i may have asked this once before in the last year.. might have been another forum though. not sure.

i am aware of many important equations given two assets that make up a portfolio.

but i have never seen an equation for the following:

you have spy and tlt (stock index and long bond index). you have variance for each. and correlation between them.. their weights in a portfolio add up to 1 (and to make it simply are both non-negative)........ what is the correlation between spy and the portfolio based on the stock weight (Ws)?....... i have never seen this before and don't want to wade through hundreds of web pages hoping i find it.

thanks in advance

i haven't found an answer yet........... BUT, i have started to get a feel that you have to move to numerical analysis or iteration pretty fast in doing this type of work.

i was doing a first derivative on sharp ratio (return over std deviation of return). the number of terms just explodes. i think it's over 30 for this derivative. and then solving a quadratic equation.

i had never thought of this before. but is there software to do equations like this? i.e collect all the terms and give you the equation you want. i'm interested in the equation itself, not just the result.

thx in advance

You posted this in the SM&P subforum before and I linked you this thread which answers your question (I think, unless I've misunderstood what you're asking):

https://quant.stackexchange.com/ques...ined-portfolio

Juk

Duke, thank you very very much.... I might have got distracted last time I asked... I'm a bit bad for that. I'll have to be more diligent in the future... again, thank you so much

thx again........

that page was helpful.. i will probably go there in next few days and ask some questions......

cliff notes in bold

i do have semi-basic question........... a person provided an answer there and it look interesting. i used it for portfolio split between SPY and TLT.

i did have a glaring question if i was going to use it for 3 asset portfolio.. say SPY, TLT, and gold (GLD)

my excel usage of his formula for covariance between stocks and portfolio D (say 50/30/20) makes use of 1) stock variance, 2) stock/bond correlation, 3) stock/gold correlation... but NOT bond/gold correlation......... the standard deviation of the portfolio would use this however.

this is more a basic probability question right now... can i derive bond/gold correlation from those other 3 numbers? i would have thought "no"

thanks again ....... there may be other solutions later in the discussion i haven't got to