Does my money have to make aliya, too?

There is no need to move all your dollar denominated investments to Israel. There are several advantages to keeping your assets in America, not the least being geographical diversification.

Moreover, you may find that as an American, you have trouble dealing with Israeli banks, they often appear to not like opening investing accounts for U.S. citizens. Additionally, there are various tax advantages in keeping your assets in the United States, such as maintaining their tax-deferred status if they are IRAs and not having to report them as assets on the FBAR form. (A FBAR form is a Report of Foreign Bank Accounts that must be filed  with the American government if you are an American person and own or have signing authority on foreign financial accounts worth a total of $10,000 or more at any time in the year. For more information about this, read: What Should You Do about the FBAR?

The resources below explain how you should set up and keep your investment and retirement accounts: