Direct indexing and implied volatility

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Walkure
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Direct indexing and implied volatility

Post by Walkure »

Here's my headscratcher of the day: The CBOE Buy-Write Index, which simulates holding equities and then writing covered calls on the index, has generally trailed the SP500 over its history.
https://www.google.com/finance/quote/BX ... XSP%3A.INX
But isn't this just a flaw in using index options? The value (premium gained from sale) of a given option increases with the implied volatility of the underlying security. But the whole point of an index is to eliminate idiosyncratic volatility, which, across the entire market, averages out to zero+beta.

Consequently, if instead of buying SPY and writing index calls, you went to a Wealthfront-type broker that offers a direct indexing service, you could buy every idiosyncratic stock and sell individual calls for each constituent of the index. In the aggregate, this would give you the exact same market exposure, but would not the calls generate significantly more premium due to the appeal they hold to prospective counterparties from their greater volatility?

Put another way, over any given length of options contract, the index may or may not exceed its historic average return. Over that same time period, we can be certain that a select few equities in the index will generate astronomical returns (causing the calls to be exercised). But we can also be certain that a far greater number of equities in the index will not even beat T-Bills over the duration of the contract. Yet because no one knows, ex ante, which equities will outperform and which will lag, the individual calls (if sold roughly at the money with sufficient time value) will be priced so that the premium one collects would be roughly equivalent to the expected future return of the market on average. By trading regular premium on all your holdings for astronomical returns on a few star performers, could one theoretically match the market return with a lower standard deviation?
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Walkure
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Re: Direct indexing and implied volatility

Post by Walkure »

I'll try restating this from an arbitrage point of view. My contention is equivalent to saying that you could sell naked calls on every constituent of the SP500, at their relative weights in the index, deep in the money, use a portion of the premium to buy a call on the entire index, also deep in the money, and still have profit left over, risk free. This should be impossible, but if so, how does the Buy-Write lag so consistently?
ChrisBenn
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Re: Direct indexing and implied volatility

Post by ChrisBenn »

Walkure wrote: Tue Oct 13, 2020 11:35 pm (...) By trading regular premium on all your holdings for astronomical returns on a few star performers, could one theoretically match the market return with a lower standard deviation?
Is this true though (that it balances/becomes advantageous)? Consider an index that went up 10% and a year, and because of the calls you sold you were capped out at 8% upside.

Now pretend that 10% index gain was driven by a 200x in stock A, and the rest of the index lost 5%. You have now capped the upside of that 200x moonshot at some value - and this is much more detrimental to your net returns than capping the index upside.

Volatility scaling your strikes won't help with this because thing causes those massive jumps are probably more idiosyncratic.
(and since volatility is already part of the options price I'm not sure if that would help anyway).

If you want to run a backtest I would find it an interesting read :) - but I am a bit dubious.
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Steve Reading
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Re: Direct indexing and implied volatility

Post by Steve Reading »

Walkure wrote: Tue Oct 13, 2020 11:35 pm Here's my headscratcher of the day: The CBOE Buy-Write Index, which simulates holding equities and then writing covered calls on the index, has generally trailed the SP500 over its history.
https://www.google.com/finance/quote/BX ... XSP%3A.INX
But isn't this just a flaw in using index options?
I don't see a flaw. Assuming options are priced as risk-neutral (assume no volatility premium, aka buyers and sellers both have zero expected returns on options), you should expect BXM to have a similar risk/return to the market. The range of outcomes is different of course. During a very strong bull market, the market will outpace BXM. And BXM will outpace the market during Bear markets or "side-ways" markets. Assuming volatility is constant.
Walkure wrote: Tue Oct 13, 2020 11:35 pm Consequently, if instead of buying SPY and writing index calls, you went to a Wealthfront-type broker that offers a direct indexing service, you could buy every idiosyncratic stock and sell individual calls for each constituent of the index. In the aggregate, this would give you the exact same market exposure, but would not the calls generate significantly more premium due to the appeal they hold to prospective counterparties from their greater volatility?
The calls should produce a much, much higher premium here, yes. Which makes sense since the equity sleeve is now far worse (since every stock has a short call associated with it, instead of the aggregate). The stock side of a portfolio of SPY and short call (say 10% OTM) can reach 10% returns. But if you instead sell 10% OTM calls on every stock, you'd only reach a 10% gain on the stock side if every stock achieved a 10% return. So the additional call premia compensates for this.
Walkure wrote: Tue Oct 13, 2020 11:35 pm Put another way, over any given length of options contract, the index may or may not exceed its historic average return. Over that same time period, we can be certain that a select few equities in the index will generate astronomical returns (causing the calls to be exercised). But we can also be certain that a far greater number of equities in the index will not even beat T-Bills over the duration of the contract. Yet because no one knows, ex ante, which equities will outperform and which will lag, the individual calls (if sold roughly at the money with sufficient time value) will be priced so that the premium one collects would be roughly equivalent to the expected future return of the market on average. By trading regular premium on all your holdings for astronomical returns on a few star performers, could one theoretically match the market return with a lower standard deviation?
I don't think I understood anything from this paragraph. I don't know how you can be "certain" that a few equities will generate "astronomical returns". Nor what that even means. Not sure how you're certain even more stocks won't even beat T-Bills. To be frank, I just don't follow your question.
Walkure wrote: Wed Oct 14, 2020 4:44 pm I'll try restating this from an arbitrage point of view. My contention is equivalent to saying that you could sell naked calls on every constituent of the SP500, at their relative weights in the index, deep in the money, use a portion of the premium to buy a call on the entire index, also deep in the money, and still have profit left over, risk free. This should be impossible, but if so, how does the Buy-Write lag so consistently?
That's nowhere near risk-free nor an arbitrage. One instance is if some of the constituents drop severely in price (say to zero) while others rise severely in price, symmetrical to one another. The index would be unaffected (so the long call isn't making money), but the profits/losses of the naked calls don't cancel each other out because call options don't have a symmetric return. Specifically, the short calls on the rising constituents have have linear losses with stock price rise, while the short calls on the losing constituents have a capped maximum return (the strike price).

