The what and why of call writing

A call option gives the owner of the option the right (but on the obligation) to buy something for a fixed price (the strike price) up until the day the option expires.  The option owner usually pays something to enter into the option contract.  The payment is called the premium.

For a call option on a stock to have value at its expiration, the price of the stock would have to be greater than the strike price of the option.  At that point, one could use the option to buy the stock at the strike price and then immediately sell the same stock in the stock market.  Otherwise, the option expires worthless.

Someone takes the opposite of every option trade.  Someone writes the options that other people buy.  Option writing is the opposite of option buying.  The payoffs are opposite, too.

Whereas the call option buyer usually pays a small premium for an unlikely but very high return, the writer of the same option earns a small premium for taking on the risk of an unlikely but very large loss.  What happens to the stock price determines who wins or loses in the deal.

Success in writing options starts with knowing how to price options.  The cost of an option is the probability-weighted expected loss of the option. One needs a good option pricing model to determine the expected loss. Then one must refuse to write options that don’t offer premiums significantly higher than the expected loss (cost) of the option. If the expected loss (cost) of the option is $1.50 per share, perhaps one should refuse to write options with premiums below $1.90 per share.  That way, one enters into the deal with an expected profit.  Whether one achieves an actual profit depends on what happens to the stock price.

Success in writing call options also depends on risk management.  Option writing carries the risk of an occasional but very large loss.  Too much bad luck could be ruinous.  Effective diversification is essential.

What we are reading on 5/30/2017

Here’s what we are reading today. We do not necessarily agree with the opinions expressed therein and we disavow any actual or implied investment advice therein. In no particular order:
Rebalancing, investment process and portfolio construction
The use of monte carlo simulations in performance evaluations
Does momentum reverse over the long term?
Is low volatility a problem?
Inside the world of investor relations officers
Focus on the process, not the score
An emerging markets risk map
Is the culture of investment risk taking shifting?
Are we in a bubble?
Should one own ag commodities or ag stocks?
Mainstreaming Behavioural Economics
Five Secrets For Steadier Workouts 1495278003
Is there a single perfect diet for everyone?
Can A Pessimist Become An Optimist?
Worrying may not be such a bad thing …
Are electric vehicles at an inflection point?
Federal Reserve Well Being Survey Shows American Economic Needs
Are Managed futures Funds A Thing Of The Past?
Momentum seems to have done really well recently
What’s going on in retail?
Paul Singer is worried
Discipline matters
FICO scores just got an (artificial) boost
Hussman’s latest

Revenue, Cost, Profit and Option Writing

We think the best way to understand and to succeed with options is to think of them as insurance, and then think of them through the lense of revenues, costs and profits.

In a typical business (e.g., a retailer or a manufacturer), costs precede revenues. The retailer first spends money on inventory. He knows his costs before he sees the revenue. How does he know his inventory costs before hand? Because the retailer has already spent the money on the inventory.

In the insurance business, revenues precede costs. The insurer collects his revenue up front (the premium). The costs, if any, come later. Using term life insurance as an example, the insurer collects a small amount of money each year. If the customer does not die, the insurer does not have to pay. If the customer dies, the insurer typically must pay an amount that is many multiples greater than the premiums collected.

How does the insurer decide to set the premium when the policy may pay out anything from zero to a very large amount of money? The insurer must calculate the expected cost of the policy and set the premium high enough so that all the expected costs are covered plus a profit. The expected cost is the based on the averages; i.e., if the insurer writes tens of thousands of policies, on average what can the insurer expect to pay out? The premiums in aggregate must cover the expenses in aggregate plus a profit.

We think of options the same way. If a life insurance policy says:

  • the customer pays a premium,
  • the customer gets nothing unless he dies, in which case the policy pays out a lot of money,
  • during the term of the policy.

A put option contract for a stock says,

  • the option holder pays a premium,
  • the option holder gets nothing unless the stock falls too much in price, in which case the option holder can sell at a higher, pre-arranged price,
  • during the term of the policy.

To us, the similarities seem obvious. We can use this insight to improve our thinking about options.

The investor who decides to buy an option should think of himself as the buyer of insurance. The cost of the insurance is the premium he pays.

We think the investor who decides to write options would do well to think of himself as an insurance company. The customer’s cost is the insurer’s revenue. As an insurer, the option writer must think through carefully the expected cost of the option. He should only write options that meet his profit target, which is the excess of the premium over the expected cost of the option.

