Decision Price vs benchmark price (Implementation shortfall)

I don’t get the concept. When calculating the realized profit or loss the numerator of formula seems to be:

Execution price - Decision price (or Benchmark price)

What’s the difference between Decision price and benchmark price? I mean, I get the concept of decision price, but I don’t know when I have to take the decision price and when the benchmark price (and what exactly means benchmark price…)

I did some Schweser and CFA exercises and it doesn’t seems to be consistent at all between the two sources.

The decision price is the initial price set. For example you decide to buy 100 shares at $50 per share. $50 is the decision price (DP).

Benchmark price (BP) is only involved if there is a delay in execution, that is the order isn’t fully executed, say only 80 shares were bought this day at $60. The close of the day is $70. $70 is the benchmark price (BP) for the next day of trading. Next day the remaining 20 shares at bought at $80.

Total IS = missed trades + delay in trades + market impact + fees.

There are no missed trades (all 100 shares are bought), there are no fees in this example so we’re left with delay and market impact.

Delay: (BP - DP) x shares = (70-50) x 20 = $400.

Market impact: (EP - DP or BP) x shares: first day: (60-50) x 80 = $800. second day: (80-70) x 20 = $200.

Total IS = 400 + 800 + 200 = $1400.

Reason why you take BP for market impact on the second day is to avoid double counting, in this example you already accounted for the difference between BP and DP as a delayed trade. Then secondly you account for the EP vs. BP and DP.

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Realized profit/loss = Execution price - previous day closing price and then divide by the benchmark price

Thank you, but Mr RS formula doesn’t seems to be correct and I tried to apply what Moonborne said but I am still confused.

Have a look at this example and calculate realized profit loss:

On Monday, CTAC shares close at GBP 12.24. • On Tuesday afternoon, Raffo directs Reynolds to buy 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, Reynolds decides to cancel the buy order for the remaining 9,000 shares and records a cancellation price of GBP 12.90.

DP = 12.45 EP = 12.51

The solution is, realized profit/loss = (EP - DP)/DP * shares bought/tot shares.

I still don’t get it why on the numerator is using DP and not BP. As Moonborne said, BP is involved only if there is a delay… there is one, but none BP is used!!

In your example I believe DP is used because, although there is a delay, the remaining buy order was canceled.

Because of that I calculate IS as 2,280.

Paper - real portfolio = 2,280

Paper portfolio g/l =(12.90-12.45)*15000 = 6,750

Real portfolio g/l = sum of components below = 4,470

  • Realized p/l = (12.51-12.45)*6000 = 360

  • Delay costs = 0 (shares canceled)

  • Cancelation costs = (12.90-12.45)*9,000 = 4,050

  • Direct (explicit) costs = -.01 * 6,000 = -60

  1. In my opinion, the realized p/l should be:

(6,000/15,000) x ((12.51-12.24)/(12.45)) = 87 bps

–>Would be great if anyone could clear that up.

  1. Delay costs: (6,000/15,000) x ((12.24-12.45)/(12.45) --> -67 bps

  2. Commission: 60/183,600= 3 bps 183.600=15,000 x 12.24

  3. Missed trading opportunity costs= (9,000/15,000) x ((12.90-12.45)/(12.45) = 217 bps

Total costs: 87 bps - 67 bps + 3 bps + 217 bps = 240 bps = 2.40%.

For the paper portfolio g/l, you would do: (12.90-12.45) x 15,000 = 6,750

Actual portfolio costs: 6,000 x 12.51 = 75,060 + commission of 60 = 75,120

Actual portfolio value: 6,000 x 12.90 = 77,400

Actual portfolio profit= 77,400 - 75,120 =2,280

Implementation shortfall: 6,750-2,280 =4,470 // 4,470 divided by 183,600 = 243 bps = 2.43%

–> I must have made a (or a few…) mistake (s) somewhere, because the two methods should give the same result :frowning:

That’s the point, we use BP if there is a delay, in this case there is one, but DP is still used. I have seen other examples where although there is a delay, the remaining buy order was canceled, but in these cases, the BP was used!

Still don’t get the point.

maybe Schweser got this wrong?

CFA mock 2014

Seems to be a known issue.Could someone else please comment?