|Author||Topic: std dev of a portfolio|
|I thought I had this down cold -- now I'm confused. The formula for computing a portfolios variance = w(1)**2 var(1) + w(2)**2 var(2)
+ 2 w(1)w(2)COV(1,2), where COV(1,2) = STD(1)STD(2)RHO(1,2) [stdev = SQRT preceding equation].
Quote from Bodie, et al "..even if the COV is positive, the port std STILL is less than the weighted ave of the individual security std's (unless perfectly correlated)". How is this possible if all the terms are (+) signed?
Then he goes on to say "...Because the cov is higher, port variance is higher when RHO is higher." Thats obvious and follows from the math, but these are all positive numbers, even though only fractions
then they conclude "...the std of a portfolio w/ a perfectly positive correlation is just the weighted average of component std's. In all other cases, with RHO < 1, makes the portfolio stdev less than the weighted average of component std dev".