The Kelly Criterion and small business bets

Small businesses have less capital than larger businesses, so they need better judgement to manage that capital. A string of unlucky outcomes can wipe out a small business more easily than a larger business. We can use the Kelly Criterion to see this in action: When you don’t have a lot of capital, each “bet” takes up a larger fraction of your total capital. When you stake more you can withstand fewer misses. The Kelly Criterion formalises this, and we can use it to show the point with some concrete (if imaginary) numbers.

The Kelly Criterion tells you what fraction of your bankroll to bet to maximise long-term returns while minimising the chance of going broke. It’s useful because streaks of “bad luck” are more common than most people intuitively expect. Bet too much and you’ll go broke. Bet too little and you won’t make as much as you could have.

It’s given by the formula:

f is the fraction of your bankroll you should bet, p is the odds of “winning”, and b is the relative payout. For example, a $2.05 payout on a $2.00 bet has b = 2.05 / 2.00 = 1.025. The magic of this is that you can run it “backwards” to estimate how good the bet needs to be, given your expected spend and payoffs.

Say your business has $10,000,000 free cash flow [1] (FCF) and you want to hire some expensive software engineers to solve a problem. In the abstract, you pay the new employees a salary in the hopes they produce more value for the organisation. For simplicity, let’s assume the payoff (b) is 1.10 – each employee produces 10% more FCF than the cost of employing them. Further, let’s assume these are expensive employees – $200,000 covers all the costs of hiring the employee for the year.

How confident does this large business need to be that they’ll get the 1.10 payoff? We know f: it’s 200,000 / 10,000,000 = 2/100 = 0.02. We assumed b = 1.10 for simplicity. Rearranging we find p = 0.487. If the large company is to make a profit hiring people on these terms, they only need even odds on their hiring. They don’t need to dig that deep to get to 50-50 odds.

What about a small business? Say the small business $500,000 yearly FCF. Running the same formula gives us p = 0.686. The small business must use a more discerning recruitment process, otherwise they have a higher risk of ruin in the long term.

The Kelly Criterion applies to other bets too. A boutique café expanding to a second location needs more confidence in the expansion than Starbucks [2].

Because of this weird effect, small businesses must bet less of their bankroll or find more appealing bets. They can’t afford to consistently mix up a 50-50 bet and a 60-40 bet.

This flies in the face of “common knowledge”. People often argue that small businesses must take big risks to capture the market or surprise the incumbent. However, small businesses are much more vulnerable to streaks of bad luck, which means they need to take more care when making bets. They need to move fast, but they must do so with more rigor than larger businesses.

There are several immediate critiques to this approach: bets aren’t independent so Kelly doesn’t apply, businesses can’t reject all unfavourable bets, start-ups don’t need to bet like this because they themselves are the bet, no-one calculates the odds or pay-offs so you can’t calculate the Kelly Criterion, and bets sometimes result in non-monetary results.

The strongest critique is that the Kelly Criterion assumes independent bets, but bets in business are not independent. In our hiring example: If you hire three people using the same process, then their odds are not independent. A bad hire can point to a bad hiring process, which means that others hired using that process are also at higher risk than expected. Investors faced this in 2008 where mortgage-backed securities should have been un-correlated, but if one person defaults, the chance of others defaulting also increases. Investors use fractional Kelly bets in their portfolios to guard against these unexpected correlations and model errors, but that’s only a heuristic. In small businesses, this points to the dissatisfying conclusion that they need to be more careful; they need better decision-making processes to uncover these hidden relationships, or take smaller bets. If you move in the angel investing or venture capital start-up space, you may think small businesses do not need to worry about the Kelly Criterion. The investors are making Kelly bets on whole companies, so each individual company doing Kelly bets would be too risk averse. However, most businesses are not funded like this. Their founders ask family and friends for money, they take bank loans, and stake their own cash [3]. In these scenarios, companies need to minimise their risk of ruin. The founders don’t want to lose their stake or get stuck with a loan they can’t pay back.

Very few people can put well-calibrated and appropriately-precise values on the odds and payoffs of the bets they take. That means that you can’t calculate the Kelly Criterion, so you’ll miss it. While it’s true that few people talk about their business investments as bets, they don’t need to. They only need to know that their business needs to be able to weather a storm. That means making the bets more favourable or lowering the stakes, which is consistent the Kelly Criterion. The important thing is the principle, not the exact numbers.

Similarly, some bets have apparently non-monetary payoffs, like improved reputation or more information. While these “intangibles” do not give direct cash benefits, they are assets. Gucci vigorously defends their brand because it’s so valuable to them. Without the brand, Gucci is just another handbag makers and forfeits their high margins. Information also has value. Good information lets you make better future predictions, which means founds have a better chance of picking more valuable options, generating more cash faster.

Founders can’t reject all unfavourable bets. Take a café as an example; they need a location, so they need to pay rent. Rent is a large expense, but owners can’t not have a physical location. They must bet their rent. However, I don’t think of these necessary expenses as bets. Bets are unforced, expenses are necessary. The overall business is the bet. That may be non-Kelly too. Some folks just want to start a business and they’re willing to make a big, possibly inadvisable, bet.

In sum, small businesses have less capital, and bets like hiring or opening a new location have a minimum size. Those bets are a larger fraction of their available capital than larger businesses. According to the Kelly Criterion, you need better odds or a better payoff to sustainably support betting a larger fraction of your capital. In other words, small businesses need to be better at discerning a bad bet from a good bet, as compared to larger businesses. On the other hand, larger businesses tend to become more risk averse over time, but that’s unjustified according to Kelly. Larger businesses can make more similarly-sized bets than a small business and only need slightly favourable odds; they can sustain poorer decision-making or more risk-taking for longer.

There are some issues with this analysis; mainly that bets in business are not independent. A bad bet on a project maybe due to the project planning process, not the project itself, which means you’re not betting on what you think you’re betting on. Another major critique is that small businesses can’t afford to turn down certain bets – like a physical location. In some sense, these are not bets, they’re forced moves. They’re part of the larger bet of starting a small business, which may or may not have been a Kelly-bet to start.