In the case of a deep in-the-money cash-covered put, performance is pretty similar to simply holding the stock. (Less deep is synthetically equivalent to a covered call.) Historically, leverage of about 2x does better when holding the index, so as a rule of thumb, a 50% covered index put seems about right, but this can be adjusted based on current volatility levels.
I touched on Kelly a little bit in How to Lose a Fair Game. To calculate Kelly properly, you need to know your payoff distribution. In practice, you can’t know this, but you can estimate it from historical price data, which is better than pulling a number out of your nose, but still highly uncertain. If you under-bet a little, your returns are suboptimal. If you over-bet a little, your returns are suboptimal, and you have to endure much higher volatility. (And if you over-bet a lot, you’ll wipe out.) Since the consequences of betting a bit under Kelly are less bad than betting over Kelly, and your return distribution is uncertain, it’s best to think of the Kelly fraction as an upper bound, rather than a target.
In particular, for a single asset, the formula becomes
f∗=μ−rσ2
Where μ is the drift, r is the risk-free rate, and σ is the volatility. Future volatility is much easier to predict than future price. Even a simple moving average of historical volatility over the last month is probably a good enough estimator for our purposes, but you can do better with a GARCH model or something.
The Kelly criterion is intended to maximize log wealth. Do you think that’s a good goal to optimize? How would your betting strategy be different if your utility function were closer to linear in wealth (e.g. if you planned to donate most of it above some threshold)?
This isn’t quite the right way to think about Kelly betting. Kelly maximises log-wealth after one bet. This isn’t quite the same as maximising long-run log-wealth after a series of such bets. In fact, Kelly betting is the optimal betting strategy in some sense (leading to higher wealth than any other strategy).
In the case of a deep in-the-money cash-covered put, performance is pretty similar to simply holding the stock. (Less deep is synthetically equivalent to a covered call.) Historically, leverage of about 2x does better when holding the index, so as a rule of thumb, a 50% covered index put seems about right, but this can be adjusted based on current volatility levels.
I touched on Kelly a little bit in How to Lose a Fair Game. To calculate Kelly properly, you need to know your payoff distribution. In practice, you can’t know this, but you can estimate it from historical price data, which is better than pulling a number out of your nose, but still highly uncertain. If you under-bet a little, your returns are suboptimal. If you over-bet a little, your returns are suboptimal, and you have to endure much higher volatility. (And if you over-bet a lot, you’ll wipe out.) Since the consequences of betting a bit under Kelly are less bad than betting over Kelly, and your return distribution is uncertain, it’s best to think of the Kelly fraction as an upper bound, rather than a target.
In particular, for a single asset, the formula becomes
f∗=μ−rσ2
Where μ is the drift, r is the risk-free rate, and σ is the volatility. Future volatility is much easier to predict than future price. Even a simple moving average of historical volatility over the last month is probably a good enough estimator for our purposes, but you can do better with a GARCH model or something.
The Kelly criterion is intended to maximize log wealth. Do you think that’s a good goal to optimize? How would your betting strategy be different if your utility function were closer to linear in wealth (e.g. if you planned to donate most of it above some threshold)?
This isn’t quite the right way to think about Kelly betting. Kelly maximises log-wealth after one bet. This isn’t quite the same as maximising long-run log-wealth after a series of such bets. In fact, Kelly betting is the optimal betting strategy in some sense (leading to higher wealth than any other strategy).