"Very, very slim
" to "almost negligible
" if you're talking about investing into one company, increasing to "slim" if the syndicate invests into a dozen or more companies.
I know I'm going to draw the ire of some of the angel crowd, most of the entrepreneurial crowd and all of the crowdfunding crowd with this response, so it's important to back it up with an explanation, namely:A majority of all new, angel-backed companies fail completely, so if you invest in only one company, the odds are that you will LOSE ALL YOUR MONEY, not just "not make a profit".
Several studies and mathematical simulations have shown that it takes investing the same amount of money consistently into at least 20-25 companies before your returns begin to approach the typical return of over 20% for professional, active angel investing
. This means the greater the number of companies into which the angel syndicate invests, the greater the likelihood of an overall positive return. However...
- Angel investing (like venture capital) follows the classic J-curve. Because unsuccessful companies tend to fail early, and big exits from the successful ones tend to take a long time to develop, when you graph it on a timeline, the overall value of an angel portfolio makes a shape like the letter "J". The value immediately begins dropping for several years as soon as you start investing, and only after a fair amount of time does it change direction and begin to be worth more than the original investment. 
- Since the average holding period for an angel investment in the United States is NINE YEARS, after only five years it is quite likely that the value of the syndicate's portfolio will still be underwater, unless it just happened to include one unusual, Black Swan, quick home run.
- A significant part of angel investing is getting access to good deal flow in the first place. The average investment PER ANGEL / PER COMPANY from an angel member of a serious angel group is about $25,000. If you're only investing $5,000 into the syndicate, and especially if you expect that to cover participation in several deals, the reality is that you would not be considered a significant investor either by potential investees, or even by your fellow investors. And a syndicate made up of even a hundred $5K investors would likely not have the resources to be taken seriously by the 'best' companies, thereby relegating it to starting with a second-tier caliber of deal flow.
- Companies always need more money, and therefore provide incentives for their investors to step up and participate in follow-on rounds. These incentives invariably come at the expense of the early investors who choose NOT to participate...which is why venture capitalists always reserve the same amount as their initial investment for them to put in later into the same company. Unless you (or the syndicate) are planning to reserve for follow-ons, your interest is likely to be significantly reduced over time.
I realize that this all sounds very depressing, and makes one wonder why on earth anyone would ever become an angel (good question, actually!) But the answer to that lies precisely in all of the cautions above:
- IF you are an Accredited Investor, and
- IF you are prepared to invest at least $50K to $100K per year, and
- IF you make sure to reserve quite a bit for follow-on financings, and
- IF you develop a strong deal flow of good companies, either through an angel group or your own contacts, and
- IF you invest consistently so that you have at least 20 companies (ideally more) in your portfolio, and
- IF you are professional in both your due diligence investigation and your deal term negotiation (including specifically with regard to valuations), and
- IF you go in with the knowledge that you are going to be in it for at least a decade, holding completely illiquid assets, and
- IF you can help add value to your portfolio companies above and beyond simply money (such as board service, contacts, fundraising, etc.)
Then (and only then) will the odds be in your favor for you to join the relatively rarified band of successful, professional angel investors who show average IRRs over their investing years of over 25% per year.
 Data Driven Patterns for Successful Angel Investing by Sim Simeonov http://www.slideshare.net/simeon... Resource Complementarities, Trade-Offs, and Undercapitalization in Technology-Based Ventures: An Empirical Analysis
by David M. Townsend and Lowell W. Busenitz