176 Frequently Asked Questions In Quantitative Finance
What is Dispersion Trading?
Short Answer
Dispersion trading is a strategy involving the selling of
options on an index against buying a basket of options
on individual stocks. Such a strategy is a play on the
behaviour of correlations during normal markets and
during large market moves. If the individual assets
returns are widely dispersed then there may be little
movement in the index, but a large movement in the
individual assets. This would result in a large payoff on
the individual asset options but little to pay back on the
short index option.
Example
You have bought straddles on constituents of the SP500
index, and you have sold a straddle on the index itself.
On most days you don’t make much of a profit or loss
on this position, gains/losses on the equities balance
losses/gains on the index. But one day half of your
equities rise dramatically, and one half fall, with there
being little resulting move in the index. On this day you
make money on the equity options from the gammas,
and also make money on the short index option because
of time decay. That was a day on which the individual
stocks were nicely dispersed.
Long Answer
The volatility on an index,σI, can be approximated by
σI^2 =
√
√
√
√
∑N
i= 1
∑N
j= 1
wiwjρijσiσj,
where there areNconstituent stocks, with volatilitiesσi,
weightwiby value and correlationsρij. (I say ‘approxi-
mate’ because technically we are dealing with a sum of
lognormals which is not lognormal, but this approxima-
tion is fine.)
