Numeracy #6: Kelly Criterion

Imagine we are given the opportunity to bet on a fair coin flip. If heads, we get 2 dollars for every dollar bet. If tails, we lose our bet. We can easily work out the expected value of a 1 dollar bet.

EV = 0.5($2) – 10.5($1)
EV = $0.50

On average, we can expect to make 50 cents per bet. How could we possibly lose? Now, imagine that we have a bankroll (investable capital) of 10 dollars. We take our 10 dollars, bet it all on heads, and lose it all. We broke the first rule of gambling, don’t get wiped out.

The solution seems obvious: never bet your whole bankroll. But how much should we bet? 9 dollars, 7 dollars, 4 dollars, 0 dollars? This is where the Kelly Criterion comes into play. The Kelly Criterion, or Kelly Optimization Model, is a formula used for determining the optimal size of a series of bets. It other words, it tell us how much of our bankroll to bet given a chance of winning and a payout.

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Analysis: Brexit

Ray Dalio, founder of investment first Bridgewater Capital, wrote an article for the FT in which he argued:

In deleveragings bad economic conditions typically lead to emotional reactions, social and political fragmentation, poor decision-making and increased conflict. When this occurs in democracies, the checks and balance system, which is intended to yield the best decisions for the whole, can stand in the way of thoughtful leadership and lead to ineffective “mob” rule. This dynamic can lead to a self-reinforcing downward spiral.

Frustrations increase, the established ways of doing things come under attack and frustrations over the ineffectiveness of government creates the perceived need for someone to gain control of the mess. Plato spoke of this dynamic. It was the reason Hitler was elected in 1933.

From Trump to Le Pen, the world seems to be getting more divided. This week, Briton voted to leave the European Union. The EU was created with the goal of allowing freer movement of goods, services, and people across member countries. The benefits of this are well-known: free movement of resources, productive allocation, an increase in overall economic welfare. This is not to say there aren’t losers. For those Britons who increasingly saw themselves as worse off, exit seemed to be the rational choice.

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