Suppose I have two time series T1 and T2.T1 has a std. dev. of 0.3 and T2 has a std. dev. of 0.6.Can we say anything about the max/min covariance of the combined time series T3=T1+T2?Thanks EDIT: Title is slightly wrongly worded, but I can't change it

Are you looking for the max/min variance of T3 or the max/min covariance between T1 and T2?

max/min variance of T3

If you stare deeply into the formula for the variance of the sum of two random variables, you should find that the one component missing so far is the correlation between T1 and T2. Consider what happens as that varies over the range from -1 to 1.

max 0.6min 0.3if t1/(t1+t2) ~ 1 then 0.3if t2/(t1+t2) ~ 1 then 0.6

Thanks for the hints:I am coming up with the following:var(T1 + T2) = var(T1) + var(T2) + 2*std(T1)*std(T2)*cor(T1,T2)= 0.36 + 0.09 + 2*0.6*0.3*cor(T1,T2)Which gives 0.81 for cor(T1,T2)=1 and 0.09 for cor(T1,T2)=-1.Why are these numbers different from "daveangel"s? Where did I go wrong?Thanks again!

QuoteOriginally posted by: dirtdogThanks for the hints:I am coming up with the following:var(T1 + T2) = var(T1) + var(T2) + 2*std(T1)*std(T2)*cor(T1,T2)= 0.36 + 0.09 + 2*0.6*0.3*cor(T1,T2)Which gives 0.81 for cor(T1,T2)=1 and 0.09 for cor(T1,T2)=-1.Why are these numbers different from "daveangel"s? Where did I go wrong?Thanks again! T1 and T2 are the time series of returns or prices ? If its prices then the weight of T1 and T2 in the portfolio is T1/(T1+T2) and T2/(T1+T2)if its returns then you have an equal weights of 0.5 and you need to modify your variance formula

@daveangel, I now see the errors of my ways ;DThanks so much for your help!

This is an interesting case where DA may have answered the question that you meant to ask, but he certainly didn't answer the one that you did ask. But if you are happy, we are happy.

QuoteOriginally posted by: bearishThis is an interesting case where DA may have answered the question that you meant to ask, but he certainly didn't answer the one that you did ask. But if you are happy, we are happy.better lucky than smart

Haha - this line cleared it up for me:"if its returns then you have an equal weights of 0.5 and you need to modify your variance formula".Guess I was tired when I posted the question.Thanks again