Assume we have two instruments A
and B
. Also time is increasing from 1 to n. Let's say that A1
is price of instrument A
at time 1
. Let's assume that A
and B
are highly correlated instruments. Then we can try to compute TruePrice
of stock B
from stock A
.
Then if Bn
is more enough than TruePrice
we sell B
, and if Bn
is less enough than TruePrice
we buy B
. I think that would be so-called statistical arbitrage
.
I would prefer not to discuss pronse and cons of this scheme in general. Cause it proved to work cause I'm using it for a long time and still profitable.
What I really want to discuss is how can we compute TruePrice
having what we have. Let me describe two algorithms:
- TruePrice = Bn * ( (A1 + A2 + .... + An) / (B1 + B2 + .. + Bn) )
- TruePrice = Bn / n * (A1 / B1 + A2 / B2 + .... An / Bn)
Also please note that Ai
and Bi
are measurements of price. This could be median
low
close
or anything else of the certain interval (i'm using median
now). The last items An
and Bn
are life
i.e. changing while trading to reflect current situation.
The question is what are prons and cons of each of these (1
and 2
) algorithms? Probably you can suggest something else?
Now I'm using 1
but I'm not satisfied with it. When instrument A
grow (so An
increase, other Ai
are fixed as they in "past") TruePrice
is not changing enough. And you can see from formula that TruePrice
of stock B
depends a lot on Bn
what is actually current B price
. So TruePrice
of stock B
depends on stock B
too much what is not good. I think TruePrice of stock B
should more depends on correlated An
, but it doesn't.
I'm not sure if 2
would solve this problem.
1
and2
from mathematical point of view. What are prons and cons of these calculations? Whatbehavior
should I expect fromTruePrice
when these algorithms are used, or they are pretty similar? $\endgroup$