To calculate the implementation shortfall attributed to realised profit/loss:
On Monday, CTAC shares close at GBP 12.24. On Tuesday afternoon, manager buys 15,000 shares of CTAC. The decision price is GBP 12.45. He purchases 6,000 shares at GBP 12.51. Trading fees total an additional GBP 0.01 per share purchased. CTAC’s closing price on Tuesday is GBP 12.50. On Wednesday, manager decides to cancel the buy order for the remaining 9,000 shares and records a cancellation price of GBP 12.90.
The CFA answer is : ((12.51 - 12.45 ) / 12.45 ) *(6000/15000)
The realized profit/loss is the difference between the execution price and the closing price of the previous day (so-called decision price), divided by the benchmark price, times the percentage of the order that was filled. So it should be : ((12.51 - 12.45 ) / 12.24 ) * (6000/15000)
Sometimes benchmark price is used, and other times decision price is used?
The curriculum book 6 section 3.1 uses the benchmark price in the denominator:
“Realized profit/loss reflects the difference between the execution price and the relevant decision price (here, the closing price of the previous day). The calculation is based on the amount of the order actually filled: 700/1,000((10.07−10.05)/10.00)=0.14%”
This is revised benchmark price when order is not filled in timely manner. Not a benchmark price. It is used in calculating Market impact segment of Information Shortfall.
One tip to solve it is to calculate total shortfall bps than bps of each component. The sum of the components must be equal to total IS in bps. If not, the first thing you probably screwed is using DP instead of BP’ in Market impact component. Make quick correction and sum again. If sum of component now is equal to total, you probably nailed it. By practicing, you may be able to solve all of above in less than 2 minutes.
If you read the question his decision is in the afternoon. The benchmark being the previous day close doesn’t make sense. If it explicity said the benchmark is that – Then run with it but with this questions the 12.24 is just a fact stated in the question.
Just when I thought I had it all figured out. I’m starting to hate IS. It should be so easy but there are always subtleties in the case that have to be quickly observed and accounted for (welcome to the whole theme of the Level III AM exam I guess).
Now I have to go over my note card on IS to make sure I have the descriptions in the terms of the calculations crystal clear.
I see the problem in relation BP* and DP. If there is no delay DP=BP. Total information shortfall would be difference between paper and real portfolio and must be sum of 4 components. If sum is not equal, first check relation BP*-DP.
However, first calculate total IS regardless if you asked for only component calculation in particular question. This would provide assurance.
So, for the question this thread, what should be the implementation shortfall? I believe it should be:
Gain on paper portfolio = (12.90 - 12.45) * 15000 = 6750
Gain on the actual portfolio = (12.90 - 12.51) *6000 - 0.01*6000 = 2280
IS = 6750 - 2280 = 4470
I am a bit confused on the gain on paper portfolio : Shall it be (12.90 - 12.45) * 15000 or (12.90 - 12.24) *15000? i.e Shall we use previous day closing price (12.24) or trade day’s decision price (12.45)?
The issue is in delay as I concluded above. You can skip delay (simply ignore it) and say that this delay bps are contained in market impact so in case it would be (12.51-12.45)/12.45. Thus Market impact would be the sum of both in bps of 19.
Realized = (Filled/Total) (Actual Price Paid - Decision Price )/Benchmark Price = (6000/15000) (12.51 - 12.45)/12.45 Since DP = BP Here
Delay = (Filled/Total) (Closing of Previous Day - Benchmark Price)/Benchmark Price = (6000/15000) (12.24 - 12.45)/12.45
Missed Opp = (Unfilled/Total) (Cancelation Price - Benchmark Price)/Benchmark Price = (9000/15000) (12.90 - 12.45)/12.45 Please note that if no Cancelation Price is mentioned, then use the closing as of the Trade Date
Explicit Cost = (Applicable Commission/(Total Amount of Shares intended to be bought * Benchmark Price))