R help - Jun 2007 - Stock Price Correlation to Index Price Levels

Hi,

This is probably trivial to most people out there, but I'm struggling with
this.

I have a data set which contains the closing prices (properly adjusted for
dividends and splits) for several hundred securities and the closing prices for
a general stock market index (S&P 500).  I have no problem getting it into R
with RODBC and manipulating it.  There are no missing values.  I can easily turn
the closing price series into a daily return series.

I'm trying to determine for each of the securities it's correlation to
the index both in terms of an overall "beta" and the variance
associated with the name.  For example a security might happen to average out to
looking like it tracks the index, but the variance may be so high that it is not
reliable.  I need to figure out how to score these names against the index.

I've looked at the cor() and cov() functions, but I couldn't figure out
exactly how to use them to get this information.

I can put this data into excel and cover up with the mean of daily return for
each name divided by the index return.  I can also come up with the variance of
this, which is a good start.  I'd much rather do this in R, and I'm sure
it's much more suited for this.  Also, there may be a better approach to
this and I would be interested in any suggestions.

To give you a practical example, at the end of the day I may have long and short
positions in twenty names in a trading account.   If there is a net exposure to
the index then I can hedge it with index futures.  But, if there's low
correlation, then I can't.

Thanks,

Josh Kalish



=============================================================================Please
access the attached hyperlink for an important electr...{{dropped}}

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.

 

Thanks,

 

Josh


	[[alternative HTML version deleted]]

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.