Options Nitpick: You can’t use equity index* option prices as true probabilities because adding hedges to a portfolio makes the whole portfolio more valuable. People then buy options based on their value when added to the portfolio, not as individual investments.
The first reason option hedges make your portfolio more valuable is preferences: people don’t just want to maximize their expected return, but also reduce the chance they go broke. People don’t like risk and hedges reduce risk, ergo they pay more to get rid of risk. However you can’t just subtract X vols to adjust as this “risk premia” isn’t constant over time.
Secondly hedges maximize long term returns (or why you shouldn’t sell options)
You want to maximize your average geometric annual return not average annual return. You care about geometric averages because if for 3 years your returns were +75%, +75%, −100%, your don’t have 50% more money then when you started but 0. The average of annual returns was 10.7% over the past 30 years, but if you’d invested in 1992 you’d’ve only compounded at 8.5% year till 2022.
Geometric returns are the the nth root of a product of n numbers and have the approximation = Average Annual Return - (variance/2). If you could reduce variance and not reduce Annual returns, your portfolio (market + hedges) would grow faster than the market.
These reasons are why despite the worst Annual return being −48% in 1931, you say there’s a 5% chance of > −50% returns based on option markets.
*I’m specifically talking index options because that’s the portfolio investors have (or something similar) and the total is what they care about. If you were to use prices as true probabilities for say a merger going through these reasons don’t apply as much and would be more accurate.
PS. I’ve referred to investors as all having the same portfolio because most people do have highly correlated index holdings and it’s at this level of generality you can think about investors as a class.
I absolutely considered writing about the difference between risk-neutral probabilities and real-world probabilities in this context but decided against because: Over the course of a year, the difference is going to be small relative to the width of the forecast
I’d be interested to hear if you think the differences would be material to my point. ie that [-60%, +30%] isn’t a ~90% range that stocks return next year and that his forecast is not materially different to what the market is forecasting.
The 2000-2021 VIX has averaged 19.7, sp500 annualized vol 18.1.
From a 2ndary source: “The mean of the realistic volatility risk premium since 2000 has been 11% of implied volatility, with a standard deviation of roughly 15%-points” from https://www.sr-sv.com/realistic-volatility-risk-premia/ . So 1/3 of the time the premia is outside [-4%,26%], which swamps a lot of vix info about true expect vol.
-60% would the worst draw down ever, the prior should be <<1%. However, 8 years have been above 30% since 1928 (9%), seems you’re using a non-symetric CI.
The reasoning for why there’d be such a drawdown is backwards in OP: because real rates are so low the returns for owning stocks has declined accordingly. If you expect 0% rates and no growth stocks are priced reasonably, yielding 4%/year more than bonds. Thinking in the level of rates not changes to rates makes more sense, since investments are based on current projected rates. A discounted cash flow analysis works regardless of how rates change year to year. Currently the 30yr is trading at 2.11% so real rates around the 0 bound is the consensus view.
The 2000-2021 VIX has averaged 19.7, sp500 annualized vol 18.1.
I think you’re trying to say something here like 18.1 ⇐ 19.7, therefore VIX (and by extension) options are expensive. This is an error. I explain more in detail here, but in short you’re comparing expected variance and expected volatility which aren’t the same thing.
From a 2ndary source: “The mean of the realistic volatility risk premium since 2000 has been 11% of implied volatility, with a standard deviation of roughly 15%-points” from https://www.sr-sv.com/realistic-volatility-risk-premia/ . So 1/3 of the time the premia is outside [-4%,26%], which swamps a lot of vix info about true expect vol.
I’m not going to look too closely at that, but anything which tries to say the VRP was solidly positive post 2015 just doesn’t gel with my understanding of that market. (For example). (Also, fwiw anyone who quotes changes in volatility in percentages should be treated with suspicion at best)
-60% would the worst draw down ever, the prior should be <<1%. However, 8 years have been above 30% since 1928 (9%), seems you’re using a non-symetric CI.
Yeah, it’s not symmetric, but I wasn’t the person who suggested it. All I’m saying is “OP says [interval] has probability 90%” “market says [interval] has probability 90%”.
The reasoning for why there’d be such a drawdown is backwards in OP: because real rates are so low the returns for owning stocks has declined accordingly. If you expect 0% rates and no growth stocks are priced reasonably, yielding 4%/year more than bonds. Thinking in the level of rates not changes to rates makes more sense, since investments are based on current projected rates. A discounted cash flow analysis works regardless of how rates change year to year. Currently the 30yr is trading at 2.11% so real rates around the 0 bound is the consensus view.
OP being my post of arunto’s?
There’s several things unclear with this paragraph though:
Stocks are currently ‘yielding’ 1.3% (dividend yield) or 3.9% (‘earnings’ yield). Not sure exactly what yield you think is 4% over bonds. (Or which maturity bond you’re considering).
“Thinking in the level of rates not changes to rates makes more sense, since investments are based on current projected rates.”. The forward curve is upward sloping, yes, but if arunto thinks rates are going to change higher than what the market forecasts that will definitely change the price of equities. “A discounted cash flow analysis works regardless of how rates change year to year.” Yes, but if you change the rates in your DCF you will change your price
“Currently the 30yr is trading at 2.11% so real rates around the 0 bound is the consensus view.”. Currently 30y real rates are −15bps after a steep sell-off after the start of the year. 30y real rates were as low as −60bps in December.
