The Calculus of Risk

The other day a nice gentleman who had a hold of my business card contacted me with an idea for a web site that he wanted me to help develop and run. He thought it could be the next Craig’s list or the like: and while the idea was an interesting one, I told him that I wasn’t interested in working on a web site.

I’m sick of web site development. If my time at Yahoo! has taught me anything, it’s that web site development sucks. Or rather, the “constant iteration” that Yahoo! practices and that I’ve read elsewhere about how web sites “should” be developed sucks, as “constant iteration” really translates (at least at Yahoo!) to “management can’t get its shit together and plan things in a reasonable way, so you’re expected to constantly be on call because no-one can plan more than 15 minutes in advance.” I don’t mind “plans are subject to change without notice because of new information that came in during execution.” I do mind “we changed our minds because we have no clue what we’re doing.” Especially when events were easily foreseen.

But I digress.

Part of what I tried to convey to this person is my own take on how I would evaluate the risk/reward of my getting involved in a new project–and that, mathematically speaking, for me to get involved in a project like his would be expensive. And I mean “oh, shit, you’re kidding!” sorts of expensive.

So let me break down my own thinking about money–and let’s put some numbers to this, shall we?

I’m a software developer with 20 years of professional experience, and I think I’m one of the best programmers out there. (Do I have an ego? Probably. But it doesn’t change the numbers.)

Let’s assume my salary is around $150,000/year. Probably not far off for someone with 20 years of professional experience in Los Angeles, when you factor in bonuses and stock options and the like.

Okay, now say I’m going freelance. Well, when you add in corporate social security matching (which is really just a hidden tax), insurance, unemployment and the like–you need to add another 25% to that number. So this brings the amount to $200,000/year. That is what I would have to bring in as a freelancer in order to match my salary.

Now lets assume I’m freelancing. (And I used to freelance, so I can attest to the following numbers.) If I’m doing real well, I should expect only about 60% of my time to be billable time. Why? Well, I’ll want to spend some time on vacation–four weeks a year cuts the number of billable hours by almost 10%. And the rest of my time will be spent searching for more freelance work–since, really, the reward of a job well done is being patted on the back and shown the door.

This translates into a base hourly rate of $200k/1200hrs or $160/hr.

Suppose I want to put together a web site for someone as an investment. Say it will take six months to assemble the web site. Well, the amount I would charge to do this as a consultant is easy: $160 * 24 weeks * 40 hours/week = $153,600.

Now this is where things get interesting. Suppose, for example, that you want me to build this web site for you, but you want me to do it at a discount in exchange for a share of the resulting internet company. So suppose you want me to build the web site for (say) $50,000. This means that I have, in effect, invested $103,600 to your project. Now suppose it takes 3 years for the company to develop, and after my initial investment in time I have no involvement at all in the company–and after 3 years, there is a 1 in 20 chance that the company will become “successful”–that is, you’ll convince Yahoo! to buy you out.

What should my return on this be?

Well, that’s simple. Currently T-Bills are getting about 5%/year. So if I were to have taken my $103,600 and instead put it into T-Bills, that would have grown to about $120,000. (The reason why I’m using T-Bills is because there is zero risk to that investment. In other words, I’m not interested in what I may be able to get for that $103,600–I’m interested in what I would get if I had taken no risk. Because any return above that amount would involve some risk–and any return below that amount means either my risk didn’t pan out or I’m an idiot.)

Using Bayesian math I can say that if my risk is 1/20 that I will get a payout and 19/20 that I won’t, then the potential reward that I would have to receive for taking a risk that 19 out of 20 times your web site will not return anything would be $120,000 * 20 or $2.4 million.

In other words, if I don’t see an upside of $2.4 million on my six months of work if there is only a 1 in 20 chance of success, I’m better off on the average keeping my day job. And, more importantly, this is the “break even” point for a web site that only has a 1 in 20 chance of success–in order to motivate me, I should receive more. In other words, we can work this math backwards–and when we do so, every $100,000 in potential reward 3 years from now is only worth around $4300 today. So if you entice me with a potential $3 million reward in 3 years–and remember, this is assuming that I am not involved at all for the 2 and a half years between completing my work and the ultimate payout; if I’m involved, this number can go up dramatically–that would be the same as if I swapped jobs and got a 15% pay raise.

Why such a large number? Because there is risk involved. And for every success story we heard about in Silicon Valley, there are dozens who found themselves screwed one way or another. It’s easy to concentrate on the successes, but we ignore the failures–after all, we think we won’t fail; we’re smarter than everyone else. In mathematical terms, we think the chances of success is like 1 in 2 or 1 in 3–not 1 in 20. Thus, we misestimate the potential for downside. We also fail to properly estimate what we are worth–that is, how much we could make if we took no risks–which is why in many cases I’ve seen people walking away having negotiated a present-value contract that earns them less than minimum wage: out of their ignorance they put themselves in a worse position than if they’d went to flip hamburgers part-time at McDonald’s.

Now me, I will factor in my abilities–and I know that I can reduce the probability of failure simply because for many companies, they fail simply because they fail to release a product. Millions in invested money later and all they have to show for it is a roughly written demo and the PowerPoint they gave the venture capitalists. So I may internally tweak the numbers: for me, it may be 1 in 15 chance of success. And of course there are more outcomes than “jackpot!” and “failure”, and sometimes even failure gets us where we want to go. After all, very few businessmen succeeded the first time out.

But ultimately this is the mathematical analysis I will apply if someone asks me to quit my day job to put together their web site. Of course the salary numbers are just numbers I pulled out of my ass–and I may factor in other intangibles, such as the potential upside in the event of failure. But don’t be surprised if I don’t quit my day job at Yahoo! simply because you think you have the next great idea and want to cut me in for 10% of your ten million-dollar idea.

(Note: The numbers above have been changed to protect the innocent. No numbers were harmed in the writing of this essay. Your mileage may vary.)

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