How To Reply to Angel Investor Intro Emails
I have had a lot of entrepreneurs ask me for introductions to various investors. In some cases the entrepreneurs use their reply to the intro email as a mechanism to gain social proof, emphasize urgency, and to reduce the friction to meeting the investor and closing their round (see e.g. VentureHacks for great tips).
Unfortunately, a lot of otherwise savvy entrepreneurs don't follow up with investors well. You have to remember that every thing you do can signal to an investor a lack of urgency/interest in your company, the fact that you are taking your startup casually, desperation, or a lack of ability to follow through. Also, if you don't create urgency or a sense that the investor may miss out on something interesting, then the angel may drag their feet in meeting with you, extending the time of your fundraise.
This post is focused on the small tactics that go a long way upon receiving an introduction.
Example Of a Bad Reply To An Investor Intro
"Thanks Ivan Introducer for the intro!
Hiya Angela Angel,
It is great to meet you! Love to connect! Let me know what works!
Example of a Good Reply (tailored to an angel round with a lead)
"[moving the person who made the intro to BCC]
Hi Angela Angel,
It is great to meet you. As introducer said, we are in the midst of a round led by well-known investor and other well known angel is also investing. We have seen really solid traction with user growth of X up Y%.  See below for team bios/key stats 
Our round is coming together quickly so the sooner we can talk the better. Are you free to chat at one of the following times?
Monday 2pm-3pm; 5pm
Tuesday 1:30pm-3pm, 6:30pm
We can also try to move things around to accommodate you - we have heard great things about you as a social media investor (in particular your investments in Tumblr and Pinterest) so would love to connect before we close the round.
Team bios 
-2008-2010 Tech lead at Facebook for newsfeed
-CS, MS degrees from Berkeley
-Side project stupidhipster.com getting 100,000 visits a month
What Is The Difference?
I added numbers to footnote the important parts of the email.
1. Move the introducer to BCC. They don't want to be on the 15 emails it takes to schedule the meeting.
2. Put social proof up front. All these great investors are part of the round! Angela angel will want to be part of the club and invest too. It also means you are more legit than the other random companies trying to talk with the same investor.
3. If you have good traction or a key stat, explain it in 1-2 lines. This is additional proof that they need to rush to talk to you.
4. Put polite pressure to chat very soon. You need to emphasize things are on a fast track for you. If things are moving slowly it suggests no one is interested in your round, which means this investor won't be interested either.
5. Add specific times. This reduces the friction to scheduling as if you leave it open ended it (a) does not convey urgency and sets up the timeframe within which you will meet and (b) makes the investor work harder to figure things out. Don't put the burden on them to suggest a time
6. Explain why the investor is relevant. This helps them understand why they are a good fit for the company. It also extends the the timeframe you can wait to meet with them if needed without looking desperate (e.g. if the can only meet in two weeks, their experience justifies you waiting for them as they are uniquely awesome for your company, rather then because you dont have other options).
7. Add team bios (2-3 lines, bulleted per team) + any key stats (if no good stats, just included bios). People will want to know who you are and why to meet with you. In some cases, even if the idea is bad they will still want to meet with you if you have a strong background. This will give you a chance in person to convince them to invest.
Hopefully, the person who introduced you already covered items 2 through 5 or 6 in either their intro, or in the email asking if the investor will talk to you. If the intro explicitly included 2-3, you can skip mentioning it yourself, but you should keep the other elements in.
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Other fundraising posts:
Party Rounds: How to Get A High Valuation For Your Seed Startup
VC Economics: Why VCs Could Care Less About Your $50 Million Exit