## #111 | Indexed UL in the Mirror – Part 3 – Volatility Skew

#### Executive Summary

All capped account options in Indexed UL products are hedged by buying a call option at the floor and selling a call option at the cap. As it turns out, the implied volatility for those two options can be markedly different, a phenomenon called volatility skew. Using data from a major IUL seller, since 2009 the average implied volatility for the cap option has been just 84% (and as low as 74%) of the floor option. In other words, capped accounts require buying an expensive option and selling a cheap option – exactly the opposite of what you’d otherwise want. This creates a structural disadvantage for Indexed UL that manifests itself in both the pricing and performance of the product, a point that has been commonly missed in IUL analysis that does not incorporate volatility skew.

Thinking about volatility in terms of VIX is like averaging a complex, ever-changing shape into a single dot. If you want to get a very general feel for how the position and weight of the shape is changing, the dot is all you need. That’s what VIX does for general observers and investors. But don’t confuse the dot with the shape – VIX is not volatility. I’ve seen far too many actuaries and insurance folks use VIX as a proxy for the entire shape of volatility, which is not only dead wrong but, as you’re going to see, dramatically changes how the pricing and performance of Indexed UL looks over time.

The most obvious way that VIX is a mismatch for Indexed UL is in its term structure. VIX reflects the annualized volatility implied over the next month. Indexed UL products credit interest at least annually, which means that the call spreads used to hedge Indexed UL have a term of 1 year or greater. Annualized volatility over one month is not the same thing as annualized volatility over one year. For one thing, one month volatility is more volatile itself than one year volatility, so looking at VIX at any given point in time is not necessarily an indication of one year volatility. We can get a sense for this by looking at VIX6M, which is identical in methodology to VIX except that it uses 6 month options. Since 2008, the standard deviation of VIX has been 30% higher than VIX6M. On any given day, the two have deviated by as much as 50%. The big daily swings in VIX coupled with the fact that life insurers hedging IUL products generally only buy options once a month means that looking at VIX, on any given day, can give you a radically different view of volatility than is actually being priced into options that life insurers are purchasing.

But there’s more to the shape of volatility than just term structure. Options can be purchased at a variety of different strike prices. In theory, the volatility priced into the options at various strike levels should be identical because volatility is a characteristic of the underlying asset, not the option. In other words, the volatility of the price of the asset is what it is, regardless of the structure of the option. And that’s true – but the actual volatility of the price of the asset is not the same thing as volatility as priced into the option, which is called implied volatility. I’ve used the two concepts interchangeably up to this point because I didn’t need to make the distinction, but now it’s essential. The easiest way to understand it is that the real volatility of the asset is a question of fact* because it can only be derived from historical data. Implied volatility, on the other hand, is always forward looking. It reflects the market pricing for the volatility of the option, which will clearly deviate from actual realized volatility**. Implied volatility is the only market-driven input in option pricing because all of the other key inputs to determining the price of an option – spot, strike, term, risk free rate – are non-negotiable. As a result, options practitioners use implied volatility as the price for the option because it allows them to see relative value of all possible options trades on a particular asset at different strikes and terms through the same lens of implied volatility. The degree to which implied volatility varies by strike price is referred to as volatility skew.

Volatility skew is a hugely important concept for understanding Indexed UL. In order to support a capped account option, a life insurer buys a call option equal to the floor crediting rate, which is usually 0% and therefore the option is at-the-money (strike = spot). The life insurer then *sells* a call option at the strike level equal to the stated cap in the product, which is obviously greater than 0%, to offset the cost of the at-the-money option. This reduces the price of the total package to equal the option budget. However, thinking in terms of options pricing, the two trades that constitute a call spread (at-the-money and out-of-the-money) will have different implied volatilities because they have different strikes. The relative advantage of the trade, therefore, is necessarily dependent on the implied volatility pricing for each leg. A capped indexed account option is basically a volatility skew trade. So how do we know if this is a good deal for Indexed UL buyers or not?

Fortunately, a few life insurance companies trade each leg of the call spread (as opposed to buying a single packaged call spread) individually and record each leg in their statutory filing. This makes for easy analysis, since we already know all of the other inputs to the option pricing formula and can solve for implied volatility. I picked a life insurer that documents both trades and has been hedging their Indexed UL product since 2009. Take a look at the data on the average implied volatility for both the ATM and OTM legs of the trade and the average OTM/ATM volatility ratio in each of the years specified below. For 2009 and 2018, only 3 months of data were available.

