Implementation Shortfall Question

From Wiley: A fund manager decides to begin building a position in 100 shares of Ceramic Industries Inc. when the share price is $70. The trading desk immediately purchases half the order at $70.10, paying $0.10 per share commission. The stock closes that evening at $71. The next day the trading desk purchases the remaining shares for $68, paying the same commission per share. The shares close the day at $65. The implementation shortfall for this trade is closest to:

Answer is: 1.21%. I can’t seem to calculate to this, any ideas what I’m doing wrong?

My work:

Commissions: (.1)(50) + (50)(.1) / 7,000 = .14%

Delay: (50)(70-70) + (50)(71-70) / 7000 = .71%

Realized P/L: (50)(70.1-70) + (50)(68-70) / 7,000 = -1.36%

Total = -0.51%

When the question asks for only the IS you don’t need to calculate it’s individual components, this is long winded and doing many calculations gives more room for error. The quick way is to compare the actual gain/loss to the paper portfolio gain/loss. In the above question: Paper portfolio lost (65-70)×100 shares = - $500 Actual = [((65-70.2)×50)+((65-68.1)×50)] = - $415 Difference = 85. Divide this by the paper portfolio total value for the IS = 85/(100×70) = 1.21% In this case the actual portfolio lost less than the paper portfolio so the IS is positive, not a cost but a benefit.

You can do it the long way too. In your realized P/L, you didn’t update the DP to the BP* for the second trade. You should have $71 in for the BP* instead of 70 for the second trade so: (68-71) * 50. Then add the rest and it should work.

Realized Gain Loss = EP - DP or BP* x shares executed