[R] Stock Price Correlation to Index Price Levels

[Moshe Olshansky]

Josh Kalish wrote:

>Thanks to all of the people who responded.  What I
>was trying to do is 
>to
>turn my matrix or frame containing index level
>returns and stock 
>returns
>into a matrix of "betas".  I don't really need to
>worry about risk-free
>interest rates.  I just need to be able to come up
>with a number that 
>shows
>the expected index correlation.  

 

>I was able finally to figure out how to use cor() to
>get what I think 
>is an
>R^2 value.  But, I'm trying to also figure out the
>ratio of 
>correlation.
>For example, some stocks correlate very well and
cor() returns a value 
>of
>.92.  But, how do you then figure out if the stock
>should have a 1.5:1
>correlation? 

 

>The way I would do it by hand is to turn the closes
>into daily returns 
>and
>then get the mean() return for each stock against the
>index by day.  I 
>can't
>find an example as hard as I look, but this must be
>very common.

 
If X is a vector of daily returns (today's close -
yesterday's close) for your index (in dollars) and Y
is the vector of daily returns for your stock (in
dollars), then to hedge 1 share of your stock you need
to hold u = -(1/r)*(Sy/Sx) units of the index, where r
is the correlation coefficient, Sx is the standard
deviation of daily returns of the index and Sy is the
standard deviation of daily returns of Y.
In R,
u <- -(1/cor(X,Y))*(sd(Y)/sd(X))
 
In this case your stock is "fully" hedged by the index
(but the index of course is not "fully" hedged by the
stock, unless the correlation coefficient is +/- 1).

Hope this helps,

Moshe Olshansky.