Shakespeare's Options

Options

What are Options?

Options are a complex and poorly-understood area of investing. As with preferreds, professional assistance (or a good deal of reading) are a prerequisite. Options trading requires filing a separate clearance form with your broker.

In Canada, options are traded on the Montreal Exchange (MX). US options are traded on the Chicago Board Options Exchange (CBOE), Amex/NASDAQ, the Pacific Stock Exchange, and the Philadelphia Stock Exchange. The US exchanges offer far greater liquidity [ease of trading] and better accountability than the MX, and should be used whenever possible.

Material on options can be found at the following sites:

   The Options Industry Council
   Investment FAQ's
   E-trade

Recommended books include:

McMillan, Lawrence G. "Options as a Strategic Investment", Prentice-Hall Press, 1992 and later.

Thomsett, Michael C. "Getting Started in Options", Jossey-bass Inc., 2001.

Definitions

Call options: the right (but not the obligation) to buy a stock at a certain price (the "strike price") on or before a future date.

Put options: the right (but not the obligation) to sell a stock at a certain price (the "strike price") on or before a future date.

Covered call writing: the practice of selling ("writing") call options on a stock which the writer also owns. This approach is used by some retirees to supplement their income.

Cash-covered put writing: a mathematically-equivalent tactic to covered-call writing. The writer sells a put option which is covered by cash in his account. [If the stock goes down and the put is exercised, the cash will be needed to buy the stock.]

Strike price: is the value at which the option can be exercised.

Premium: the amount received by the option writer (before commissions).

Expiration date: the date after which the option becomes worthless. These are always on the third Friday of a month. American options can be exercised before or on the expiration date. European options can only be exercised on the expiration date.

Simplified Explanation of Covered-Call Option Writing

I do not intend to give a full explanation of options trading here. Anybody who seriously wants to trade options should investigate the matter thoroughly, peruse several texts, and try it out in an imaginary account for several months before actually venturing into the market. I am simply going to give an overview of the simplest strategy, "covered-call writing", which is claimed by some authors to enhance returns.

Options traders are buying and selling probabilities - which is something insurance companies (and gambling operations) do for a living. A covered-call writer is selling, for the premium, the probability of an increase in price of a company above the strike price. In other words, the writer is forgoing the chance of a large gain for the certainty of the premium.

Let's consider an example.

In the January 19 2002 Globe and Mail Report on Business, the Bank of Nova Scotia is listed as having closed at $48.10. If I have 500 shares, I can write a covered call by writing 5 call options contracts (each contract is for 100 shares). I must first choose the option expiry date. Suppose I select options expiring in April 2002 (the third Friday). I must then select the strike price. A call option with a strike price above the current stock price is said to be out of the money; the $50 contract has a bid price of $1.35 and an ask price of $1.40. The next lowest contract is for $47.50 and is in the money; it has a bid price of $2.45 and an ask price of $2.60.

These prices are based on a sophisticated mathematical estimate of the probabilities (the Black-Scholes Equation, see Appendix). In effect, the equation calculates the probability that the stock will exceed the strike price during the time-to-expiry. This probability is then used to calculate a price, which is then corrected (discounted) using the treasury-bill rate and further corrected for dividends received by the stock holder but not the options holder. If the equation is accurate, the resulting price is fair to both buyer and seller.

In selecting the strike price, I must decide whether to write an in-the-money call or an out-of-the-money one. An in-the-money call will be exercised on or before expiry and must be bought back if I don't want to sell the stock; an out-of-the-money call is safer if I have a large embedded taxable gain. Suppose I decide to write the out-of-the-money call closest to the current price - the $50 one. That's the one with the highest premium. I would receive a premium of about 500×$1.35, or $675, less commissions (which can be quite high) - say, $37.50 from a prominent discount broker (you may do better), for a net of $637.50. This gives an annualized return over the three-month time-to-expiry of about 11%. The commission is 5.6% of the gross.

If the stock is above $50 in April (or earlier; the call can be assigned at any time), the buyer of the call (who is probably a professional trader) will exercise the call and call the stock from me. I will receive 500×$50, less normal stock trading commissions, on top of the $637.50 already received. If I have a capital gain on my shares, and they were in a non-registered account, I will have to pay the tax due. (To keep the stock from being called I could have bought back the option at whatever price was necessary.) On the other hand, if the stock finishes below $50, the call expires worthless and I pocket the $637.50. The trader who bought the call will manage his risk in such a way as to make a profit however the stock price moves.

Covered-call writing is selling the upside for a modest premium.

It can be used to enhance income without selling the stock, and is favoured by some retirees for that purpose (note the 11% annualized yield on the Bank of Nova Scotia option). Options writing also reduces portfolio volatility and provides extra income in flat or down markets. For a given volatility, there is a relation between the options premium and the probability of the call being exercised: lower probabilities give smaller premiums. The premium is also higher for high-volatility stocks. The implied volatility of a stock is the volatility (obtained from the Black-Scholes equation) corresponding to the market premium of its options, and can vary due to market conditions. It may be advantageous to write options only when the stock's implied volatility is above average.

