Implied Volatility Is a Forecast. Realised Volatility Is the Receipt.

Two Different Measurements

Realized Volatility It's arithmetic. Take the daily returns of an asset over a period calculate the standard deviation and annualize it. The answer describes what has already happened and is not up for debate

implied volatility It's the other way around. Take the price at which an option is trading and work backwards through the pricing model for the volatility factor that would produce that price. The answer describes what the market is charging for future movements

One looks back and it's a fact. The other looks forward and it's an opinion with money attached

Everything interesting about volatility trading comes from the fact that these two numbers are quoted in the same units are printed on the same screen and measure completely different things

The Persistent Gap

Across all stock indices and over long-term horizons implied volatility has averaged above subsequent realized volatility. Historically the market has expected more movement than it received

This is not a market error waiting to be corrected. It is a risk premium. Options sellers offer insurance and insurance is sold above the expected losses otherwise no one would write it. The buyer pays for the certainty of protection and that certainty has a price

A Worked Example: Pricing a Month of Movement

Volatility numbers remain abstract until you convert them into money so here's the conversion into a stock priced at $100 with a one-month duration

Step one: convert the annual volatility into a daily movement. Volatility increases with the square root of time so divide the yearly figure by the square root of the number of trading days in a year which is the square root of 252 or about 15.87. With 20 percent implied the expected daily movement is 20 divided by 15.87 which is about 1.26 percent. The 15 percent realized it is 0.95 percent. Those twoNumbers look close on a screen and are not close at all together

Step two set the price of the straddle. There is a standard approximation for an at-the-money option that is accurate enough for this purpose: the straddle option costs about 0.8 times the spot price multiplied by the volatility and multiplied by the square root of time in years. A month is one-twelfth of a year and the square root of one-twelfth is 0.289

So 20 percent implies: 0.8 times 100 times 0.20 times 0.289 which is approximately $4.62

Step three: assess what really happened. A trader who sells that option and continually hedges the delta ends up paying when rebalancing costs roughly what the same formula gives with realized volatility. If the stock actually moves at 15 percent annualized: 0.8 x 100 x 0.15 x 0.289 which is equivalent to about $3.46

Step four the benefit. Collect 4.62 pay 3.46 and keep about $1.16. With a premium of 4.62 this represents a return of approximately 25 percent of the position in one month with a difference of five points between the forecast and the result

That's why trading attracts capital. Now run the same arithmetic in the direction that no one puts on the presentation deck

Look at the shape of that column. Realized volatility can only drop to zero so the best possible month returns 100 percent of the premium. There is no upside limit so a single month at 80 percent of proceeds costs three times all of proceeds

Volatility ranging from 20 to 80 is not hypothetical. Indices volatility has done considerably worse than that in a matter of days more than once. These are rounded illustrative figures that use an approximation rather than a full pricing model but the asymmetry they show is not an artifact of rounding. It is the structure of the trade

How the Trade Works

A trader who thinks the implied volatility is too high sells options and hedges the delta continuously eliminating directional exposure. What is left is a bet that the actual move will be less than the price paid for it

If the stock moves less than implied rebalancing costs less than the premium charged and the position makes a profit. If it moves more hedging losses exceed the premium. Trading is a pure comparison of the forecast with the result

The contrarian position exists for anyone who thinks the market is too complacent. Buy options hedge the delta and take profits if the move made exceeds what you paid. That side bleeds slowly and wins rarely and violently which is a psychologically miserable way to make a living and a reason fewer people do it

Why the Forecast Runs High

Several forces push what was implied above. The demand for protection is structurally one-sided because institutions hedge portfolios and rarely sell insurance on them. Losses hurt more than equivalent gains help so buyers accept unfavorable prices. And the memory of past declines lingers in prices longer than in data

There is also a real danger regarding price. The insurance seller faces losses much greater than the premium charged. Charging above the average expected loss is compensation that way not greed

Let's add one more force that is less frequently mentioned: the seller needs capital to survive the bad month and capital has a cost. Part of the premium is rent on a balance sheet large enough to be there afterward

Reading the Relationship

Comparison itself is a market signal. Implied far above actual means that the market is nervous about how things are actually trading. Implied close to or underperformed means complacency or that a period of genuine turbulence has begun and expectations have not caught up

Case Study: The Week the Short Volatility Trade Died

The clearest demonstration of the table above occurred on February 5 2018 and it is worth going through because everything in this article was visible in a single afternoon

During 2017 stock markets were unusually quiet. Observed volatility was near record lows implied volatility remained above it as usual and anyone who systematically shorted the gap raised month after month. The most popular retail vehicle for that trade was an exchange-traded note called XIV which offered the inverse of short-term VIX futures. In 2017 it roughly doubled.to obtain what everyone described as a reliable risk premium

