PM wants if his view is 'the sector is fine, the market is not'.
What it does not achieve.
- It leaves the stock's residual risk untouched: 31.7% volatility, 40% of tracking error today and nearly half after the add. You would be short the market and long one concentrated stock; measured against an equity benchmark, active risk can rise, because the futures position is itself an active bet.
- It does not fund redemptions. Short futures consume margin and generate no cash. To pay $59.5m of redemptions the fund must sell assets, and the least sellable asset is the one being added to.
- It introduces basis and roll risk, and the hedge ratio must be monitored as beta and the futures price drift.
Decision. Separate the two questions. Is the stock thesis strong enough to hold 9.5%? If yes, hold it, but fund redemptions from the liquid sleeve or pre-arrange a credit facility rather than fire-selling an 81-day position. Use futures only if the objective is explicitly to lower market beta - and state it as such, with a documented limit on basis risk and a review trigger if tracking error approaches 5.8%. Doing both - adding to the illiquid name and shorting futures - leaves the fund with the worst of both: unchanged concentration risk, an unfunded liquidity mismatch, and a hedging programme that consumes risk budget without addressing either.