 # Quick question from Book 1- QUANT

I thought variance cannot be calculated as the sum of weighted probabilities, as per below example…can someone clarify? Thanks, e.g. probability: 0.15 0.45 0.24 0.16 respectively, EPS: 2.6 2.45 2.2 2.00 Therfore, variance = 0.15(2.6-2.34) + 045(2.45-2.34) + … + 0.15(2-2.34)

yes it can.

just make sure you square the (brakets)^2. e.g. 0.15(2.6-2.34)^2+0.45*()^2… then you can use it.

So maybe I’m confusing this with a portfolio of stocks? Because you can’t say that if half your portfolio is made up of stock A, then the variance of the portfolio will consist of half of stock A’s variance…?

variance of a portfolio: var§=w1^2*var1^2+w2^2*var2^2+2w1w2*cov(1,2) var of a stock is simply {(value-mean)^2/n} or with probabilities as pointed out above

i think you are don’t compare the variance of one stocks own returns with that of a portfolio created of more than one stock. just because the covariance/correlation of the stocks. if the stocks have 0 correlation then you can consider the weighted variance

vnysot Wrote: ------------------------------------------------------- …Because you can’t say that if half your > portfolio is made up of stock A, then the variance > of the portfolio will consist of half of stock A’s > variance…? this is only true if correlation coeff = 1. perfect positive correlation or you add an risk free asset to a risky portfolio

barthezz correlaton coeff 1 or 0?

florin, var§=w1^2*var1^2+w2^2*var2^2+2w1w2*cov(1,2) with cov(1,2)=rho*var1*var2 if rho=correlation coefficient=1 then var§=w1^2*var1^2+w2^2*var2^2+2w1w2*var1var2*1 this is equal to: var§=(w1var1)^2+2w1var1w2var2+(w2*var2)^2 from (a+b)^2= a^2+2ab+b^2 var§=(w1var1+w2var2)^2 std§=w1var1+w2var2 thus linear function for rho=1 /// quod erat demonstrandum same thing for rho=-1 then just offsetting effect: std§=w1var1-w2var2 do not get confused with the risk free asset + risky portfolio – in this case we have std(risk free)=0 and the result is the CML.

Barthezz, regarding your second thread: "variance of a portfolio: var§=w1^2*var1^2+w2^2*var2^2+2w1w2*cov(1,2) var of a stock is simply {(value-mean)^2/n} or with probabilities as pointed out above " -How do we know whether to use n or n-1 in the denominator? Thanks

the text will say: use sample or population variance – then sample variance: n-1 population variance: n

That mathematical proof also clarified another question- many thanks.

BY THE WAY: substitute var with std in all my formulas. SORRY for the confusion… the end result should be: std§=w1std1+w2std2 i’m going to bed… cannot see straight… lol…