Execution Algorithms and Returns

Question 1

Execution Algorithms

Answer 1

Used to automatically split the large volume and execute it incrementally (called iceberging) in an attempt to hide the existence of the large order and minimize price impact.

Question 2

Benchmarks of EA

Answer 2

• Volume-Weighted Average Price
• Time-Weighted Average Price
• Implementation Shortfall

Question 3

Notation For Trades

Answer 3

For a sequence of trades, we can use this:

(t1, p1, v1), (t2, p2, v2), …, (tn, pn, vn)

where:
- t is time of trade
- p is price of trade
- v is volume of trade

Question 4

VWAP

Answer 4

sum(price x volume of price) / sum(volumes)
VWAP of the order is compared to the VWAP of the market.
The goal is to do at least as well as VWAP of the market.

Question 5

TWAP

Answer 5

sum(price x (time elapsed)) / (total time elapsed)
VWAP of the order is compared to the TWAP of the market.
The goal is to do at least as well as TWAP of the market.

Question 6

Implementation Shortfall

Answer 6

(Execution Price - Benchmark Pirce) x Quantity

Difference between the price (midprice) of an asset at the time of a trading decision and the (average) execution price.
Thus it is a similar concept to “slippage”.
The goal is to minimize the implementation shortfall.

Question 7

VWAP v TWAP

Answer 7

VWAP will place:
- low weight on the prices during periods with low
volume.
- high weight on periods with high volume.

TWAP will place:
- equal weight on prices from all possible time periods.

Question 8

VWAP Strategy

Answer 8

Model the volume distribution of the market using historical data.
Slice trades according to predicted distribution.

Question 9

TWAP Strategy

Answer 9

Inputs: Order size, time period.
- Split order into slices (e.g. 1 lot).
- Divide time equally to give the correct number of trading points for the size of each slice.

Question 10

Implementation Shortfall Strategy

Answer 10

Need to decide if the price is going to move favourably or not.
Trade-off market impact (place order now) with volatility risk (wait and risk-averse market moves).

Question 11

Relative Return Types

Answer 11

• simple returns
• log returns
  Simple and log returns are essentially the same thing, just stated on a different scale.

Question 12

Simple Return

Answer 12

p(t-1) - p(t) / p(t) == (p(t) / p(t-1)) - 1

Question 13

Log Return

Answer 13

log(Pt/Pt − 1) = log(Pt) − log(Pt − 1)

Question 14

Simple Correspondence

Answer 14

rt = log(1 + Rt)
Rt = e^rt − 1.

Question 15

Simple v Log Returns

Answer 15

For large simple returns, the two start to diverge.
When a non-zero price goes down to zero:
- -1 is the simple return (smallest possible)
- -infinity is the log return (smallest return)

One advantage of using log returns is that they have some desirable mathematical properties, particularly when analyzing the performance of an investment over multiple periods.

Question 16

Positions

Answer 16

Long - we have bought (prices will go up)
Flat - we have neither bought nor sold
Short - we have sold (prices will go down)
These can be seen as the direction of the position.

Question 17

Simple Difference

Answer 17

Pt − Pt-1

Question 18

Returns v Price Differences

Answer 18

Returns contain normalisation.