Suppose I offer you two games:
A) You put up ten dollars. I flip a fair coin. Heads, I give it back and pay you one cent. Tails, I keep it all.
B) You put up $100,000. I flip a fair coin. Heads, I give it back and pay you $100. Tails, I keep it all.
You have the edge, right? Which bet is riskier? The only difference is scale.
What if we iterate? With game A, we trade some tens back and forth, but you accumulate one cent per head. It’s a great deal. With game B, I’ll probably have to put up some Benjamins, but eventually I’ll get a streak of enough tails to wipe you out. Then I keep your money because you can’t ante up.
The theoretically optimal investing strategy is Kelly, which accounts for this effect. The amount to invest is a function of your payoff distribution and the current size of your bankroll. Your bankroll size is known, but the payoff distribution is more difficult to calibrate. We could start with the past distribution of returns from the asset. Most of the time this looks like a modified normal distribution with much more kurtosis and negative skew.
The size of your risk isn’t the number of dollars you have invested. It’s how much you stand to lose and with what probability.
Volatility is much more predictable in practice than price. One can forecast it with much better accuracy than chance using e.g. a GARCH model.
Given these parameters, you can adjust your bet size for the forecast variance from your volatility model.
So volatility is most of what you need to know. There’s still some black swan risk unaccounted for. Outliers that are both extreme and rare might not have had time to show up in your past distribution data. But in practice, you can cut off the tail risk using insurance like put options, which cost more the higher the forecast volatility is. So volatility is still the main parameter here.
Given this, for a given edge size, it makes sense to set the bet size based on forecast volatility and to pick assets based on the ratio of expected edge to forecast volatility. So something like a Sharpe ratio.
I have so far neglected the benefits of diversification. The noise for uncorrelated bets will tend to cancel out, i.e. reduce volatility. You can afford to take more risk on a bet, i.e. allocate more dollars to it, if you have other uncorrelated bets that can pay off and make up for your losses when you get unlucky.
Suppose I offer you two games:
A) You put up ten dollars. I flip a fair coin. Heads, I give it back and pay you one cent. Tails, I keep it all.
B) You put up $100,000. I flip a fair coin. Heads, I give it back and pay you $100. Tails, I keep it all.
You have the edge, right? Which bet is riskier? The only difference is scale.
What if we iterate? With game A, we trade some tens back and forth, but you accumulate one cent per head. It’s a great deal. With game B, I’ll probably have to put up some Benjamins, but eventually I’ll get a streak of enough tails to wipe you out. Then I keep your money because you can’t ante up.
The theoretically optimal investing strategy is Kelly, which accounts for this effect. The amount to invest is a function of your payoff distribution and the current size of your bankroll. Your bankroll size is known, but the payoff distribution is more difficult to calibrate. We could start with the past distribution of returns from the asset. Most of the time this looks like a modified normal distribution with much more kurtosis and negative skew.
The size of your risk isn’t the number of dollars you have invested. It’s how much you stand to lose and with what probability.
Volatility is much more predictable in practice than price. One can forecast it with much better accuracy than chance using e.g. a GARCH model.
Given these parameters, you can adjust your bet size for the forecast variance from your volatility model.
So volatility is most of what you need to know. There’s still some black swan risk unaccounted for. Outliers that are both extreme and rare might not have had time to show up in your past distribution data. But in practice, you can cut off the tail risk using insurance like put options, which cost more the higher the forecast volatility is. So volatility is still the main parameter here.
Given this, for a given edge size, it makes sense to set the bet size based on forecast volatility and to pick assets based on the ratio of expected edge to forecast volatility. So something like a Sharpe ratio.
I have so far neglected the benefits of diversification. The noise for uncorrelated bets will tend to cancel out, i.e. reduce volatility. You can afford to take more risk on a bet, i.e. allocate more dollars to it, if you have other uncorrelated bets that can pay off and make up for your losses when you get unlucky.