information we can tease from Beta (std. dev & corr)
 

background: i'm doing a portfolio analysis and there are allocations to individual stocks. i'm a little too lazy to go hunting for the return streams (from which i could get the actual std. deviation and correlation w/ the s&p500) but not lazy enough to ignore or make up #s.

the portfolio analysis is very rough and by no means meant to be final.

i just want to get a sense for the risk in the portfolio.

as such, i want to break beta down into something i can use and present more intuitively (i.e. st.dev & correlation vs. beta)

so thinking out loud, i think it makes sense to use beta*std.dev of S&P500 as a proxy for the individual stock's standard deviation, however, what could i get for correlation.

literally, a 1.2 beta means that (assuming alpha is 0 and normally distributed errors) a 1% move in the S&P500 results in a 1.2% move in the stock. so i feel OK using the standard deviation (but wanna check to make sure it makes sense to you all as well).

but i'm less comfortable and need help with the correlations. obviously any beta that is positive is positively correlated with the S&P500 and any beta that is negative is negatively corelated with thS&P500.

but to what degree. while standard deviation is captured fairly well i think by beta (even though beta is not a great measure overall), correlation may not be.

any thoughts on what correlation info i can get out of a beta.

what would a beta of .5, 1.0, or 1.5 mean in terms of corerlation (or covariance if that is easier mathematically)?

thanks for your thoughts,
Barron

Re: information we can tease from Beta (std. dev & corr)
 

well, since beta is cov/variance(market), beta * var(m) will give you covariance with the market, not standard deviation.

since beta (or covariance, since they have the same informational content about the security) only gives you one piece of information about the return series of the security, there's no good way to parse out what portion of that is attributable to volatility and what part is attributable to standard deviation.

Re: information we can tease from Beta (std. dev & corr)
 

[ QUOTE ]
well, since beta is cov/variance(market), beta * var(m) will give you covariance with the market, not standard deviation.

since beta (or covariance, since they have the same informational content about the security) only gives you one piece of information about the return series of the security, there's no good way to parse out what portion of that is attributable to volatility and what part is attributable to standard deviation.

[/ QUOTE ]

thanks, been a while since i dug into thtis stuff.

i just looked over all the formulas and found the best i can do is:

std(stock)*correlation(stock,market)

which still doesn't give us anything useful.

good news is that i found a way to get the individual stock returns on yahoo [img]/images/graemlins/smile.gif[/img] (pretty easy actually)

thanks agian,
Barron