Taken from the book:
$\Delta{S}$ - Change in spot price, S, during a period of hedge.
$\Delta{F}$ - Change in futures price, F, during a period of hedge.
If we assume that the relationship between $\Delta{S}$ and $\Delta{F}$ is approximately linear, we can write:
$\Delta{S} = a + b\Delta{F} + e$
where a and b are constants and e is an error term. Suppose that the hedge ratio is h (futures size position/exposure).
EVERYTHING IS CLEAR TILL NOW
Then the change in the value of the position per unit of exposure to S is
$\Delta{S} - h\Delta{F} = a + (b-h)\Delta{F} + e$
- If I understand correctly, $\Delta{S}$ - $h\Delta{F}$ is change of spot price - change of futures price related to my position. Let's assume that hedge ratio is 1. Then $\Delta{S}$ - $h\Delta{F}$ is just a difference between spot price change and futures price change, why do I need it?
- Why in $a + b\Delta{F} + e$ b was replaced by (b - h) when I subtracted $h\Delta{F}$ from $\Delta{S}$ ?
- What is the main idea of my calculations?