evaluating new asset before adding to the portfolio

hi everybody, with that u do well in your studying

book 4 page 363 they provide us the formulla of how we evalauting the diversification benefit of new asset beofre adding it to the portfolio

and the formulla states the the E(Rnew)=RF+ (standard deviation of new asset) * correlation of the new asset and portfolio) divided by stanard deviation of the portfolio * ( E(Rp)-RF).

my question if why we should use only the standard deviation of the new asset to determine the covaraince in the numerator??

Thank You

Remember that this term:

(standard deviation of new asset) * correlation of the new asset and portfolio) divided by standard deviation of the portfolio

is the beta of that new asset. Recall the definition of beta:

beta=cov_im/var_m= corr_im *std_i* std_m/std_m^2

cancelling yields:

beta=corr_im * std_i/std_m

thank you tartaglia

can anyone make it more clearly?

If let me know, which part is not clear, I can try to explain it more clearly.