The random calls and puts was more of an existence proof of the option seller’s edge than an actual strategy.
Still, selling puts on big index ETFs is a good strategy, but it’s one with negative skew. When the market crashes (and it eventually will), you’ll lose a lot of money. As always, don’t bet over Kelly. It’s been working well for me so far, but I’m also hedging with VIX calls so I don’t get wiped out next crash. The VXTH index uses a straightforward algorithm you could do manually to defend your short index puts with VIX calls. You’ll get the best returns by selling slightly in-the-money (ITM) puts. (I’m not comfortable with that much variance, so I use out-of-the money (OTM) puts and hedge more than that at the cost of profits, but you might be OK with it.)
Selling straddles on big index ETFs is arguably a better strategy (if you can stomach it), but in small amounts since it’s even more skewed than puts alone. The advantage here is that only one side can expire in the money, so playing both sides doesn’t affect your margin requirement much, but almost doubles your premium. You could also use the VXTH defense on these, plus maybe a cheap far-OTM call, since short risk is potentially unlimited otherwise. You still need a big enough account to handle that much skew without betting over Kelly.
Negative skew is easier to deal with the more your account is diversified, since it tends to not happen all at once that way. These shouldn’t be your only strategies.
As always, don’t bet over Kelly. [...] without betting over Kelly
You mention Kelly twice in the context of selling options on indices, but it’s not clear to me how a “average LW retail investor” is supposed to calculate their edge.
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).
The random calls and puts was more of an existence proof of the option seller’s edge than an actual strategy.
Still, selling puts on big index ETFs is a good strategy, but it’s one with negative skew. When the market crashes (and it eventually will), you’ll lose a lot of money. As always, don’t bet over Kelly. It’s been working well for me so far, but I’m also hedging with VIX calls so I don’t get wiped out next crash. The VXTH index uses a straightforward algorithm you could do manually to defend your short index puts with VIX calls. You’ll get the best returns by selling slightly in-the-money (ITM) puts. (I’m not comfortable with that much variance, so I use out-of-the money (OTM) puts and hedge more than that at the cost of profits, but you might be OK with it.)
Selling straddles on big index ETFs is arguably a better strategy (if you can stomach it), but in small amounts since it’s even more skewed than puts alone. The advantage here is that only one side can expire in the money, so playing both sides doesn’t affect your margin requirement much, but almost doubles your premium. You could also use the VXTH defense on these, plus maybe a cheap far-OTM call, since short risk is potentially unlimited otherwise. You still need a big enough account to handle that much skew without betting over Kelly.
Negative skew is easier to deal with the more your account is diversified, since it tends to not happen all at once that way. These shouldn’t be your only strategies.
You mention Kelly twice in the context of selling options on indices, but it’s not clear to me how a “average LW retail investor” is supposed to calculate their edge.
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).