I agree that it is not unethical. Some things that probably ARE unethical and/or illegal that you should probably keep in the forefront of your mind:
1. Don't use tax payer funded items to do your own investing (i.e. FD phone, fax, email, vehicle) or during shift any time you are engaging in that activity (basically theft)
2. Don't use your position to scare, intimidate or otherwise influence the minds of the people you are working with (abuse of power)
Now I know we see these things at the highest levels of our government but they have legal teams and power to back them. If my local FD chief was an investor and on the up and up, you bet I'd be cool with it as would most of the other citizens you serve. In fact it would be nice if local gov employees were more engaged, as they would understand the problems we as professionals face and help improve the marketplace, either through policy or procedures; making the community more successful in general.