Beta volatility and correlation

β = (σ / σ_m)r

That is, beta is a combination of volatility and correlation. For example, if one stock has low volatility and high correlation, and the other stock has low correlation and high volatility, beta can decide which is more "risky".

In other words, beta sets a floor on volatility. For example, if market volatility is 10%, any stock (or fund) with a beta of 1 must have volatility of at least 10%.

Another way of distinguishing between beta and correlation is to think about direction and magnitude. If the market is always up 10% and a stock is always up 20%, the correlation is one (correlation measures direction, not magnitude). However, beta takes into account both direction and magnitude, so in the same example the beta would be 2 (the stock is up twice as much as the market).