Case 085Execution and market microstructureCore

Arohavi decided to buy 1 lakh shares at Rs 500. The order reached the market at Rs 502, 80% filled at an average of Rs 506, and the stock closed at Rs 515 with the rest unfilled. Decompose the implementation shortfall into delay, execution and opportunity costs.

The situation

At the morning meeting, Arohavi Investments' portfolio manager decides to buy 100,000 shares of an invented consumer company trading at Rs 500, a Rs 5 crore position. The order is sent to the trading desk, waits for approval and reaches the market when the price is Rs 502.

The desk buys with a limit of Rs 509. The stock rises through the day, 80,000 shares fill at an average of Rs 506, and the limit stops the rest. The stock closes at Rs 515 with 20,000 shares never bought. Commissions are small enough to ignore here.

Your task

Measure the implementation shortfall against the decision price and split it into delay, execution and opportunity costs, then say what the split tells the desk.

Quick check

Which part of the shortfall is largest?

Worked solution

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

30-second answerThe answer to give first

The shortfall is Rs 7.8 lakh, 156 basis points of the Rs 5 crore order: delay Rs 1.6 lakh, execution Rs 3.2 lakh and opportunity Rs 3.0 lakh. The paper portfolio would have gained Rs 15.0 lakh; the real one gained Rs 7.2 lakh. The 20,000 unfilled shares cost almost twice the delay, so the limit that saved a few rupees a share was expensive.

Step 1What is implementation shortfall measuring?

Suppose you decide to buy a flight ticket at Rs 5,000, wait a day for approval, then find it at Rs 5,200, pay Rs 5,400 after taxes and seat fees, and miss getting a ticket for your second traveller as the fare jumps to Rs 6,000. The cost of the trip is the gap between the plan and what happened, including the ticket you never bought. Implementation shortfall compares a paper portfolio that bought everything at the decision price with the real one, both marked at the same later price. The paper portfolio buys 1 lakh shares at 500 and gains Rs 15.0 lakh by the close. The real one bought 80,000 at 506 and gained Rs 7.2 lakh. The difference, Rs 7.8 lakh, is the cost of implementation.

Step 2How does the shortfall split?

Walk along the day. Delay is the drift between decision and arrival on the shares that were bought: Rs 2 on 80,000, Rs 1.6 lakh. Execution is the gap between arrival and the average fill: Rs 4 on 80,000, Rs 3.2 lakh. Opportunity is the move from decision to close on the shares never bought: Rs 15 on 20,000, Rs 3.0 lakh. The three add to Rs 7.8 lakh, and in basis points of the Rs 5 crore order they are 32, 64 and 60.

The relationship
IS=qf(Pa−Pd)⏟delay 1.6+qf(Pˉf−Pa)⏟execution 3.2+qu(Pc−Pd)⏟opportunity 3.0=7.8 lakh\text{IS} = \underbrace{q_f(P_a - P_d)}_{\text{delay } 1.6} + \underbrace{q_f(\bar{P}_f - P_a)}_{\text{execution } 3.2} + \underbrace{q_u(P_c - P_d)}_{\text{opportunity } 3.0} = 7.8 \text{ lakh}
q f, q ufilled and unfilled shares, 80,000 and 20,000
P d, P adecision and arrival prices, 500 and 502
P f baraverage fill price, 506
P cclosing price used to mark both portfolios, 515
What it says in wordsThe shortfall is the drift before trading on the shares bought, plus the cost of trading them, plus the move missed on the shares never bought.
From the paper gain to the real one: the unfilled shares cost more than the delay51015015.0Paper gain300 bps-1.6Delay32 bps-3.2Execution64 bps-3.0Unfilled60 bps7.2Actual gain144 bps
Arohavi's paper gain of Rs 15.0 lakh shrinks to an actual Rs 7.2 lakh through delay of Rs 1.6 lakh, execution of Rs 3.2 lakh and Rs 3.0 lakh of gain missed on the 20,000 unfilled shares.

One convention point is worth saying aloud, because interviewers ask it. Some desks charge delay on all 1 lakh shares, Rs 2.0 lakh, and measure opportunity from arrival, Rs 2.6 lakh. The total is the same Rs 7.8 lakh; only the labels move, so state the convention before comparing two desks' reports.

Where each rupee of shortfall comes from along the day50050551051580,000 shares fill hereaverage fill 506decision 500arrival 502close 51520,000 unfilled:missed 500 to 515Trading day, decision to close
Arohavi decided at Rs 500, reached the market at Rs 502, filled 80,000 shares at an average of Rs 506 while its own buying and the news lifted the price, and missed 20,000 shares as the stock closed at Rs 515.
Step 3What does the split tell the desk?

Each part points at a different fix. The delay of Rs 1.6 lakh is an approval process problem, the execution cost of Rs 3.2 lakh is a trading speed and impact problem, and the opportunity cost of Rs 3.0 lakh came from a limit price that was too tight for a stock that was moving. The limit saved perhaps Rs 3 to 4 a share on the last 20,000 shares and then missed Rs 15 a share of gain. On a day with news, buying faster would have raised the execution cost and cut the opportunity cost by more. The limitation: one day is one draw. On a day the stock fell back, the same limit would have looked wise, so the desk judges the policy over many orders, not one.

Where candidates lose it

The common loss is measuring cost only on the shares that traded: 80,000 shares at 506 against an arrival of 502 looks like Rs 3.2 lakh and a decent day. The shares not bought are part of the decision, and their missed gain is the largest single surprise here.

The second is using the arrival price as the benchmark and so hiding the delay. The portfolio manager's decision was at 500; the two rupees lost waiting for approval are a real cost of the process.

What the interviewer asks next

  • The stock had closed at 498 instead. Recompute the three parts and say what changes in the verdict.
  • How would you set the limit price for an order like this on a news day?
  • Why does buying faster usually raise the execution cost and lower the opportunity cost?
  • How would you compare this desk with another that uses VWAP as its benchmark?

Company names and figures are illustrative.