It was my 2nd class of risk management yesterday. During a calculation I saw that beta's formula is identical to correlation. Searched out some resourceful stuff form internet.
Beta Definition
Beta is a measure of the systematic, non-diversifiable risk of an investment
Beta is a measure of the systematic, non-diversifiable risk of an investment
A
misconception about beta is that it measures the volatility of a security
relative to the volatility of the market. If this were true, then a security
with a beta of 1 would have the same volatility of returns as the volatility of
market returns. In fact, this is not the case, because beta also
incorporates the correlation of returns between the security and the market.
Beta = Correlation of Asset to Market * (Std
Dev of Asset / Std Dev of Market)
For
example, if one stock has low volatility and high correlation, and the other
stock has low correlation and high volatility, beta cannot decide which is more
risky.
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%.
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 1 (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).
Correlation
Definition
Correlation – measures the degree to which two variables relate to each other. It’s a standardized measure (unlike Covariance) of the strength of the linear relationship between two variables. When you say that two items are correlated, you are saying that the change in one item effects a change in another item.
Correlation – measures the degree to which two variables relate to each other. It’s a standardized measure (unlike Covariance) of the strength of the linear relationship between two variables. When you say that two items are correlated, you are saying that the change in one item effects a change in another item.
Correlation = Covariance
of Asset to Market / (Std Dev of Asset * Std Dev of Market)
Beta and
Correlation both measure the relationship between 2 variables. If you study the
formulas you will see that correlation is just covariance expressed as a
normalisation of covariance - that is it is scaled by the standard deviations
of the 2 variables. Beta is however the Covariance of the 2 assets divided by
the variance of the benchmark asset.
Intuitively what it really means is Beta is distinct from correlation in that correlation is more indicative of direction, while beta is also incorporating magnitude. If we say a market is up 15% always and the stock is always up 30%, then the correlation will be 1. However as beta gives us both the direction and the magnitude we would get a beta of 2.
Intuitively what it really means is Beta is distinct from correlation in that correlation is more indicative of direction, while beta is also incorporating magnitude. If we say a market is up 15% always and the stock is always up 30%, then the correlation will be 1. However as beta gives us both the direction and the magnitude we would get a beta of 2.
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