Case 092Rebalancing, implementation and costsHard

A fund must sell a Rs 900 crore stake in a stock that trades Rs 45 crore a day. Compare selling in the market over 20 to 60 days with a block deal at a 4% discount.

The situation

Vaibhav Value Fund owns 6% of Dronagiri Chemicals, worth Rs 900 crore. The thesis has played out and the fund wants to exit. Dronagiri trades about Rs 45 crore a day, so the stake is 20 days of the entire market's volume, and the stock's daily volatility is 2.2%.

A broker offers to place the whole stake with institutions in a block deal at a 4% discount to today's price. Alternatively the desk can sell in the market. Use a square-root impact modelA widely used rule of thumb that the price cost of trading grows with the square root of the share of daily volume you take, scaled by the stock volatility.: impact cost = volatility x square root of the share of daily volume taken. Count each point of standard deviation in price risk as a quarter of a point of cost.

Your task

What does selling over 20 to 60 days cost against the block? Which route do you take, and why?

Quick check

Selling over 60 days instead of 20 lowers market impact. What does it do to the total cost?

Worked solution

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

30-second answerThe answer to give first

The best market route, about 31 days, costs about 3.54% risk-adjusted against 4.0% for the block, but the saving is small and the range is wide. Expected impact is Rs 15.9 crore against Rs 36 crore for the block, yet a one standard deviation move while selling is worth Rs 64 crore either way. The better answer is a split: place half as a smaller block at an assumed 3% discount and sell the rest over 30 days, for about Rs 19 crore expected with half the risk.

Step 1Why is this stake hard to sell at all?

Selling a house in a small town where two houses change hands a year: list it at the going price and wait, or accept a discount from a dealer today. Rs 900 crore of a stock that trades Rs 45 crore a day is 20 full days of everyone's trading, so the fund is the market for weeks. Every sale pushes the price down, and the longer the selling takes, the longer the unsold shares sit exposed to news.

Step 2What does market selling cost at different speeds?

Over 20 days the fund must be 100% of daily volume, doubling the stock's normal trading; impact is 2.2% x the square root of 1.0, or 2.20%. Over 60 days participation falls to 33% and impact to 1.27%. But the unsold stake's price risk grows with the square root of the days: a spread of 5.68% over 20 days, 9.84% over 60. At a quarter point of cost per point of risk, the total is 3.62% at 20 days, lowest at about 31 days, 3.54%, and back up to 3.73% at 60.

Selling slowly cuts impact but adds risk; the block discount buys certainty1%2%3%4%5%1020304050607080Days taken to sell in the marketBlock at 4% discount: certainbest: 31 days, 3.54%impactrisk chargetotal
Selling Vaibhav's Rs 900 crore stake slowly cuts impact from 2.20% at 20 days to 1.27% at 60 but raises the price risk charge, so the total cost is lowest at about 31 days, 3.54%, only a little under the 4% block discount.
DaysShare of daily volumeImpactPrice risk, 1 sdRisk-adjusted total
20100%2.20%5.68%3.62%
3165%1.77%7.07%3.54%
4050%1.56%8.03%3.56%
6033%1.27%9.84%3.73%
Block4.00%0.00%4.00%
The market route's risk-adjusted cost bottoms at 3.54% near 31 days, a saving of only 0.46 points on the 4% block, while its price risk over that period is a 7.07% standard deviation.
Step 3What is the block discount really buying?

Certainty. The block costs Rs 36 crore for sure; the 31-day route costs about Rs 16 crore on average but leaves Rs 64 crore of price swing either way while the fund still holds stock. The model also flatters the market route. Other traders notice a steady seller within days, and a stake exiting for weeks invites them to sell ahead, which raises the real impact above the formula. A fund that has decided its thesis is finished has no reason to keep a 7% standard deviation of exposure to it.

Expected cost against the range of outcomes, Rs croreMarket, 31 days15.9+63.6 in a bad monthBlock, 4% discount36.0Half block, half 30 days19.2+31.3 in a bad month0Red bar: one standard deviation of price moves while the fund still holds unsold stock; it runs both ways.
Selling Vaibhav's stake over 31 days costs about Rs 16 crore expected with Rs 64 crore of price risk, the block costs a certain Rs 36 crore, and a half-block, half-market split costs about Rs 19 crore with Rs 31 crore of risk.
Step 4So which route?

Split it. A block for half the stake should need a smaller discount, assume 3%, because buyers can absorb Rs 450 crore more easily. Sell the other half over 30 days at 33% of daily volume, impact 1.27%. Expected cost is about 2.14% of the stake, Rs 19 crore, with price risk of Rs 31 crore, half the pure market route's. Say the limits: the impact coefficient and the 3% discount are assumptions to test with brokers, and block deals and large stake sales carry exchange windows and disclosure rules to confirm before trading.

Where candidates lose it

The common loss is comparing the block's 4% with the impact alone, finding the market cheaper at 1% to 2%, and choosing it. That ignores weeks of exposure to the stock the fund has decided to leave.

The second is assuming slower is always cheaper. Beyond about a month the price risk grows faster than impact falls, and the total rises again.

What the interviewer asks next

  • The stock falls 8% in the first week of market selling. What do you do?
  • How would you negotiate the block discount down?
  • How does the answer change if the fund must sell because of redemptions rather than a finished thesis?
  • Why might a broker offer a smaller discount for a stock with more natural buyers?

Company names and figures are illustrative.