February 27, 2011

What Stock Option Pricing Models Tell You about Courting Controversy

“There’s no such thing as bad publicity” was surely coined by an otherwise bad publicist. Of course there’s such a thing as bad publicity, if you’re already famous.

If you’re not famous, there’s a tradeoff: at some point, it’s better to piss off most of your audience and impress a few people, rather than having no audience at all.

The Black-Scholes model provides a helpful way to look at this. The Black-Scholes formula allows you to price a stock option knowing only a few data points—the current price of the stock, the strike price and maturity of the option, the risk-free interest rate, and the stock’s volatility.

The great thing about this is that you can use it to model other decisions. Black-Scholes tells you the tradeoff between price and volatility, which can tell you when it’s okay to accept a worse average outcome in exchange for a better chance at the best possible outcome.

It’s great for modeling situations in which the default case is failure. For example, look at startups: the default outcome is complete failure, but there’s a huge variation in how rewarding it can be to not-fail. A startup thus behaves like an out-of-the-money call option. The startup can accept a worse average outcome in exchange for more volatility. That might include hiring non-traditional employees, scrapping an old business model, or holding a risky press stunt.

To quantify this, look at the tradeoff between value and volatility in two cases.1 In each case, we’re considering something that reduces the immediate price of the asset by 25%, but doubles its volatility. Situation #1 is an asset trading at 50% above its strike price. In situation #2, it’s 50% below the strike price.

Situation #1: the low-volatility outcome has a present value of $60.28, and the high-volatility outcome has a value of $51.30.

Situation #2: $16.50 value for the low-volatility outcome, and a $19.26 value for the high-volatility outcome.

The same choice is value-creating for a startup (the higher odds of a great outcome mitigate the fact that it’s slightly more worthless upfront), whereas it’s value-destroying for a big company.

This is another way to explain why big companies accumulate rules and small companies don’t: at a small company, if your customer service rep curses out a customer, you’ve lost that customer, but nobody will care. If Amazon hires a customer service rep who curses out a customer, they could lose tens of millions of dollars in brand value. So Amazon is naturally more likely to hire based on minimizing downside, while a new startup can only afford to hire based on potential upside.

A few other cases where this Black-Scholes model makes sense:

Diplomacy: The status quo is the worst-case scenario for a country like North Korea or Libya. They can be completely insensitive to risk.

Hiring: There’s probably a 90% chance that your resume will get a five-second rejection. If you raise that to 95% in exchange for raising the “This person might be crazy, but they might be brilliant!” rate from 0% to 1%, you’re still ahead.

Dating: Unattractive people are disproportionately likely to tell inappropriate jokes to near-strangers. That’s pure Black-Scholes thinking.

Building a professional reputation: I got a few dozen pieces of hate mail after my over-the-top attack on index funds. But I’ve also gotten a few notes from people who enjoyed the piece—who wouldn’t have heard about it if it hadn’t riled up so many other folks. (I’d like to give a special thank-you to the critics who blogged about this piece, or wrote about it on forums. What I lack in Public Relations I can now make up for in PageRank.)

This attitude is underused. In the face of long odds, most people are needlessly cautious—they’ll take incremental increases in expected value over big increases in variance. But in winner-take-all fields like finance, marketing, and startups, that’s completely irrational. High-variance strategies aren’t just optimal; they’re undervalued.

(For more on this, see Scott Locklin’s excellent applications of financial ideas to everyday life.)

[1]I’m holding maturity constant at five years, and using a 3% risk-free rate. I used this Black-Scholes calculator.(return)

  • Anonymous

    this is the same strategy Snooki used !