Inflation monitor as of 5/26/2017

Inflation has been trending downwards for decades.  We think the following factors have created this long-term trend:

  • an aging population that buys less
  • wage competition from third-world countries, due to globalization.

With talk of border taxes and rolling back globalization (at least partially), can we assume that the downward inflation trend will continue from here?  We don’t know, but we intend to track the numbers.  This post reviews a wide range of market-based and statistically derived measures of inflation.

Our takeaway:  the annual rate of inflation is probably 2.0%-3.0%.

Backward-Looking Measures

Consumer Price Index (CPI) – changes

The CPI is calculated by the government.  More than a few investors view the index with a degree of skepticism.

CPI:  +2.21%

Median CPI:  +2.31%

Core CPI:  +1.86%

Sticky CPI:  +2.24%

Trimmed Mean PCE:  +0.83%

Producer Price Index (PPI) – changes

The PPI is calculated by the government.  Some investors regard it with suspicion:

Finished Goods:  +4.11%


Wages are very important because they account for such a large portion of the cost of goods and services.

Average hourly earnings:  +2.59%

An increase in average hourly earnings does not translate into an equal amount of inflation.  Increases in productivity can offset (entirely or partially) the inflationary effect of higher wages.

Billion Prices Project

The billion prices project estimates the annual rate of inflation by using prices posted by online merchants.

As of the last publicly available data point, BPP estimates the U.S. inflation rate at annualized rate of about +0.1%.

Purchasing Manager’s Index

The Institute for Supply Management publishes the results of a monthly survey of their members, including a price diffusion index.  A diffusion index doesn’t tell us the rate of inflation, but rather what percentage of the survey respondents are seeing prices go up or down.

The survey results suggest no significant inflationary pressures.

Manufacturing Prices:  68.5

Services Prices:  57.6

Forward-Looking Measures

Treasury Inflation Protected Securities

In addition to ordinary bonds, the U.S. Treasury issues inflation-protected securities (TIPS).  By comparing the yields, one can infer the inflation forecast of the capital markets.

Ordinarily one should assign high credibility to this type of information. However, caution may be appropriate given extensive central bank manipulation of the credit markets.

Five Year Forecast:  +1.73% per annum (5Y Treasury Yield5Y TIPS Yield)

Ten Year Forecast:  +1.81% per annum (10Y Treasury Yield10Y TIPS Yield)

5-Year, 5-Year Forward Inflation Expectation Rate

Inflation expected from 5 years from now to 10 years from now:  +1.89%

Michigan Consumer Sentiment

1-Year Expected Rate of Inflation:  +2.6

5-Year Expected Rate of Inflation:  +2.4

ECRI U.S. Future Inflation Gauge

ECRI +0.0

Trend-based indicators

Crude Oil:  Uptrend = inflationary pressure

Copper:  Uptrend = inflationary pressure

U.S. Dollar:  Downtrend = inflationary pressure

Options, Implied Volatility and the Limits to Arbitrage

We think success in option investing comes down to the relationship between expected volatility (i.e., implied volatility) and actual volatility. To the extent that expectations do not match reality, the options market offers a profit opportunity because volatility is a significant determinant of the price of an option.  We also believe that the greatest mismatches between the two are likely to be found in the options offering the highest degree of skewed return distributions.

Although the opportunities are not difficult to identify, capitalizing on them presents significant challenges.  The most mispriced options tend to offer small premiums in relation to the capital at risk in the worst case scenario.

For example, let’s imagine an investor who maintains at all times sufficient funds in cash to cover the worst case scenario.  If he focuses on writing at-the-money put options with a one-year expiration, he might earn premiums of roughly 5% per year for an implied volatility of 15%.

5% may sound like a nice return, but it ignores the losses that happen if the stock price is below the strike price at expiration.  There is about a 50% chance of the stock price being below the strike price at expiration. Accounting for the potential deficit results in an expected net return considerably less than 5%.

To improve the return dynamics, the investor considers writing out-of-the-money put options.  Out-of-the-money options have skewed returns. The skewness of the returns tends to frighten investors; thus the implied volatility is 30% for an option written on exactly the same stock as in the preceding paragraph.  With such a high implied volatility, the price of this option likely is too high.  In addition, because the option is out-of-the-money, the stock must fall quite a bit before it is below the option’s strike price.  Thus, the probability of a loss at expiration is much, much lower.

