Say I'm trying to diversify my portfolio along multiple asset classes and countries. Many of those assets are in different currencies. For example, I'm based in the UK and I'm evaluating a 3 asset portfolio:
- US large-cap mutual fund in USD
- UK mid-cap mutual fund in GBP
- Japanese bond fund in JPY
I'm looking for the optimal weights for the three assets. Should I convert the amounts in USD and JPY to GBP before I compute the returns, and compute the correlation matrix using the GBP returns? Or just use the returns in each currency to calculate the correlation matrix?