Naked and covered in Monte Carlo: a reappraisal of option taxation.

The market for equity options and related derivatives is staggering, covering trillions of dollars worth of assets. As a result, the taxation of these instruments is inherently important. Moreover, the importance is made even more acute by the use of options in creating more complex transactions and in avoiding taxes.

Consider an equity call option, which entitles, but does not obligate, its holder to buy stock at a set price at a set time in the future. Option theory gives us a way to break the option down into more fundamental units. For example, an equity call option over 10,000 shares of stock might be equivalent to buying 7500 shares of stock itself.

This financially equivalent synthetic option should serve as the model for taxing an actual option. That is not the approach of current law. Nevertheless, a Monte-Carlo simulation I wrote shows that current law does a good job of approximating the tax liability generated by the synthetic option--but only when we view the option in isolation.

The results are radically different when the investor already owns some of the stock subject to the option. If such an investor sells (rather than buys) a call option, she has effectively sold a portion of the owned stock at fair market value. For example, the issuer of a call option over 10,000 shares may have effectively sold 7500 shares that she already owns. Option theory gives us a way to measure how much stock she has effectively sold. Taxing the sale of stock implied by many option and related contracts would reflect economic reality and curtail tax-motivated investments.

I. INTRODUCTION

Finding the correct tax treatment of equity options is a crucial task for three reasons. First, the market for equity options and other equity derivatives is enormous. In June 2006, equity options and related contracts covered assets worth almost $6.8 trillion, or about one half the U.S. gross domestic product. (1) The sheer size of the market warrants attention. Second, more complex financial contracts are often based on options. (2) Finding the right tax treatment of options will thus help us find the right tax treatment of these other contracts. Third, options and related contracts are often used to avoid taxes. (3) Thus, taxing options correctly would eliminate inefficient tax arbitrage and ensure equitable treatment of taxpayers. (4)

Let us start with a call option, which entitles (but does not obligate) the holder to buy stock at a set price at a certain time in the future. For example, Maya might buy a call option over XMPL Corp. stock that entitles her to buy 10,000 shares of XMPL Corp. stock for $100 per share in five years. Suppose that XMPL Corp. stock is currently worth $100 per share. The call gives Maya a valuable right because she will enjoy any appreciation in the stock over $100 per share without any risk of decline below that price. The Black-Scholes model (5) gives Maya a concrete way of valuing her option. Using that model (and other assumptions discussed later), the option is worth $350,000. (6)

The magic of the Black-Scholes model is that it equates Maya's call option with a combination of (1) ownership of XMPL Corp. stock itself and (2) borrowed funds. We will see later how Maya's call option is equivalent to her owning about 7500 shares of XMPL Corp. stock (worth $750,000) purchased partly with borrowed funds of $400,000. (7) This combination of stock and borrowing has the same net value as the call ($350,000). And, it is the starting point in a process called delta hedging that will closely approximate the economic return on the call option itself. So, we can think of the stock and borrowing combination as a synthetic option.

In due course, this article will explain how delta hedging creates synthetic options. The important point for now is that the Black-Scholes model gives us not only a way to value the call option but also to recreate it using stock and borrowing. The Black-Scholes model (8) has been spectacularly successful, winning Nobel prizes for its inventors (9) and serving as the linchpin for the multi-trillion dollar market for derivatives. It does not, however, served as the basis for taxing options. When Maya buys her call option, she is not taxed as if she bought XMPL Corp. stock with borrowed funds. Instead, the tax treatment is held open while Maya waits to see if she will actually exercise (or perhaps sell) the option. In taxation, timing is almost everything, (10) and long-term deferral can potentially be the same as tax forgiveness.

Prior commentators have argued that tax policy should strive to tax economically equivalent transactions similarly. (11) Tax policy can achieve this goal by what has been termed "bifurcation"--if a transaction can be bifurcated or broken down into more fundamental units, then the transaction should be taxed based on the tax treatment of these units. Inconsistent treatment between the fundamental units and the transaction creates the potential for economic distortions, tax arbitrage, and inequities.

Theoretically, then, the proper way to tax Maya's call option is to tax her as if she bought 7500 shares of XMPL Corp. stock (worth $750,000) purchased partly with borrowed funds of $400,000. Doing so is theoretically possible but practically difficult. The primary difficulty is that the precise amount of stock and borrowing will need to change over time. For example, suppose Maya really did decide to replicate the option with the stock and borrowing combination. If XMPL stock goes down in value, Maya would need to sell some stock (using the proceeds to pay of some of the borrowing she incurred). If XMPL stock goes up in value, Maya would need to buy some more stock (using additional borrowing to pay for it). So, the synthetic option is a dynamic mixture of stock and borrowing, representing countless sales and purchases of the underlying stock and changes in the associated borrowing. The 7500 shares financed in part with $400,000 of borrowed funds is merely the starting point. Taxing the transactions that occur after the starting point would be administratively infeasible, even though the approach is theoretically correct.

Nonetheless, this approach is a valuable policy tool, and it is possible to examine the taxation of the synthetic option and its countless transactions using a computer simulation. The simulation tells us what the expected tax consequences will be on that dynamic combination of stock and borrowing that replicates the call option. Ideally, the tax consequences on the actual option would be the same as those produced by the simulation. In reality, we should aim for a practical system that achieves results roughly the same as the ideal results produced by the simulation. Later in this article, I report the results of a computer simulation I created using the MATLAB programming language. Surprisingly, the simulation shows that current-law treatment of options is, for the most part, the best approximation of the theoretical ideal. The current-law taxation of options survives the toughest test that tax theory can apply, but with one exception.

That exception relates to so-called covered calls, which are the sale of a call combined with ownership of the stock. (12) To illustrate, suppose we change the example so that Maya already owns 10,000 shares of XMPL Corp. stock. Her adjusted basis in the stock is zero, meaning she would realize gain of $1 million if she sold the stock today. Let us also assume that Maya sells a call option over 10,000 shares rather than buying one. So, she is now obligated to sell 10,000 shares of XMPL Corp. stock for $100 per share in five years if the buyer exercises its right to do so. (And, the buyer will exercise its right only if the stock is over $100 per share at that time.) Maya receives cash of about $350,000 for selling this option. Even though Maya receives cash of $350,000 today, she is not taxed today under current law. As before, she waits for five years to see whether she must perform on the call.

Maya's call option is the equivalent of her buying 7500 shares (worth $750,000) purchased partly with borrowed funds of $400,000. In contrast, when Maya sells the call, the equivalent combination is inverted. Now, it is as if she sells 7500 shares (obtaining funds of $750,000) and lends a portion of the proceeds she obtained (again, $400,000). Thus, Maya should be taxed as if she sold 7500 shares of XMPL stock today, recognizing immediate gain of $750,000. Instead, current law improperly allows Maya to defer the tax consequences of the implicit sale for five years while she waits to see if she is called upon to perform under the option.