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

Finally, David Schizer has suggested an approach for dealing with equity collars based on the delta of a stock. Recall that an equity collar combines a long put with a short call and acts as a substitute for a short sale. (84) If the spread in an equity collar is wide enough, it will avoid the constructive sale rules. Schizer notes that one could calculate the delta of the equity collar in order to determine the extent to which any collar should trigger the constructive sale rules. (85) Schizer does not, however, develop this idea fully, stating "although the delta approach is theoretically intriguing, it is probably not practical." (86) Part III.B already gave a preliminary example of this approach. Part VI.D of this article will attempt to develop this idea more fully and will ultimately propose it as a way of dealing with covered calls, protective puts, and equity collars. (87)

IV. THE SYNTHETIC OPTION AS A POLICY IDEAL

A. Theoretical Case for Taxing True Options According to Synthetic Options

Option theory works in financial markets because it equates options with liquid, easy-to-value transactions. Owning a call option is financially equivalent to owning a certain amount of the underlying stock and borrowing a certain amount of money. (88) The difference in value between the stock ownership and the indebtedness--the equity in the position--should closely approximate the value of the option. Thus, one could say that option theory successfully bifurcates call options into stock and debt. The goal of this article is to apply this approach to the taxation of options.

Taxing financial contracts according to their constituent parts is theoretically the strongest policy response to financial contract innovation. (89) A particular strength of this bifurcation approach is its "continuity," (90) which ensures that small changes to a transaction do not result in large changes to its tax treatment. Recall the problem of equity collars, described in Part III.B. An equity collar is used as a substitute for a short sale by taxpayers. Unlike short sales, however, equity collars can be structured to avoid the constructive sale rules of section 1259. Yet at some point the spread between the call and the put becomes too narrow, and the constructive sale rules are engaged. Thus, the current-law taxation of equity collars is discontinuous.

Bifurcating the equity collar into a short sale and bond avoids this discontinuity. By definition, an equity collar is a long put and short call, both of which can be decomposed into short selling and debt investing. By determining the amount of short selling inherent in the long put and in the short call, we can determine the extent to which any equity collar should trigger the constructive sale rules. Small changes in the equity collar would thus result in small changes in the amount of constructive sale that is triggered.

A similar approach can be taken with the synthetic bond described in Part III.B. There, we saw that a bond can be created by buying stock, buying a put, and selling a call. This combination is similar to the equity collar (a long put and short call) plus stock ownership. As we just saw, a long put and short call are both combinations of short selling and lending. In this case, it is the implicit lending that is important. If the tax laws imputed interest income on this lending, then the synthetic bond would offer no tax benefits.

Prior commentators have criticized the bifurcation approach as being unsound because of the lack of unique units by which transactions can be analyzed. (91) One commentator quipped, "There are no fundamental individual particles such as quarks in the financial world." (92) Yet, breaking transactions into fundamental particles is precisely what the Black-Scholes method does. The four fundamental units are owning stock, short selling stock, borrowing money, and lending money. Setting aside short selling for a moment, we should see that the tax rules for the other three transactions are familiar and unlikely to change in the foreseeable future. (93) Stock ownership gives rise to dividend income and gain or loss upon sale. Borrowing and lending money gives rise to interest expense and income. These three transactions are not commonly considered to be "derivatives," as we do not think that the economic returns on borrowing, lending, and stock ownership are based on other financial transactions. As for short selling, it is not as familiar as the other three transactions and its tax treatment is perhaps less stable, being radically changed in 1997. (94) Yet, short selling should still be considered a fundamental transaction because it is the inverse of stock ownership.

Thus, our fundamental particles are two pairs of inverse transactions: (1) borrowing and its inverse, lending, and (2) stock ownership and its inverse, short selling. These transactions are the fundamental building blocks that option theory uses to price options. They are also the building blocks that this article uses to examine the taxation of options.

B. The Timing of Tax Items

The total gain or loss on a synthetic option will be very close to the total gain or loss on a true option. After all, the whole point of the synthetic call is to replicate the economic return from a true option. As a result, we can be sure that current law gets the amount of gain or loss on options right. The interesting issue is whether the timing of gain or loss is correct.

Under current law, an option generates only one tax item--either gain or loss at some realization event (e.g., upon exercise or expiration). Under the approach of this article, an option generates several tax items based upon the tax items that a synthetic option generates. Recall that long calls and short puts are replicated with stock ownership and borrowing. (95) These options produce gain or loss from trading in the stock and interest expense from the borrowing. Short calls and long puts are replicated with short selling and lending. These options produce gain or loss from the short selling and interest income from the lending.

Unlike current law, the delta-hedging approach of this article does not defer all tax items to some future realization event. Measuring the timing of these tax items requires some assumptions, which are summarized as follows:

1. All tax items are taken into account immediately. So, interest income that is paid on October 1 is taken into account immediately, rather than on December 31 or April 15 of the following year. This assumption simplifies the calculations in the simulation.

2. Characterization is disregarded. The focus is solely on the timing of income. This assumption may well be the most limiting, as characterization has such a dramatic effect on tax rates under current law. (96)

3. Deductions for losses and interest are fully useable. (97)

4. Interest expense is deductible immediately, even though the simulation calculates interest as being capitalized. (98)

5. All positions are liquidated at the expiration date. So, gain or loss is not deferred past the expiration date, giving us a set period during which to compare the timing of tax items from the true option and the synthetic option.

The synthetic option produces a series of tax items over its lifetime. The future value of these items can be determined as of the expiration date. We can view this future value as the ideal measure of gain or loss on the option. This future value can thus be compared with the current-law treatment of the true option, which produces gain or loss only upon the exercise date.

The ultimate goal is the accurate timing of income, subject to the realization requirement. Some might assert that an even more accurate measurement of income would come from mark-to-market taxation of the synthetic option. (99) However, mark-to-market taxation of the synthetic option is the same as mark-to-market taxation of the option itself, (100) because the economic value of the synthetic option should track the economic value of the true option. Because the realization rule is so firmly entrenched, this article does not consider a mark-to-market system for taxing options.

The simulation must measure the timing of two types of tax items: (1) interest expense or income and (2) gain or loss from trading. Measuring the timing of interest is computationally straightforward. Recall for example that a synthetic long call is created by the purchase of delta shares of stock, financed in part by borrowing. We can assume that the borrowing generates interest at the same rate used in the Black-Scholes formula. Measuring the gain or loss from trading is more difficult. As time passes and the stock price fluctuates, the investor would need to rebalance the debt/stock portfolio. The goal is always to have the number of shares owned equal delta. When delta falls, for example, the investor would need to sell some stock, generating gain or loss on the sale. Measuring this gain or loss requires us to adopt some system of inventory accounting, discussed using an example in the next section.

C. A Simple Simulation

Recall the ABC stock example used above, drawn from Professor Hasen's article:

ABC stock is worth $30 on Day 1 and has moderate volatility of 30%. On

Day 1, when the risk-free rate of interest is 10%, B sells A an option

to buy ABC stock at $33 on Day 2, one year later. The price of the

option is $3.64. At all times from Day 1 to Day 2 B is the record

owner of the ABC stock. ABC stock pays no dividends. (101)