Implementation shortfall - 2 partial transactions

A trader wants to purchase 1000 shares.

  • On Monday, the shared closed at $ 59.90 /share
  • On Tuesday, 500 shares were purchased at a price of $ 61.05 per share. Commissions and fees were 50. The shares closed at 62.07 per share.
  • On Wednesday, no shares were purchased. The shares closed at $ 63.00 per share.
  • On Thursday, 200 more shares were purchased at $ 62.05 per share. Commissions and fees were $20. Shares closed at $61.03 during the same day.
  • On Friday, no more shares were purchased and the order was canceled. The market closed at $ 62.00 per share.

Could you determine

  • Decision price
  • Benchmark price ( price s )
  • Execution price
  • Cancelation price

and after that, calculate the 4 cost components of the total IS?

Decision price = 59.9

Benchmark price

  • Tuesday = 59.9
  • Wednesday = 62.07
  • Thursday = 63
  • Friday = 61.03

Execution price

  • ​​​​​​​Tuesday = 61.05
  • Thursday = 62.05

Cancelation price = 62

Basically, yestarday’s closing price becomes the new benchmark price.

Thank you. I see more clearly the total IS.

Just for my own practice, correct me if I’m wrong:

Cancelled trades: 300 x (62.00 - 59.90) = 630

Delayed trades: 200 x (63.00 - 59.90) = 620

Market impact: 500 x (61.05 - 59.90) + 200 x (62.05 - 63.00) = 385

Trading costs: 50 + 20 = 70

Total IS: 630 + 620 + 385 + 70 = 1705

Verifying total IS via hypothetical portfolio method:

Paper portfolio gain: 1000 x (62.00 - 59.90) = 2100

Actual portfolio gain: (700 x 62.00) - (500 x 61.05 + 200 x 62.05) - (50 + 20) = 395

Total IS = 2100 - 395 = 1705

1 Like

@Moonborne, I think your result is correct.

so is there only 1 DP of all time, and the BP is constantly changing with daily closes?

i thought it was actually the DP thats constantly changing with daily closes?

also @moonborne confused by this:

Market impact: 500 x (61.05 - 59.90) + 200 x (62.05 - 63.00) = 385

im confused: wouldnt the DP (59.90) be there instead of the 63.00 in the second term of the equation?

@Tommyjohn, no, he is correct. In fact, Market impact = nbuy * (ExecutionPrice - BenchmarkPrice) so you must use Benchmark price, not DP.

got it. the BP price is prev day close. thanks!

Moonborne- why do you not divide the components by shares and BP? Is this because you are looking for a cash amount? If you were looking for a bps amount you would divide for example cancelled trades by 1000 and 59.9?

Can I also check that the below formulas are correct?

slippage: DP-BP/ BP x shares traded/ total shares

executed P&L: EP-DP/BP x shares traded/ total shares

missed opp cost CP-BP/BP x shares not traded / total shares

commission: commission/ total sharesxDP?

Thanks!

It’d be divided by the original paper portfolio value (I.e. 1,000 shares * 59.9 = 59,900).

@GAAPIFRS

Slippage should be reversed, i.e. BP - DP. A positive number wil mean a loss due to slippage (price has increased which you did not capture).

Price impact is either EP - DP or EP - BP in case there is slippage. If there is only 1 trade (whether fully executed or not), then it is just EP - DP and no slippage.

Missed opp. should be CP - DP in any case.

Then divide everything by total shares times initial DP if you want to express it in basis points.

God, I hate Implementation shortfall.

I hope we don’t get a question on it. If it’s on PM, I’ll just guess and move on :grin:

so far, practices regarding implementation shortfall (online) is simple and clear-cut with only 1 trade/transaction. having multiple transactions over multiple days really amplify the headache.

sticking with the hypothetical portfolio method makes everything so much simpler

thank you moonborne!!

Agree the hypothetical is really easy if total IS is asked. And most times the exam asks either total IS or one specific part.

@GAAPIFRS No problem!