If I have 40% of my portfolio allocated for "secure" investments (such as bonds) are fixed index annuities a reasonable choice to use in this allocation?
There are two primary risks of fixed (or fixed but having a moving rate) annuities.
Any fixed insurance product is held on the balance sheet as an asset of the insurance company, and is therefore at risk if the insurance company fails and is unable to pay it back to you. You can mitigate this risk by choosing strong insurance companies.
Annuities (both fixed and variable) are not liquid. You cannot sell them and get your money back. You must fill out paperwork and ask for a withdrawal. Early withdrawals are usually charged a fee.
For indexed annuities, be sure you understand what limits there are to the rate the insurance company can give you. If the S&P 500 makes 25% one year, for example, you're not likely to get a matching rate on the indexed annuity.