Implementation Shortfall

CFA Level III Portfolio Management
#1

I found this following sample question in this forum. Can someone help calculate the paper portfolio and real portfolio returns and arrive at IS? Thanks.

Day 1: At the close of the market, XYZ shares are priced at $40. The portfolio manager decides to sell 5,000 shares at $41 per share and places a limit order that will expire at the end of the next day.

Day 2: No shares are sold and the stock closes at $39.50

Day 3: Before the opening, the portfolio manager submits a new 1-day limit order to sell 5,000 shares of XYZ at price of $39.60. As the trading day winds down, 4,000 shares fill at $39.70 plus $75 commission. XYZ shares close at 39 and the order was canceled.

#2

Return on paper portfolio = (41-39) *5000 = 10,000

Actual sales price = (39.70 * 4000) -75 = 158,725

Implicit buy price = (4000*39) = 156,000

Return on actual portfolio = 158,725-156,000 = 2,725

Implementation shortfall = 10,000 – 2,725 = 7,275

IS (%) = 7275/(41*5000) = 3.55%

#3

I used 40 as the DP since that’s the 1st day’s closing price.

–

DP = 40

CP = 39

BP* = 39.5

–

Paper portfolio = (40-39)*5000 = 5,000

Missed opportunity = (39-40)*1000 = -1,000 --> (CP-DP)*shares not filled

Explicit = 75

Delay = (39.5-40)*4000 = -2,000 --> (BP*-DP)*Shares sold after delay

Mkt impact = (39.7-39.5)*4000 = 800 --> (EP-BP*)*Shares sold after delay

Add all those up to get the IS.

IS = -2,085 or

IS = -2,085 / (5000*40) = -1.04%

Since the shares are being sold, and the subsequent price that it gets sold at (relative to the paper portfolio) is less, I would think the implementation shortfall should be negative.