What is "fair game" for a Master's thesis in Economics? I am a currently in an MSc program in economics, and I'll be writing my master's thesis in about a year. I have a variety of interests, including game theory, statistics, and trading strategies. I'm also on the fence about applying to PhD programs in economics and finance. My question is as follows:

Given that economics is a broadly defined field that, in a certain sense, encompasses finance, how appropriate would it be to write a thesis on, say, the effectiveness of a particular type of trading strategy, or more broadly, on the use of certain statistical methods in finance? Would the department react negatively to my choosing something that is maybe more closely related to statistics or finance than it is to economics? Or would they welcome proposals that are somewhat multi-departmental? 

Maybe I'm looking at this in the wrong light, but I don't know much about master's thesis expectations.
How your department looks on any given topic is up to them and no one here can tell you what that would be without knowing (a lot) more. In the US and many other places you need an advisor to bounce such questions off of. If you don't have one yet, find someone who is amenable to your ideas or has ideas of her/his own that you would want to explore. 

Ultimately, your advisor must sign off on your work. Both at the beginning stage when you make the proposal and at the end when you submit results. Others (a committee) may also be involved, but it is the advisor's job to be your guide and your advocate. 

Some places (and advisors) will welcome multi-disciplinary work. Others would not. Remember that this thesis is only your first major work. Hopefully it isn't your last. You don't need to try to make an international reputation at this point, but only get yourself in harness to pull for the long term, either in academia or industry. 

Advisor: good. Winging it: bad. 

A different answer may be valid in other places, of course, though I'd still recommend an advisor to work with even if it isn't required under the rules.