Unfortunately, much, much lower risk of loss means much, much lower premiums.  The premiums are quite high in relation to the expected loss as indicated, but are low in absolute terms.  If the investor could expect a 5% premium for the at-the-money option, he might earn only 2% gross premiums for a 25% out-of-the-money option.

The problem with the 2% gross premium is that one must hold cash in reserve in the case that the stock declines by a large amount.  Holding cash in reserve means forgoing other money-making opportunities.



Implied Volatility and Skew

Let’s imagine two games.  Which one would you prefer playing:

Game #1:

  • 50% chance of making 20.0%
  • 50% chance of losing 5.0%

Game #2:

  • 99% chance of making 8.5%
  • 1% chance of losing 90%

Most people prefer Game #1 over Game #2 because Game #2 carries the 1% risk of losing 90%. But if one does the math, Game #2 offer a slightly better average result than Game #1:

  • Game #1:  50% x 20% + 50% x (5%) = 7.500%
  • Game #2:  99% x 8.5% + 1% x (90%) = 7.515%

We believe investors have an aversion to the possibility of a large loss that exceeds the probability of the large loss.  The greater the possible loss, the more likely the overestimation of the loss probability.

We see this effect in the pricing of stock options.  Stock option prices are very sensitive to investor expectations about the future volatility of the underlying stock.  Assuming rational investors and certain assumptions about the distributions of future returns, a higher option price means investors expect higher future volatility of the underlying stock.  The Black-Scholes Model can be used to calculate implied volatility.

The options market makes available a variety of option contracts on each underlying stock.  Thus, for a hypothetical company XYZ, one might see dozens of option contracts each with slightly different terms.

If one were to plug the features of each option contract into the Black-Scholes Model, one might be shocked to discover that the implied volatilities are not the same, even though they are all based on the same underlying stock.  Yet this happens.

Let’s consider a representative example.  For varying degrees of out-of-the-moneyness, the implied volatilities of put options for a specific stock might look like this:

Out-of-the-moneyness Implied Volatility
0.00% 10.2%
2.10% 12.4%
4.30% 15.7%
6.40% 20.8%
8.50% 21.9%

All of the options are based on the same underlying stock, which will have only one future volatility.  Yet clearly, the options themselves are priced in ways that suggest varying perspectives on the same stock.  Why?

We think it has to do with the skewed return distributions.  In this case, as skew increases there is a decreasing probability of a larger and larger loss:

Out-of-the-moneyness Relative Skew Implied Volatility
0.00% lowest 10.2%
2.10% low 12.4%
4.30% high 15.7%
6.40% higher 20.8%
8.50% highest 21.9%

We believe that investor aversion to the possibility of a large loss may distort the pricing of out-of-money stock options.  A larger possible loss scares the person who writes the option.  They will not write the option unless they get a higher price for that option, which shows up in the form of a higher implied volatility.

What we are reading on 5/23/2017

Here’s what we are reading today. We do not necessarily agree with the opinions expressed therein and we disavow any actual or implied investment advice therein. In no particular order:
The quants dominate Wall Street
Fat but fit is a myth
Cable cutting is tough on the tertiary channels
Is one’s college major important for later earnings?
Silicon Valley takes aim at indoor farming
Why Value Stocks Have Disappointed
Taking a social media fast
What’s happening to the volatility of volatility?
Is the Left winning the battle of ideas?
Do liars look a certain way?
What does it mean when AI can reproduce?
Is housing constraining the Fed?
Factor research problems
We are in the age of behavioral finance
Ford made the head of autonomous its new CEO
Hussman’s latest
Do anomalies replicate as much as they should?
Is CAPE broken?

Is Option Writing an Income Strategy?

We think option writing is an arbitrage strategy.

Income strategies* typically have many small positive returns punctuated by the occasionally large loss. For example, when one purchases an investment grade bond, one expects to receive a stream of interest payments that are small in relation to the capital invested.  Each scheduled payment carries a small risk that the borrower may not be able to pay the interest, in which case the bond may lose a substantial amount of value.

One can create a similar pattern of payoffs using options: many small returns with the occasional large loss.  When one writes an out-of-the-money put option on a stock, one receives a relatively small payment.  If the underlying stock price declines below the option’s strike price, one may be stuck with a loss, potentially a big loss if the stock price falls materially below the strike price.  But one can minimize the risk of loss by writing put options with very low strike prices.  Because the risk of loss is low, one should not expect to receive much premium.