2009 | 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | |

ATM Vol | 20.7% | 20.0% | 19.8% | 16.7% | 13.2% | 12.9% | 14.1% | 13.7% | 11.3% | 13.4% |

OTM Vol | 18.4% | 17.3% | 17.0% | 14.2% | 11.6% | 10.9% | 11.2% | 11.1% | 9.0% | 10.4% |

OTM/ATM | 88.8% | 86.4% | 85.4% | 85.6% | 88.1% | 84.4% | 79.9% | 81.0% | 79.8% | 78.1% |

In its most basic form, this data is showing you that Indexed UL products are constructed using a call spread that buys an expensive option and sells a cheap one. Or, in other words, exactly the opposite of what you’d otherwise want the life insurance company to do. It is a bad volatility trade. If you were playing your cards right, you’d want to sell the expensive one and buy the cheap one…which is exactly what the investment bank is doing when they sell packaged call spreads to life insurers. Little wonder, then, why the CBOE has built a whole suite of indices designed to show the attractiveness of *selling* options and, in particular, selling call and put spreads that take advantage of volatility skew. Those indices are promoted as ways to reduce volatility and enhance the returns of the underlying equity index – in other words, that systematically selling options is profitable and advantageous***. Why? Because of being on the right side of a volatility trade. What does Indexed UL do? It puts customers on the wrong side of a volatility trade.

Not only is it a bad volatility trade, but it also happens to be a big volatility trade, at least in terms of what it does to price of the call spreads. You can see above that the ratio of OTM volatility to ATM volatility has floated from an average of almost 89% in 2009 all the way down to 78% in 2018. Individual trade observations have ranged from 89% (9/15/2009) to 75% (11/15/2017, 2/15/2018). To see the impact of skew on call spread pricing, let’s hold all of the other pricing parameters constant and just change the skew of the volatility between ATM and OTM pricing. Take a look at the price of a 12% option or, from the other angle, the affordable level of the cap holding the budget constant as the volatility skew changes.

Risk Free
Rate |
ATM Vol |
OTM Vol |
OTM/ATM Ratio | Cap | Call Spread Cost | Cap with 4.16% Budget |

1.00% | 15.00% | 15.00% | 100% | 12% | 4.16% | 12.00% |

1.00% | 15.00% | 14.25% | 95% | 12% | 4.41% | 11.00% |

1.00% | 15.00% | 13.50% | 90% | 12% | 4.65% | 9.75% |

1.00% | 15.00% | 12.75% | 85% | 12% | 4.88% | 8.75% |

1.00% | 15.00% | 12.00% | 80% | 12% | 5.10% | 7.75% |

1.00% | 15.00% | 11.25% | 75% | 12% | 5.31% | 6.80% |

Compared to the impact of changing LIBOR and general volatility levels, volatility skew is a significantly larger piece of the puzzle. In a lot of ways, it’s actually the dominant driver of the price of the option in that a relatively slight change in the OTM/ATM volatility ratio can wipe out benefits derived from lower LIBOR or overall lower volatility levels. And, to make things more confusing, volatility skew isn’t highly correlated to overall volatility levels or interest rates. Note that the ratio hit 88.7% twice – once at 20.99% ATM volatility and another time at 13.14% ATM volatility. And at roughly that same 13% volatility level, the 2018 trade posted a ratio of just 79%. When both ATM volatility and LIBOR were extremely low in 2014, the ratio was 83%, just a smidge higher than in 2017, when ATM volatility was low and LIBOR was more than twice as high as in 2014. In other words, volatility skew is a phenomenon unto itself.

It also happens to be an extremely well established and well documented phenomenon. CBOE actually publishes an index on volatility skew, there are numerous academic papers on the topic and you can even see examples of skew pricing in annuity products with indexed-linked accounts that have prospectuses. If you want to see skew for yourself, go to the SPY option chain, grab a term and run it through a Black-Scholes calculator. At this exact moment, with SPY at 275.5 and LIBOR at 2.77%, a 6/21/19 option with a 275 strike has an implied volatility of 12.6%. The 6/21/19 option with a 300 strike has an implied volatility of just 10.25%, or 81% of the ATM volatility. Vol skew is real, y’all.

But what does it mean for Indexed UL? The implications are profound and pervasive. First, and foremost, it means that capped account options are the wrong side of a volatility trade. If you’re looking for proof positive that Indexed UL has “structural” advantage, then you’re really going to hate vol skew because it proves that Indexed UL actually has a structural *disadvantage*. If vol skew didn’t exist, Indexed UL would perform better than it actually does. Ironically enough, I saw more than one actuary during the AG49 debate do back-testing on IUL structures and calculate theoretical historical caps using *only at-the-money volatility for both legs of the trade. *Little wonder that Indexed UL showed strong performance in the analysis.

Second, as mentioned earlier, volatility skew is not a natural phenomenon. It’s a market phenomenon. That makes it both unpredictable and unexplainable, at least without getting into some pretty esoteric conversations about options pricing theory and market pricing for extreme outcomes. And yet, it’s a major part of the Indexed UL story as it relates to what “fair market” is for a cap that will impact these products over the long run. Good luck explaining that to clients.