Hedging

Writing covered calls can be used very effectively to hedge the potential loss (and manage the risk) when buying distressed companies. Beaten-up stocks usually have options with a very high premium (and therefore a very high implied volatility). An investor who feels a temporarily-distressed company is fundamentally sound will buy the stock when he thinks it is near its bottom and immediately write a long call. The call premium for such stocks can reduce the cost base significantly, thus substantially reducing the amount at risk. The hedged position will not be at a loss unless the stock falls by more than the option premium, whereas a similar unhedged dollar investment would drop with any further decline in stock price. If the company survives, the stock will likely eventually be called, which limits the upside for the hedged position but can give a very high annualized return on the reduced cost base. The unhedged position would, in that case, get a better total return, but also has greater risk.

Drawbacks

Options writing is inherently a zero-sum game: for every winner, there must be a loser. In fact, since commissions and bid-ask spreads are quite high, it becomes a negative-sum game: there are more losers than winners. The amateur options trader is placing a bet with a professional, who almost certainly has more knowledge and experience, doesn't pay commissions, benefits from the bid-ask spread, and can use sophisticated techniques to lay off the bet - making money from you, the writer, at no risk. In addition, there have been reports of sharp trading practices on the Montreal Exchange which can further trap the unwary; the American exchanges, which have better accountability, should be used for all options trading.

Successful option trading needs a fair bit of study and trial-and-error learning (in an imaginary account). If the stock is held in a taxable account, assignment of a call may result in a significant tax liability.

I am not convinced that "selling the upside" is the road to riches. In steady or down markets, it provides extra cash - but in rising markets, the stocks are either called or the option must be bought back. See, for example, the following argument, by Don Chance: Misconceptions about Covered Call Writing . Call option writers are forgoing the possibility of a large gain. Although that possibility may be small, the resulting infrequent - but large - gains can, over the long run, account for a significant portion of a portfolio's performance. As Nassim Taleb discusses in his book "Fooled by Randomness", the options market underestimates the cost associated with improbable events. Covered-call writing suffers from full participation in the downside while being inadequately rewarded for the upside, so, in the long run, it is return-limiting. It is not possible to guarantee that the option can be bought back as soon as it is in the money, because a stock would be halted on major news (say, a takeover) - and will reopen at a higher price. The price of covering a "bad call" could easily equal that of many premiums. Alternatively, if the stock is called, the foregone gain is a hidden cost that many traders don't take into account.

It has also been pointed out that the options writer whose stock goes down faces the question of what to do if his previous option expires while the stock is depressed: if he writes another one at the depressed price, the stock could be called on the way back up.

The question is not whether one can make money by writing covered calls; it is whether more money can be made than by simply holding the stock. After all, if you didn't think a stock would go up, why did you purchase it in the first place? And if it does go up, it will be called.

I suspect there is a fundamental incompatibility between covered-call writing and the dividend growth strategy outlined in the section on Canadian stocks. Covered-call writing gives the largest premiums with stocks with high volatility (and high risk): but these stocks also may lose value catastrophically. Dividend-growth investing favours conservative, low-volatility stocks with small options premiums. Such stocks often have limited downside; selling the upside makes no sense.

Some authors claim that there is little chance of an option being assigned before its expiry date. I suppose I must be uncommonly unlucky, since the first option I wrote (an in-the-money call; I should have just sold the stock, which I considered overpriced) was assigned about three weeks before expiry. An investment club for which I was treasurer also had an option assigned a couple of weeks before expiry. If the tax liability on embedded gains is significant, I don't think covered-call writing is worth the risk. If you want some extra income, why not sell just a little bit of the stock? This completely avoids the risk of a large tax penalty if all the stock is called.

For those who want to study options material and start writing calls, good luck. There are also many other more sophisticated options strategies that can be used. But I think a small amount of money can be made more safely (and with less work) by trading preferred shares.

Appendix: The Black-Scholes Equation

The Black-Scholes Equation (the derivation of which received the Nobel Prize) is commonly used to evaluate options prices. The data required by the equation are:

the current stock price
the option strike price
the time-to-expiry
the option type (put or call)
the 30-day treasury bill rate ("discount rate")
the stock dividend rate (if any dividend is due before the time-to-expiry)
the stock's annual volatility

All inputs except the volatility are known.

The Black-Scholes Equation calculates the probability that the stock price will exceed the strike price by assuming a log-normal price distribution, which means that a plot of probability versus the logarithm of the stock price has the usual "bell curve", or Gaussian, shape. The volatility is proportional to the width of the distribution. This assumed distribution tends to underestimate the observed probabilities at the "tails" of the curve; i.e. in real life it underestimates the likelihood of large price changes. Traders will therefore adjust the option premium upwards (which is equivalent to assuming a higher volatility - the implied volatility) if they feel that a large price change is possible.

The CBOE calculates a market volatility index (symbol: VIX) that is the average implied volatility of eight put and call options. This index is usually between 20 and 30 (i.e. an implied volatility of 20 to 30%), but can move sharply upwards if large market swings are anticipated. A very high implied volatility is usually an invitation to write options, not buy them.

A Gummy Tutorial on the Black-Scholes Equation is here.