What should we do if our users are expecting a free service, but we are unable to meet the cost?

They expect it to be a free service because there are other free services that do something similar.
In order to get income you can either
1) Get people to understand that your product is substantially better (for their actual needs) than the free competition. You will then be able to charge money for your service.
2) Find out how your free competition is getting income and copy them (ads?)

If you do in fact have features that are better than the free competition, I would recommend making two versions of your service:
A) A free version which has basic features that are shared with the free competition
B) A paid version which also has the 'pro' features which your free competition does not have. This could for instance be an ability to better customize the types of alerts you can get, or change the sound of audio alerts, etc.
C) (optional) It will also help you get sign ups for your paid service if you add a third option which is a little more expensive than option 'B'. Simply the presence of a more expensive option will make people see option 'B' as a better deal, than if there was no more expensive option 'C' (it's a psychological thing). Option 'C' should be everything you get with 'B', but also comes with something extra. This something extra could for instance be an email that the user gets once a week summarizing 4 - 5 news stories about the stock market, or anything else you can think of. In the end though, this is not about 'tricking' anyone into paying for a product they don't want, it's about helping them make the decision to get something they will be happy with. In other words, your product (option 'B') should be fairly priced for the value they will get out of it.

Keep in mind, that even if your product doesn't have any obvious abilities that your free competition has, if you package your product in a more easy to access, and pleasing to use way (i.e. make signing up easier, make the UI more intuitive and pleasing to look at, etc), many people might be willing to pay for that too, even though you might not see it as a feature.

Well I'd start by mentioning somewhere on the site that it isn't a free service. There isn't one piece of text or menu item that says anything about it being a paid service. Add a 'pricing' menu item, or show the pricing right up front on the home page.

The problem may not be the price of your service or the messaging around it. The problem may be that you're attracting the wrong target customer.

If you need help researching and testing for the appropriate target demographic for your service, the one who will find the most value in it, and then positioning your marketing plan to engage those clients, let's talk.

I think you have a few different options here.

1: Make it clear that it's a paid service
2: Quickly highlight the main benefits of the service
Perhaps with some testimonials and social proof.
3: Go with a freemium mode. E.g. 3 alerts on a free account and then users have to pay on a subscription model for different level alert packages.

I've read all the answers provided and even though I think they are valid, I believe they miss one critical thing. The value of you obtaining a customer is not the $9.99 that you may get from them (or whatever you are charging), but the data you gather. In the financial industry to the contact is worth far more then anything you could ever charge a monthly fee for. The devil is in the details but I have lots of ideas on how you could monetize. We can talk further if you'd like.

Looks like a great site! Since you have a nich audience I would go after sponsors in the financial space. Maybe find contacts via LinkedIn at a stock brokage to help you find the people you need to talk to. Although some would question your ethics, you have a lot of valuable data, you might be able to sell that data to a company that would find it useful.