Correlation and Beta market, standard, mkt

wonderfuldream

When calculating the correlation coefficient

P1,2 = (COV1,2) / (standard deviation 1) X (standard deviation 2)

(given that 1 is stock 1 and 2 is stock 2)

Now, when considering beta; we standardize the systematic risk in units of "market risk" by:

Beta1 = (COV1,mkt) / (variance mkt)

What I want to know is why in the correlation formula standard deviation is in the denominator and when calculating beta, variance is used in the denominator?

siavosh

Because that's the formula and it’s perfectly logical.
btw Variance mkt = st deviation mkt x st deviation mkt
in both cases you divide with % squared in order to standardize the measurement unit (i.e. you get the unit free number)

bapswarrior

can anyone help with this?

spartanag07

Hi,
just wanted to add a second part to this question,

why is it (mkt std * mkt std) on the bottom instead of (mkt std * stock1 std)?

let me know if my question isnt clear

FVPV

variance market = mkt std * mkt std

This is because beta measures the sensitivity of the stock's return to market's return (therefore, not mkt std*stock1 std at the bottom), which is the non-diversified risks, the risks that get awarded.

In other words, since the total risk of the stock is measured by its standard deviation, the covariance (stock, market) measures the risk of the stock relative to the market. After standardized for the market covariance, we get the standardized beta to compare across firms in the same industry.

Hope this helps.

ramdabom

mrbrownstone Wrote:
-------------------------------------------------------
> Hi,
> just wanted to add a second part to this question,
>
>
> why is it (mkt std * mkt std) on the bottom
> instead of (mkt std * stock1 std)?
>
> let me know if my question isnt clear

Because std mkt * std stock 1 would be the correlation equation.