Thus, the expected return pattern for option writing can resemble the expected return pattern for an income investment.

But a similar appearance does not mean a similar reality.  The drivers of returns are different.

Over the long-term, the profitability of the option strategy depends on the options being overvalued.  Option valuation depends on investor expectations of volatility.  If investors expect future returns to be more volatile than what actually happens, writing options might be a worthwhile investment strategy.  On the other hand, if investors are too complacent about future volatility, the odds of success at option writing are likely to be low.  Thus, the success of option writing depends on the misjudgments of other investors.  The opportunity is the arbitrage between expectation and reality.

In contrast, the profitability of an income strategy depends on the creditworthiness of the borrower.  For bonds held to maturity, the risk of loss is low if the borrower can make the payments.

*In this post, we limit “income strategy” to holding to maturity bonds with a fixed or floating rate of interest, in which the investor pays no more than par value to own the bond.

What we are reading on 5/19/2017

Here’s what we are reading today. We do not necessarily agree with the opinions expressed therein and we disavow any actual or implied investment advice therein. In no particular order:
What to do about the unknown unknowns?
Maybe low spending is how they go rich?
Are you ready for a volatility increase?
Managed futures and volatility
Cryptocurrency bubble?
Do companies tailor dividend policies to investor preferences?
The real estate flipping boom
Insights into the student loan mess
The importance of thinking time
Are older physicians less competent?
Is the Trump trade over?
EV/AV coming faster than expected?
Message boards may not be a good source of stock ideas
Precious metals research survey
The Right Dose Of Cannabis Reverses Brain Ageing. What about the wrong dose?
Is shorting the VIX a crowded strategy?
Why pay money to go the gym?

Options and Skewness

Options have the effect of changing the degree of skewness in the distribution of expected returns.

Skewness has a very specific definition.  Wikipedia offers a good overview, and includes this helpful graph demonstrating both left (negative) and right (positive) skew superimposed over a bell-curve for comparison purposes:

Options can have a similar distorting effect on returns.  A call option on a stock allows the option owner to purchase the underlying stock at a fixed price (the strike price) until the option expires.  As one increases the strike price of a call option, the skewness of the expected returns increases.

Without getting into a formal calculation of skewness, let’s look at the payoffs for a stock and call options on the stock.  We’ll consider a base case of the stock at $100 initially and then advancing to $150, and how the returns are different depending on the design of the call options.  For call option prices, we use the ERI pricing model.  This doesn’t mean we endorse the model as part of an investment process.  We use it merely for convenience sake.  We use in the model a time horizon of 1 year with an interest rate of 2%:

Starting Price Ending Price % change
Underlying Stock 100.00 150.00 50%
Call Option, Strike Price = 10 90.20 140.20 55%
Call Option, Strike Price = 20 80.40 130.40 62%
Call Option, Strike Price = 30 70.59 120.59 71%
Call Option, Strike Price = 40 60.79 110.79 82%
Call Option, Strike Price = 50 50.99 100.99 98%
Call Option, Strike Price = 60 41.21 91.19 121%
Call Option, Strike Price = 70 31.58 81.39 158%
Call Option, Strike Price = 80 22.54 71.59 218%
Call Option, Strike Price = 90 14.81 61.81 317%
Call Option, Strike Price = 100 8.92 52.13 485%
Call Option, Strike Price = 110 4.94 42.70 764%
Call Option, Strike Price = 120 2.55 33.81 1228%
Call Option, Strike Price = 130 1.23 25.80 1994%

In all the cases, the underlying stock moves the same amount, from $100 to $150.  We can see that the call options behave differently, with increasingly skewed returns (in the % change column) as the strike price rises from $10 to $130.

We can see that the call options behave differently, with increasingly skewed returns (in the % change column) as the strike price rises from $10 to $130.  If we think in terms of a bell curve of potential returns, the right side, positive returns are much higher with the high-strike-price call options than with the low-strike-price call options or the underlying stock.

If owning the call option can create positive skew, writing the very same option can create negative skew – i.e., the risk of a large potential loss.

Note that the above table says nothing about the likelihood of achieving a return, just the payoff if the underlying stock should move from $100 to $150.