# CFA Level III: Implementation Shortfall

Good evening,

A quick post tonight to discuss a topic of Trading, Rebalancing and Monitoring part of the Level III curriculum called Implementation Shortfall. The reason why I chose to do this is because it took me some time to overcome the naming conventions of the CFA institute, which are, with all due respect, very counterintuitive in my opinion.

The idea is very simple: you would like to be able to measure the quality of the execution of a trade compared to an ideal execution.

From what I’ve seen in mock exams and exercises, they always give you a little story like the following one:

• At some point, the investment manager decides to buy 10 Manchester United stocks, which trades at 20.
• This is called the benchmark price (BP), for some reason.
• Then (usually the following day), a limit order is placed in the market, say at 19.95 and is not executed at all. The market closes on that day at 20.10. Too bad.
• You pay 0.05 per share of commission.
• The following day, the order is revised at like 20.15 and 8 stocks (i.e not the whole 10) are filled at that price, and the market closes at 20.20.

What happens there? Well, assume you are able to magically implement your trading ideas instantly at no cost: this is called the paper portfolio. What is your profit at the end of the story?

• You buy 10 shares at 20 for 200.
• At the end of the story, your stocks are worth 20.20 each, which gives you a total of 202.
• You earned 202 – 200 = 2

In the real world, it did not work out that way:

• You bought 8 stocks at 20.15 for 161.2
• You pay 0.4 in commission
• At the end of the story, your stocks are worth 20.20 each, which gives 161.6
• You earned 161.6 – 161.2 – 0.4 = 0

The implementation shortfall is defined as follows:

$$\frac{\text{paper portfolio gain}-\text{real portfolio gain}}{\text{paper portfolio investment}}=\frac{2}{200}=1.0\%$$

This means that 1.0% of the potential investment was lost (or, more precisely, not won)  in the implementation, due to different frictions.

The CFA Institute then provides a way to split this difference in different components.

First the explicit costs, which consists in all the obvious transaction costs that are expressed in the trade:

$$\frac{\text{commission}}{\text{paper portfolio investment}}=\frac{0.4}{200}=0.2\%$$

That’s fine. But then comes the bizarre naming conventions.

Some extra costs come from the fact between the moment when the investment manager decides to buy the stock and the day when the order is partially filled, the market moved.

The slippage or delay costs is the difference between the benchmark price and the closing price, the day before the execution day (which is called, poorly the decision price, I don’t understand why) divided by the benchmark price, times the percentage of the order that was filled. In order case we have:

$$\frac{20.10-20.00}{20} \cdot \frac{8}{10}=0.4\%$$

It is the portfolio of the implementation shortfall that was lost because of the delay between the time the manager saw the opportunity and the day the trade was partially executed.

Then, the realized loss is the difference between the execution price and the closing price the previous day (so-called decision price), divided by the benchmark price times the percentage of the order that was filled:

$$\frac{20.15-20.10}{20} \cdot \frac{8}{10}=0.2\%$$

This is what was lost during the execution day.

Finally the missed trade opportunity cost is the difference between the price at the end of the story and the benchmark price divided by the benchmark price time the proportion of the order that was not filled:

$$\frac{20.20-20.00}{20} \cdot \frac{2}{10}=0.2\%$$

This is what was lost by not being executed.

If you sum all the components, you get 0.2% + 0.4% + 0.2% + 0.2% = 1.0%, the total implementation shortfall.

So you are able to see that, in this example, the main component of the implementation shortfall is the delay between the trade idea and the trade execution day. The limit order at 19.95 was too ambitious and resulted in a loss.

Notice also that all the examples I saw are examples where the market goes in the trade direction (i.e. market goes up after a buy decision). It could be possible that the market goes adversely, which would result in a negative implementation shortfall… i.e a gain.

That’s all for today.

I’ll be back soon with more.

Cheers,

Jeremie