Beta Vs Correlation

[dpjohn00]

This is probably a simple topic but I am having trouble explaining it in simple terms. I understand(kind of) that correlation doesn’t explain anything about volatility and that beta is the slope of the correlation and the formulas and all that. I guess I am having trouble understanding why volatility doesn’t affect correlation.
For example, say the correlation between sp 500 and gold is .20, yet gold has a beta of 3.50. Why doesn’t the additional movement in gold due to beta change the correlation? It seems like the additional price movement up would get the returns closer to one another and strengthen correlation. Any help would be appreciated.

 

[MFE]

” understand(kind of) that correlation doesn’t explain anything about volatility”
not sure how you got that one.
Beta (a) = Cov (a,p)/(stdev(p))^2
where Cov (a,p) = correlation * stdev(a) * stdev(p)
if correlation where to assume constant (as i assume you meant) & volatility = stdev(a)
therefore as volatility of “asset a” rises as does the beta.

 

[rohufish]

intuitively, think of volatility and correlation as two separate, independent risk factors. you seem to be inferring an obvious relationship - a common mistake. that formula is a circular one - covariance and correlation are related measures (correlation is just a standardised measure of covariance) - so does not represent a relationship between volatility and correlation.
if there are 2 RVs jointly distributed (two asset prices or returns), volatility relates to a single RV’s properties and could vary over time as well (heteroskedasticity). covariance/correlation is a linear co-movement measure for both RVs and could remain constant while the individual RV volatilities oscillate around their LT mean.
actually, truly speaking, you need to be looking at copulas to fully define two RV’s co-movement. think of correlation as a local linear approximation of the copula relationship (kinda like taylor series approximation conceptually). this topic is on a much looked-forward-to future reading list for me.

 

[NakedPuts]

intuitively, think of beta as something nice and fun for CFA land, and then use 12% as your discount rate. Maybe 15% for small caps. If you must use beta, just use “company specific risk premium” to get around it.

 

[bchad]

Beta and correlation are related. If you express X and Y (say, S&P_Return and Gold_Return) as standardized variables, the correlation is the slope of the best fit line. Beta is the slope of the best fit line if the variables are unstandardized. Standardizing them just means expressing each variable as the distance from its mean divided by the standard deviation. Since standard deviation is how volatility is expressed, there is a relationship.
Now, beta tells you your best estimate of how much you expect the return of Gold to be for each 1% return (excess return, usually) in the S&P. In your example, it means that you expect Gold to go up 3.5% for each 1% that the S&P goes up. The volatilities are somewhat related here, in that some of the market’s variability and gold’s variability appear to be coming from the same source.
However, not all of gold’s variability comes from the market. There are other “idiosyncratic” and possibly speculative things that are affecting gold that are completely independent of what the S&P is doing. All of these things affect Gold’s volatility, and do so in ways that have nothing to do with the rest of the market. The best estimate of what Gold does is *still* that it will go up 3.5% for every 1% in the S&P. If the ideosyncratic component of volatility is high, then a scatterplot will have points widely scattered around a line with a slope of 3.5. If it is low, then they will fall pretty close to that line.
The correlation coefficient basically tells you how scattered the points are around the line. So you can have a high beta, and yet a fairly low correlation. That means that S&P has a strong effect on Gold returns, but that lots of other things are influencing Gold and/or the S&P independently. You can have the opposite: low beta and high correlation - that means that large market movements don’t seem to affect the asset price very much, but that whatever changes do happen to the asset price come mostly from the market.
Beta: How much does market movement affect your asset’s movements
Correlation: How completely does market movement explain your asset’s movement (i.e. how much other stuff is contributing to your asset’s return)
Does that help at all?

 

[rohufish]

dpjohn00 Wrote:
——————————————————-
> I guess I am having trouble
> understanding why volatility doesn’t affect
> correlation.
>
here’s yet another way to look at it.
i’ll give you two assets that have huge volatilities - pick a crazy number. but they have no relationship whatsoever, and their movements relative to each other are totally random. they will have huge volatility, and zero correlation.