Beta & covariance formulas

CFA Level III
#1

Multiple ways to derive these formulas, driving me nuts. Are these correct?

Beta:

Beta = cov (i,m) / variance (m)

Beta = correlation * (st dev i / st dev m)

Beta = correlation * st dev i * st dev m / variance m

Beta = variance i * variance m / variance m

CoVariance

Cov = variance i * variance m * correlation(i,m)

Cov = B * variance m

Cov = B1B2 * variance m (ICAPM)

Cov = correlation * (st dev i / st. dev m)

#2

B= Var i* var m/ var m is absolutely wrong. It equates to B= Var i; which is not right

Cov = cor * SD i * SD m (not Var; SD=SQRT of Var)

They’re all related. Just get the basic ones and then play with algebra

for eg: B= Cor * SD i/ SD m . & = Cor SDi * SD m / (SD m * SD m) = Cor SD i* SDm/Var m

another example:

Cov= Cor * SDi* SDm ; multiply the right term by SDm/SDm ; leads to Cov= Cor* SDi * (SDm*SDm)/SDm;

(SDM * SDM) = Var m & (Cor*SDi/SDm) = B ; this leads to Cov= B * Var m

Just few practices and playing with the terms and you’ll imprint this in your brain

#3

I only remember below. It should be able to derive others.

Beta = cov (i,m) / variance (m) = cov (i,m) / st dev (m)^2 Correlation (i,m) = cov (i,m)/ st dev i * st dev m

#4

so which one of these are wrong?

#5

the last Beta one is wrong

#6

Thanks for these.