when we are using covariance in the formula for risk of the portfolio we use coVariance = (r*sd*sd) , but we also use formula CoVarience=E(Xy)- E(x)E(y). why do we use 2 different formulas for covariance
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The first formula is not a direct formula of covariance, it was derived from the formula of correlation coefficient. The second formula is derived from the covariance formula by expanding it
Which one should be used and when could you please elaborate more deeply. Than you for responding.
We should use the normal covariance formula and the formula derived from s.d. The E(xy) formula is used only When joint probabilities are given
you have to see what are the data given in the question. if sd of x and y, and correlation coefficient between x and y are given in question then use formula r*sd of x*sd of y. if you are given data like x ki values given y ki value given or inki probabilities given then use second formula you mentioned above. see you can also use first formula here but you compute sd and r.
It is not using two formula its just depending on the data set to calculate it differently. we use different formulas based on the data in the question.