I understand how to calculate portfolio beta if the holdings in the portfolio are all tied to the same index. My question is how do you calculate portfolio beta that is invested in 90% U.S stocks and 10% International stocks?

The U.S stock holdings’ beta can be calculated against a common index, say the S&P 500. Additionally, the international stock holdings’ beta can be calculated against an international index, such as MCSI. However, I am having trouble figuring out how to calculate the overall portfolio beta when you have 2 different benchmarks for which you are calculating the Beta against.

In all, my main objective is to see what the systemic exposure (beta) is of my portfolio to the U.S Stock Market. I want to know how I can incorporate the international stock beta into this calculation since the beta for international stocks is tied to a different benchmark and thus distorts my overall systemic exposure calculation to the U.S equity market.