Equity Curves and Perfect Returns

Question 1

Position (Signal) Vectors

Answer 1

Let k be some integer, and a lot is the standardised number of units of an asset being traded:
-k < 0 -> Short k lots
0 -> Flat
k > 0 -> Long k lots

Question 2

Signals

Answer 2

Time series of positions; trades occur when the value of the signal changes.

Question 3

Aggregating Returns / Cumulative Return

Answer 3

Given a sequence of simple returns, they are aggregated by:
* adding 1 to each of them, multiplying them together, and then subtracting 1 from the product.
Given a sequence of log returns, they are aggregated by:
* adding them up

This produces the cumulative return.

Question 4

Perfect Return

Answer 4

Computed via the perfect position; going long when the market goes up and short when it goes down.

Question 5

Copycat Strategy

Answer 5

If the close if higher than the open, buy the next day.
Otherwise, sell the next day.