10y real rates are more like −75bps (up from −110bps in December).
“the 0 bound” is something people talk about in nominal space because the yield on cash is somewhere in that ballpark. (These days people generally think that figure should be around −50 to −100bps depending on which euro rates trader you speak to). For real rates there’s no particular reason to think there is any significant bound − 10y real rates in the US have been negative since the start of 2020; in the UK they’ve been negative since the early 2010s.
Options Nitpick: You can’t use equity index* option prices as true probabilities because adding hedges to a portfolio makes the whole portfolio more valuable. People then buy options based on their value when added to the portfolio, not as individual investments.
The first reason option hedges make your portfolio more valuable is preferences: people don’t just want to maximize their expected return, but also reduce the chance they go broke. People don’t like risk and hedges reduce risk, ergo they pay more to get rid of risk. However you can’t just subtract X vols to adjust as this “risk premia” isn’t constant over time.
Secondly hedges maximize long term returns (or why you shouldn’t sell options) You want to maximize your average geometric annual return not average annual return. You care about geometric averages because if for 3 years your returns were +75%, +75%, −100%, your don’t have 50% more money then when you started but 0. The average of annual returns was 10.7% over the past 30 years, but if you’d invested in 1992 you’d’ve only compounded at 8.5% year till 2022.
Geometric returns are the the nth root of a product of n numbers and have the approximation = Average Annual Return - (variance/2). If you could reduce variance and not reduce Annual returns, your portfolio (market + hedges) would grow faster than the market.
These reasons are why despite the worst Annual return being −48% in 1931, you say there’s a 5% chance of > −50% returns based on option markets.
*I’m specifically talking index options because that’s the portfolio investors have (or something similar) and the total is what they care about. If you were to use prices as true probabilities for say a merger going through these reasons don’t apply as much and would be more accurate.
PS. I’ve referred to investors as all having the same portfolio because most people do have highly correlated index holdings and it’s at this level of generality you can think about investors as a class.
I absolutely considered writing about the difference between risk-neutral probabilities and real-world probabilities in this context but decided against because: Over the course of a year, the difference is going to be small relative to the width of the forecast
I’d be interested to hear if you think the differences would be material to my point. ie that [-60%, +30%] isn’t a ~90% range that stocks return next year and that his forecast is not materially different to what the market is forecasting.
The 2000-2021 VIX has averaged 19.7, sp500 annualized vol 18.1.
From a 2ndary source: “The mean of the realistic volatility risk premium since 2000 has been 11% of implied volatility, with a standard deviation of roughly 15%-points” from https://www.sr-sv.com/realistic-volatility-risk-premia/ . So 1/3 of the time the premia is outside [-4%,26%], which swamps a lot of vix info about true expect vol.
-60% would the worst draw down ever, the prior should be <<1%. However, 8 years have been above 30% since 1928 (9%), seems you’re using a non-symetric CI.
The reasoning for why there’d be such a drawdown is backwards in OP: because real rates are so low the returns for owning stocks has declined accordingly. If you expect 0% rates and no growth stocks are priced reasonably, yielding 4%/year more than bonds. Thinking in the level of rates not changes to rates makes more sense, since investments are based on current projected rates. A discounted cash flow analysis works regardless of how rates change year to year. Currently the 30yr is trading at 2.11% so real rates around the 0 bound is the consensus view.
I think you’re trying to say something here like 18.1 ⇐ 19.7, therefore VIX (and by extension) options are expensive. This is an error. I explain more in detail here, but in short you’re comparing expected variance and expected volatility which aren’t the same thing.
I’m not going to look too closely at that, but anything which tries to say the VRP was solidly positive post 2015 just doesn’t gel with my understanding of that market. (For example). (Also, fwiw anyone who quotes changes in volatility in percentages should be treated with suspicion at best)
Yeah, it’s not symmetric, but I wasn’t the person who suggested it. All I’m saying is “OP says [interval] has probability 90%” “market says [interval] has probability 90%”.
OP being my post of arunto’s?
There’s several things unclear with this paragraph though:
Stocks are currently ‘yielding’ 1.3% (dividend yield) or 3.9% (‘earnings’ yield). Not sure exactly what yield you think is 4% over bonds. (Or which maturity bond you’re considering).
“Thinking in the level of rates not changes to rates makes more sense, since investments are based on current projected rates.”. The forward curve is upward sloping, yes, but if arunto thinks rates are going to change higher than what the market forecasts that will definitely change the price of equities. “A discounted cash flow analysis works regardless of how rates change year to year.” Yes, but if you change the rates in your DCF you will change your price
“Currently the 30yr is trading at 2.11% so real rates around the 0 bound is the consensus view.”. Currently 30y real rates are −15bps after a steep sell-off after the start of the year. 30y real rates were as low as −60bps in December.
10y real rates are more like −75bps (up from −110bps in December).
“the 0 bound” is something people talk about in nominal space because the yield on cash is somewhere in that ballpark. (These days people generally think that figure should be around −50 to −100bps depending on which euro rates trader you speak to). For real rates there’s no particular reason to think there is any significant bound − 10y real rates in the US have been negative since the start of 2020; in the UK they’ve been negative since the early 2010s.