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

Imputing interest to calls may improve the performance of option taxation even without imputing trading gains or losses. Recall that that the long call produced interest expense and trading losses. (130) Recognizing only the interest expense would mitigate the shortcomings of current law.

It is not difficult to estimate the expected interest on a call option. Recall that our synthetic long call is initiated as follows: Buy [[DELTA].sub.c]= 0.7663 shares of XYZ stock for $38.32, and finance this purchase with an out-of-pocket contribution of $16.25 (which is the option value). The remainder, $22.07, comes from borrowing. (131) We could assume that the taxpayer actually does create this initial position when buying an option, but never changes it over the life of the option. Using the same 5% rate used to price the options, we see that the hypothetical interest should come to $6.27 (132)--a result that is almost exactly the same as reported for the Monte-Carlo simulation reported above. We should assume that the interest accumulates on a daily basis. Projecting that daily interest forward to future value yields about $7.08--again, very close to the same as for the Monte-Carlo simulation reported above.

This system is, however, counterintuitive. Even though the buyer of a call expects to gain from the transaction, the system imputes a deduction until a realization event occurs. The inverse is true for a call writer, who pays money for a call yet faces imputed interest income. Professor Shuldiner's system of imputing interest is more intuitive and typical, as it imputes interest income, not expense, to the call holder. Greater consistency with the synthetic-call ideal clashes with tax aesthetics.

Even if the strangeness of imputing interest according to the synthetic call does not deter us, some practical considerations may. Granting an interest deduction to a cash-method call holder may not even be consistent with the proper taxation of the synthetic call. (133) A synthetic-call holder might face serious difficulties in achieving an interest deduction before expiration under the cash method. Granting interest deductions to call holders may also open the door to tax avoidance (134) unless the deduction is subject to complex systems like the straddle and wash-sale rules. (135) Moreover, current law may approximate the overall, correct result by denying call holders any interest deductions while excusing call writers from any interest income. If call holders and writers have the same marginal tax rate on average, then current law reaches the same result as the synthetic-option approach.

Thus, taxing the interest implicit in an option may be both difficult and of limited ultimate value. More limited reforms may be feasible. Although section 1258 imposes ordinary-income treatment on a synthetic bond created by a combination of stock, a long put, and a short call, section 1258 does not alter the timing of the income from the synthetic bond. (136) Even though section 1258 treats the synthetic bond as a bond for characterization, timing of the income is still determined under the realization standard. This analysis shows why section 1258 should also impute the interest income on an annual basis.

F. Conclusion

In Part IV above, I argued that a synthetic option is the theoretical ideal for taxing equity options. This section attempts to implement this ideal, focusing on naked options. Because the taxation of synthetic options depends on the actual path that the stock price takes, synthetic-option taxation can be measured only with a computer simulation. According to the simulation, current law appears to tax put options (long and short) correctly. However, current law appears to overtax long calls and undertax short calls. These results are consistent with a qualitative account of the tax items associated with synthetic options.

Yet, achieving the perfect result for a call option is probably not feasible. Although synthetic options produce gains and losses from trading, imputing these tax items to true options is not feasible. Synthetic options also produce interest income and expense. Imputing such items to call options is feasible but ultimately unwise. Interest expense would be imputed to the long call, but allowing a deduction for this expense may present opportunities for abuse. Imputing interest income to short calls would not lead to such opportunities. Imputing interest income to options would destroy the current symmetry between short and long positions in the same option. Overall, the system for taxing options may work well, even though short calls are undertaxed and long calls are overtaxed.

The taxation of short calls and long puts will be examined again in the next section. There, the options are combined with a position in the underlying stock. The result--covered calls and protective puts--would ideally trigger the recognition of unrealized gain in the underlying stock itself.

VI. TAXING THE COVERED CALL AND PROTECTIVE PUT: A MONTECARLO SIMULATION

A. Covered Calls and Protective Puts

A covered call is a short call combined with ownership of the underlying asset. Because the writer of the call receives premium income, prior commentators and courts have struggled with the issue of whether the writer should be treated as having sold the underlying asset. Current law answers with a definitive "no." This section will show that covered calls are best analyzed as implicit short sales. It will then extend this analysis to protective puts (long puts combined with ownership of the underlying asset). Under this approach, the taxation of covered calls and protective puts depends on the delta of the position, rather than the amount of premium income received.

To illustrate the problem of covered calls, suppose that Maya owns 10,000 shares of ABC stock. She has a $0 per-share basis in the stock, which is currently worth $30 per share. Next, suppose that Maya sells call options on the stock, exercisable in one year at $33 per share. Maya will receive cash for writing the call, perhaps $36,393 ($3.6393 per share) if we use the assumptions from above. (137) The problem arises in determining whether tax law should treat Maya as having sold the stock when she writes the call on it.

Under current law, Maya would pay no tax for writing this call. (138) The explanation for this treatment is that the short call and the stock are separate transactions, although the historical basis for this treatment comes from abstruse reasoning involving the character of the premium received. (139) Although this result is settled under current law, the taxation of covered calls has attracted significant attention from commentators. (140)

Option theory bifurcates Maya's short call into a short sale and a risk-free bond. The number of shares that Maya must sell short in order to replicate the short call is given by the delta of the call. In our case, the delta is 0.5658. (141) As Maya's short call covers 10,000 shares, she has essentially made a short sale of 5658 shares. A true short sale of ABC shares would implicate the constructive sale rules of section 1259 because Maya holds an appreciated position in 10,000 shares of ABC stock. (142) If a short call was equated with short selling, however, then Maya would be deemed to have sold 5658 of her owned ABC shares short at current fair market value when she wrote the call option.

Note that Maya's gain does not directly depend on the amount of the premium she received. (143) Maya would have a gain of $169,740, (144) even though she has received a premium of only $36,393. Her gain would depend on three factors. First, the delta of the option determines the number of shares that were implicitly sold short. Second, the fair market value of the stock determines the amount realized implicitly. Third, the adjusted basis in the stock Maya actually owns is used to determine the amount of gain.

The delta standard would apply even if the taxpayer pays a premium. Let us assume that, rather than selling a call, Maya bought a put over 10,000 shares of ABC stock. If we use the same parameters as before, the put would cost her $34,989. (145) The delta for the put is -0.4342. Thus, buying this put option is the same as implicitly selling 4342 shares of ABC stock short. Current law does not tax Maya upon buying the put, even if she already owns ABC stock. Yet, the delta standard of this section would treat Maya as executing a short sale over 4342 shares, producing gain of $130,260.

Thus, option theory gives tax policy a way of dealing with the ancient problem of covered calls and the related problem of protective puts. In order to ensure consistency between the taxation of short sales and the taxation of options, these options should be treated as constructive sales (based on the Black-Scholes delta calculation). (146) The example given above shows only the initial consequences of the covered call and protective put under the delta model. It does not follow through to the end of the options. Exploring the tax consequences over the entire life of the options is the goal of the next two sections.

B. Fluctuating Deltas and Constructive Sales