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Kelly Criterion

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Avatar for annayks
Written by   124
6 months ago
Topics: Investing

Often we do it all wrong and make a mess with our investments. When realizing losses and write-off investments we are not failing as investing comes with a risk.

Our investment is mathematically impossible to go all wrong. It will be our mistake having a big part of our net value in only one asset, or maybe even in just a few.

Since we are in the Cryptocurrency World, we often read about diversifying and we think this means to buy even more cryptocurrencies. But diversification in cryptocurrencies works only during bull runs and not as a safety mechanism.

Diversification in Crypto

When Bitcoin drops the altcoins are going down rapidly, they crash faster and with huge effect to our investments.

During the last two bull markets, the prices of altcoins were rising faster than Bitcoin and taking a big piece of the market cap. This is observed easier using the BTC trade pairs. The satoshi terms will be rising significantly during alts season.

But because of the extreme volatility of alts, they will drop faster and create huge losses to our investment, when things turn bearish. This is how historical charts explain this market. One month after the bear market begins, our altcoins investments will be losing 80%. A year later another 90% making our investments worth practically zero.

It happened again and it will keep happening. XRP for example, is valued today at $1.40. Not even close to the $5 it was trading at, four years ago. There are too many investors that bought at $3 and higher, and most of them decided to writeoff this bad investment and sell years ago. Losing 95%, a bad investment.

All cryptocurrencies had similar behaviour. Bitcoin for some reason has some huge support and doesn't drop below designated levels. I don't know why it reacts like that and why for example in 2019 it didn't drop to $1000. It was going there, but a few unexpected incidents combined saved it.

It doesn't matter a lot, it did an 80% loss from ATH, this is a standard Bitcoin move. Altcoins though, they were destroyed. And all those that were making millions, in just a few months were losing.

Diversification means we should not invest everything in one sector of an economy, but spread into many assets. We can invest in stocks, bonds, gold, crypto and we can also find hedging opportunities for safety.

Odds and Expected Value (or Expected Returns)

What is investing many are asking. Some will tell you it is putting our money in good use, by supporting startups, companies, or buying assets we expect their price will rise in the long run. We also invest when there is an opportunity and we expect a profit from our investment.

However, in all investing there is one common denominator. The odds.

When we invest we basically bet. We open a bet with the expectation that the odds are with us and eventually our investment (or bet) will turn profitable. And we have levels to take the profit too, which will be our winning strategy.

Investing is just like gambling. We bet that the housing market is not in a bubble, so we invest in real estate. There are ways to calculate the odds by looking at historic price action of the assets we are investing in. And there is risk management that calculates the odds of us losing.

Before making our bets, we calculate the expected value. This is the outcome we expect from our investment at some future point.

The formula of expective value or EV is this:

Expected value is described and explained in this page from investopedia:

It is a simple mathematic formula, that multiplies each possible outcome with the odds these outcomes can happen. The most difficult part in investing is finding the odds, or else the likehood for each outcome.

The Kelly Criterion

When we bet on an investment, or when we bet on blackjack or poker, we have a decision to make.

How much do we bet?

John Larry Kelly Jr., a researcher at Bell Labs (now called "Nokia Bell Labs"), described in 1956 the formula that solves this puzzle.

The Kelly Criterion gives the absolute value we should bet (or invest) that will provide the maximum return for our bet. It is a formula that under certain circumstances and assuming we already know the expected value, calculates the optimum bet sizing we should make to maximize our profit.

It is a strategy based on what is called "the long run". In an infinite number of bets our investment will have the optimum results under the Kelly criterion. Of course this doesn't mean every investment will be successful.

In the poker game of Texas Holdem there is optimum strategy that can be applied by those studied the game enough and manage to "beat the game". Poker bets vary and often you will read about players being perfect at playing 500NL cash games, but being unable to beat higher or lower stakes. This is because the dynamics (win ratio, winning probability) of each game are different and the Kelly criterion, the bet size of these poker players is adjusted to the 500NL table, making it unprofitable for other stakes.

The Formula:

This is the formula. The Kelly Criterion is displayed as a percentage.

  • K: The Kelly Criterion (How much of the bankroll we risk on each bet)

  • W: The odds (probability) we win the bet

  • R: The payout of the bet (winning percentage)

The Kelly criterion is what determines our bet size percentage wise and maximises expected profitability.

Bankroll management in gambling is also important. Building or allocating a bankroll for gambling, or perhaps for investing will also require research before allocating funds for these reasons. Bankroll management is also, what separates the professional (and winning) poker players from the rest of the pack.

Conclusion

Bet sizing is very important in both gambling (the beatable games) and investing. Going all-in with our investment funds in only one asset, is a lossing strategy in the long run. Choosing how much money we should allocate to our investment is given by the Kelly Criterion.

Financial decision making process is never absolute, the Kelly Criterion has been adjusted depending on circumstances as often may recommend betting a big part of our bankroll. The fractional Kelly could be a better methodology depending on the situation.

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Avatar for annayks
Written by   124
6 months ago
Topics: Investing
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