The above risk is lower the lower the strike price but then again, I'm willing to bet the "pocketed profit" also drops as the strike price is lowered. So as strike price approaches $0, the strategy approaches an arbitrage like you mention but the profits of the arbitrage approach zero as well.
Walkure wrote: Wed Oct 14, 2020 4:44 pm This should be impossible, but if so, how does the Buy-Write lag so consistently?
Probably because it was a bull market and a Buy-Write strategy always has lower beta than just the stocks themselves. Also, the VIX remains elevated, so there's some in-sample bias. But not much.
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Topic Author
Walkure
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Re: Direct indexing and implied volatility

Post by Walkure »

Steve Reading wrote: Wed Oct 14, 2020 5:42 pm
Thanks for the very clear explanations. I think you've exposed where my thinking was off; it seems like the phenomenon boils down to three simple things: 1. the different risk profile in the equity sleeve, 2. the asymmetry of the individual options payoffs, and 3. the general bull market of late outpacing a low-beta strategy.
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Uncorrelated
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Re: Direct indexing and implied volatility

Post by Uncorrelated »

It's important to realize that options are not priced in a risk neutral world. If you insure yourself against a catastrophic loss, the insurance will cost more than than average loss if the even happens multiplied by the probability the event happens. This happens because other market participants are only willing to sell that insurance to you for a healthy premium. After all, who would like to increase their exposure to catastrophic losses?

You can exploit this by purchasing insurance to events that you think are scary, and sell insurance to events you think are not scary. If you do this correctly (= your risk preferences are different from the market), you can indeed match the index expected return at "lower risk".
JackoC
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Re: Direct indexing and implied volatility

Post by JackoC »

Walkure wrote: Tue Oct 13, 2020 11:35 pm Here's my headscratcher of the day: The CBOE Buy-Write Index, which simulates holding equities and then writing covered calls on the index, has generally trailed the SP500 over its history.
https://www.google.com/finance/quote/BX ... XSP%3A.INX
But isn't this just a flaw in using index options? The value (premium gained from sale) of a given option increases with the implied volatility of the underlying security. But the whole point of an index is to eliminate idiosyncratic volatility, which, across the entire market, averages out to zero+beta.
Holding the SP and writing at-the-money calls has significantly less risk (measured as std dev of return) than just holding the S&P. So I'd first challenge the apparent premise before getting into anything about individual stock v index options: why would you expect BuyWrite to have as high a return as the S&P itself?

The anomaly wrt BuyWrite is not that it has trailed the S&P, but that it has noticeably trailed PutWrite, where you just write monthly at-the-money puts on the S&P. Since S&P index options have european style exercise, those two strategies are theoretically identical. The first article explores why PutWrite has had higher return than BuyWrite, technicality of settlement at expiry where BuyWrite essentially just holds the S&P for a few hours on option expiry dates whereas PutWrite has no position at all for the same few hours. The second paper summarizes the results of PutWrite v S&P from inception in 1980's to end of 2018. PutWrite had CAGR 9.54% v S&P 9.80% but PutWrite's std dev of return was only 9.95% v S&P's 14.93%, so significantly higher Sharpe Ratio. The Sharpe Ratio's should be the same in a simple and efficient mean-variance world, not the returns.

PutWrite v BuyWrite
https://www.aqr.com/Insights/Research/W ... s-Here-Too
PutWrite v S&P 500 through end of 2018, see Exhibits 4 and 5
https://www.cboe.com/micro/buywrite/bon ... w-2019.pdf
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firebirdparts
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Re: Direct indexing and implied volatility

Post by firebirdparts »

This just makes me wonder what the ideal buy write strategy is. The index to me seems like something you wouldn’t choose to do. I might do 2% OTM. I might do putwrite ATM. I Guess I am an incurable optimist. Cboe now has a “30 delta” index too.

I have not tried to get historical option prices. I’m not sure how easy it would be to study that. I did find a short paper At neuberger berman comparing some of these indices by googling bxm vs bxy.
A fool and your money are soon partners
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