RunAs identity is not being propagated when first bean in unsecured.

Issue

I have a unsecure EJB_1 which calls another unsecure EJB_2 which in turn calls a secured EJB_3. All of the EJBs are EJB3 and located in the same application. All calls are executed through local interfaces.
ie.

client ---> EJB_1 --> EJB_2 --> EJB_3

I annotated EJB_1 with RunAs("EJB3Role") but the call on the EJB_3 fails with security exception. I had to put this annotation on EJB_2 in order for my call to EJB_1 get executed without a security exception.

I don't want to put the RunAs on EJB_2, I need it to be applied only for one method of EJB_1.

How can this be acheived?