Via Artemis Capital [13], “Volatility of an Impossible Object: Risk, Fear, and Safety in Games of Perception” by Christopher Cole [13]
Why owning a UST bond is mathematically as risky as shorting an equity put option...
We all know shorting volatility is dangerous. We learned our lessons from the financial crisis. We all meticulously read “The Black Swan” and then watched the scary movie adaption of the book starring Natalie Portman. We all know that this method produces a steady stream of smooth returns making people think you are a genius until the inevitable disaster forces you to pawn off your Nobel Prize. We all know that shorting volatility will cause you to go insane with a twisted psycho-sexual obsession to master the art of ballet. It’s picking up pennies in front of a convexity steamroller. Don’t do it. Ever!! Worst of all... If you ever... ever... short volatility... Nassim Taleb will personally insult you and hurt your feelings.
Knowing these facts I would like to pose a question...
Which is riskier right now?
Shorting a collateralized far out-of-the-money S&P 500 index put or buying a “risk-free” US treasury bond? In the “bull market for fear” and “bubble in safety” the paradox is that these two vastly different investments have shockingly similar risk to return profiles (albeit to different risk factors). This goes against everything you have ever been taught in business school or on a CFA exam. In fact I will attempt to make a semi-compelling argument that the collateralized far-OTM put sale offers… gasp… a better risk to return profile than a long-dated UST. For the record I don’t recommend either.
First off measuring the risk to reward of a volatility short position is often a complex endeavor involving greeks like gammas, vegas, volgas, and vanna whites.
Let’s just simplify that entire process and “pretend” a put option is an alternative form of a bond. As an investor in this hypothetical “volatility bond” you receive an annualized “volatility yield” represented by the premium of the option divided by the capital commitment required to fund the obligation.
In return for this yield you assume the risk of “default”, essentially meaning an obligation to buy the S&P 500 index at a pre-defined discount to current market value (say -25% or -50%). Now you will collateralize that option by setting aside the dollar amount of monies over the specified term needed to cover that purchase commitment. That collateral is equivalent to the “face value” of the bond and the “yield” is the option premium divided by that collateral and annualized. If the default event is a $100 stock falling to the -50% strike price in one year you would set aside $50 for the term of the commitment to cover mark-to-mark losses on the short option position. If you receive $2.5 in premium for selling the put option your yield is 5% (against a face value of $50).
We looked at several different types of hypothetical “volatility bonds”. The first requires you to purchase the S&P 500 Index at a -25% discount to the current price for the duration of a year. The second obligates you to buy the S&P 500 index near the March 6, 2009 lows (650 strike price or -55% lower) for the duration of a year. We also obtained bank pricing on a 10-year over-the-counter put option at the 2009 low of 666. We can then compare these “volatility yields” to traditional fixed income yields. No complex greeks required.
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[14]
For the first time in history the volatility bond yield is consistently competitive with the yield on a wide variety of traditional fixed income investments (see above).What does it say when the market will compensate you more in annualized yield for the obligation to buy the S&P 500 index at the 2009 devil’s bottom of 666 (1.90% annualized yield for 10-year OTC put) than it will to own a government bond (1.87% yield for 10-year UST) of equivalent maturity? Consider that the 1-year volatility bond with a -25% SPX purchase commitment currently yields 2.69% annually or 82 basis point over the 10-year UST (chart below).
[15]
In periods of equity market duress the spread can go much higher hitting 454 basis points over the 10yr UST this past May. I know what you are thinking... what about the risks?
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[16]
The volatility bond and the UST bond have opposite risks factors as the first is exposed to deflation (stocks crashing) and the second inflation (higher interest rates). For the purposes of this analysis we assume a neutral macro-economic view. As a baseline for comparison our stress test uses historical bond and equity prices over multiple decades to match the equivalent probability of each stress event. It may feel as if a 325 basis point increase in rates is extraordinary but it is easy to forget that the historical probability of that occurring is much greater (13%) than that of a 2008 style crash in equities (2%). Of course this is backward looking. Ultimately the true future probability estimate is always left to the best judgment of the investor.
Mark-to-Market Risk: Fair comparison of risk includes analysis of potential unrealized losses for both investments when exposed to adverse market conditions as modeled by the stress tests above. The volatility bond will experience a mark-to-market loss if stocks decline and vol rises, however if the short put option remains out-of-the-money by maturity those losses will not be realized and the investor will keep the full premium. In a similar manner the UST bond will have negative price swings if rates increase but could still make all payments on time. The investor holding either instrument to maturity may be none the wiser if he received his principal back in full and never looked at mark-to-market prices (a retired broker once told me this was how client reporting of fixed income worked at his firm back in the rising rate environment of the 1970s). Important to note that both positions have convex return profiles and prices will not change linearly given shifts in volatility or rates.
Default Risk: I think it is funny when academics claim that the US government will never default because it can just print money to pay off its debt obligations. That is the logical equivalent of saying my house will never be burglarized because if someone tried to break in I could just light it on fire. For the UST bond inflation and currency devaluation are alternative forms of default. For the volatility bond the definition of default is not as complex. If the short put ended in-the-money at maturity the investor would be obligated to own the discounted SPX at the higher strike rate resulting in a loss on posted collateral. This “default” scenario may not be a bad thing if the investor doesn’t mind owning stocks at a -50% or -25% discount from today but it still counts for our purposes. Hence the volatility bond has much higher risk here. One unique attribute of the volatility bond is that it is a contractual obligation to ignore behavioral bias and purchase stocks only during periods of deep discounted value.
When the “bull market in fear” meets a “bubble in safety” a collateralized short volatility position and “risk-free’ UST bond have shockingly similar risk-to-reward payoffs. Of course you would rather own the UST bond in deflation or the volatility bond in inflation but we are assuming a risk neutral world. To this effect both investments suffer comparable losses to their worst case scenarios. Without endorsing either investment, when evaluated on a pure risk-to-reward framework the volatility bond (with embedded short optionality) is superior to UST bonds at current prices.
What kind of world do we live in where the risk-return pay-off of short selling equity volatility is equal or better to that of a supposedly “risk-free” government bond? The UST bond market is one of the most liquid markets in the world where investors look to first for preservation of capital during periods of crisis. Now the market for safety has an efficient frontier on par with the penny in front of the steamroller trade?
If you don’t find that scary then you’re not paying attention. It used to be that you would post margin against your tail risk options using risk-free UST bonds. Now those risk-free assets are the source of the tail-risk.
[17]
When risk-free is risky maybe it is time to buy volatility on safety itself (see chart above).