On February 5 the VIX index nearly doubled in a single session the largest daily move in its history. The mechanics that madehours approximately $1.9 billion in value disappeared

He was not alone. The LJM Preservation and Growth Fund a mutual fund whose name now seems like satire ran a short volatility strategy lost the vast majority of its value in the same episode and went out of business

Two things about that week matter more than the size of the losses. The first is that the strategy didn't fail. It did precisely what the results table above says it does when realized volatility explodes beyond what was implied. Nothing broke. The insurance company simply paid a claim

The second is that the underlying event was small. There was no bank failure no sovereign default and no war. A reasonably ordinary pullback in stocks was enough to erase four years of accumulated premium because leverage and position convexity did the rest. If that's what an ordinary pullback costs the right question is not how much the strategy earns in a normal year but how much it survives in an abnormal one

Twenty years earlier Long Term Capital Management had learned a structurally identical lesson on a much larger scale having been described in its heyday as the central bank of volatility. The instruments change. The form does not

Where the Strategy Fails

Volatility selling makes profits in most months and loses in rare ones. The distribution of results is many small wins versus occasional large losses which is a way that favors short histories and disguises real exposure

A strategy that produced consistent returns for four years can deliver them all in one week. That's not the strategy that breaks. That's the strategy that does exactly what an insurance company does when the claim finally comes in and is why the premium exists

The measurement problem makes this worse. Standard return statistics assume approximately symmetrical returns and short-volatility returns are the opposite of symmetrical. A Sharpe ratio calculated on a smooth three-year sample will appear extraordinary and will describe the premium collected while carefully omitting the liability incurred. It's not a lie. It's a statistic that answers a question no one asked

The Case Against Calling It a Risk Premium

I have argued that the gap is compensation rather than poor pricing. That view is well supported and not the only defensible one so we present the arguments against it here

The first objection is crowding. If the premium is genuinely reliable capital flows into it and the flooding itself compresses the spread until the compensation no longer covers the risk assumed. The premium and the crowd cannot be at the same time stable. Something that pays you to accept tail risk while everyone else also accepts tail risk is paying you less than the label suggests

The second objection is measurement. The comparison people usually cite is thirty-day implied volatility versus realized volatility which is a look back at a forecast in different windows. If we line them up properly forecast them based on the observed volatility of the corresponding future period and the gap narrows. It doesn't go away but a significant portion of the famous spread is an artifact of comparing two wrong numbers

The third objection is concentration. Long-term averages hide the fact that the premium is not distributed evenly over time. A large part of the total accumulates in the months immediately after a shock when implied volatility remains high and observed volatility has already calmed down. If you sell volatility indiscriminately in all regimes you will get a much smaller premium than the general average although with the same tail

The fourth is survival and the XIV is the test. Exploiting strategies and funds leave the data set. Studies based on surviving vehicles measure the premium earned by those who did not die

My own position after weighing this up is that the premium is real but smaller and more conditional than the standard version suggests. This is a genuinely controversial view among people who do this professionally and I hold it with due humility

How I Actually Look at Volatility

I do not trade options and I want to be clear before describing a process. What follows is how I read the relationship as an analyst trying to understand what is troubling a market

I start by converting the implied volatility into a daily move using the division by 15.87 from the worked example. A VIX of 20 means the market expects the index to move about 1.26 percent per day

Second I look at the term structure rather than a single number. One-month versus six-month implied volatility indicates whether the market is worried about a specific dated event or the general state of the world. Those are different concerns and are resolved differently

Third I treat implied volatility as a sentiment instrument rather than a forecast. It has been a mediocre predictor of realized movement and a very good description of current anxiety. Used the first way it disappoints. Used the second way it is one of the clearest reads available because unlike a survey it is what people paid and not what they said

Fourth whenever I see a strategy that advertises consistent returns with a high Sharpe ratio and a short track record I ask what the short is. Often the honest answer is volatility which goes by a different name. The 2018 episode is my constant reminder that the smoothest stream of returns in a portfolio is usually the one that hasn't yet been asked to pay a claim

That's all what I think not advice on what someone should do with the money

The Bottom Line

Implied volatility is what the market charges for future movements. Observed volatility is the movement that actually occurred. The long-term gap between them is real and is a payment for taking on tail risk

Arithmetic sets the terms honestly. Sell a one-month straddle at 20 percent implied by a $100 stock and you'll get about $4.62. If the realization is 15 percent you're left with about a quarter. If the realization is 60 percent you owe double everything you cashed in and the upside is limited to the premium while the downside is not limited at all

February 2018 is what that column looks like when it rolls around. A quiet year a doubling of the VIX in one session a 96 percent loss in the most popular vehicle for trading and a fund with the word Preservation in its name that closed shortly after

Collecting the premium is a legitimate strategy as long as you never confuse a quiet stretch with the absence of what you are paid to absorb