Third, and perhaps most interesting, volatility skew points to the idea that uncapped account options are actually better for consumers than capped account options. Uncapped options, whether as a participation rate on index gains or as a “threshold” or “spread” on index gains, only trade one leg of the option, so there is no volatility skew at work****. Curiously enough, though, the data about long-term profits from uncapped account strategies is quite a bit different than capped account strategies. When Indexed UL proponents trot out data to show the sustainability of long-term option profits in excess of 50%, they invariably show capped account options – and for good reason. Capped accounts are more popular than uncapped accounts. However, as we’ve seen, profitability in capped account options using historical data or attempted historical recreations is extremely sensitive to the level of volatility skew. And, as you might guess, there’s virtually no data for historical vol skew. As a result, there have been no attempts to credibly recreate real historical performance in capped accounts because it can’t be done.

Instead, academics like Roger Ibbotson and others have used uncapped options because the historical data for at-the-money volatility is better. And what does that data show? Well, in Ibbotson’s case, that an FIA product employing an uncapped strategy would have historically performed just a smidge better than Treasuries. This has been backed up by other analysis that I saw during the AG49 debate that pointed to 10% long-term profits in at-the-money call options*****. And, for what it’s worth, I built a historical backtest model as well that shows 50% option profits if I assume no volatility skew for capped accounts, 10% option profits with average volatility skew and 10% option profits for uncapped accounts. In other words, the idea of 50% option profits in Indexed UL hinges on analysis from capped account options, which itself hinges on volatility skew. So if you want to believe in 50% option profits in Indexed UL, you’d better have an extremely good explanation for why the account option that does the wrong side of the volatility trade (the capped account) performs better than the account option that doesn’t (the uncapped account).

So, how does all of this relate to the idea of an epoch changing? Volatility skew is not well understood because, until recently, it hasn’t really had to be. But the fact that vol skew has been increasing over the last few years will force the issue. Caps will do things that don’t “make sense” based on overall movements of VIX and LIBOR because volatility skew is at work. But, more importantly, the epoch of ignoring volatility skew as a part of the discussion about the long-term viability of Indexed UL is also coming to an end. Once you put volatility skew into the analysis, suddenly capped accounts look like uncapped accounts – which is to say, they don’t show 50% option profits. And without 50% illustrated option profits, the Indexed UL epoch would most certainly change, if not end entirely.

Which brings us, finally, to the future prospects of Indexed UL as a product category.

**This is oversimplified. It is easy to define realized volatility over a specific period of time, but it is not easy to define the realized volatility characteristics of an asset because you’re never really sure if have enough data to know. Extreme outcomes are just that – extreme. They only come around every now and then. Just because one of them isn’t in the data doesn’t mean it can’t and won’t happen. Hence, realized volatility isn’t quite so simple and implied volatility reflects that uncertainty.*

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***Implied volatility deviates from realized volatility in two ways. Obviously the two will deviate over any particular date period because the market expectation of volatility isn’t a perfect predictor of realized volatility. And, actually, depending on who you ask, it can be either a great or terrible predictor (again, this raises the question of time periods and the definition of realized volatility). More importantly, though, implied volatility systematically prices higher than realized volatility. This is well documented and bulletproof phenomenon. It is partially the result of the fact that option sellers have uncertainty in pricing the option and executing the hedges and want to be compensated for taking risk. It is also the result of the fact that sellers want to earn a fee for making a market.*

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****This should not be a surprise based on the footnote above. The cleanest way to see the advantages of selling options is through the CBOE BXM, the BuyWrite Index. The strategy is simple – buy the S&P 500, write at-the-money call options, settle up monthly. Every month, in other words, is a test of whether the call option expires with a gain or not. To the extent that the BXM equals the S&P 500, it’s an indication that the call option prices have accurately captured the gains in the S&P 500. In other words, that there was no systematic profits in buying or selling options. For a long time the BXM outperformed the S&P 500, which means that selling options was more advantageous than holding the S&P 500, but in the last 5 years the S&P 500 has outperformed the BXM for all of the reasons outlined previously in this article. The BXM is yet another example of the fact that the price of options do actually reflect the risk profile of the underlying asset.*

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*****Actually, you have vol skew working in your favor with spread account options because the trade is based on a single OTM call option which has a lower volatility than the single ATM call option used for a participation rate account option.*

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******You might be wondering why buying one year options show 10% profits, roughly, when something like the BXM shows that selling options is (generally) profitable. The difference goes back to the term structure of volatility. Short term implied volatility is significantly more volatile than long term volatility. In other words, market pricing for short term volatility adjusts much faster than long term volatility. Long term volatility, on the other hand, is much slower to adjust and is harder to price because it looks further out. Uncertainty about volatility increases the risk for the option seller and, as a result, average long term implied volatility is higher than short term volatility. For example, right now, one month at-the-money options on the SPY are trading at about 11% implied vol whereas 6 month options are trading at about 12.5%. But that hasn’t been enough to counteract the fact that equity markets have been on a tear for the last 9 years and, as a result, buying long-term equity call options has been a rather profitable endeavor…for now. Those profits are an indication of volatility pricing, as evidenced by the BXM, not structural profits.*