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

Let us recall how delta hedging can be used to replicate a long call. (58) The Black-Scholes formula produces a number "delta," which is the sensitivity of the price of the long call to movements in the price of the stock. An investor can theoretically replicate an option by buying a number of shares equal to this delta, financing part of the purchase with borrowing. Consider the following example that Professor Hasen uses to describe his delta-hedging approach:

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. (59)

Hasen reports that the delta equals 56.75%. (60) A's taxable year ends six months later, at which time Hasen assumes that the stock has increased in value to $35.08. (61) Hasen reports an option value of $5 and a delta of 73.57%. (62)

A synthetic option is initialized by the purchase of delta=0.5675 shares of ABC stock, which costs $17.03. The purchase is financed by $3.64 (the price of the call) out of pocket and $13.39 of borrowing. (63) Six months later, the synthetic option will be represented by delta=0.7357 shares (worth $25.81) and borrowing of $20.81 (i.e., the value of the shares minus the value of the option). Professor Hasen's goal is finding the appropriate tax treatment for this six-month period. The problem, however, is that a synthetic option involves daily or more frequent trading to ensure that the number of shares always equals delta. We cannot know what tax consequences these trades and the related borrowing have based solely on the value at the end of six months.

In order to approximate the actual tax consequences, Hasen posits a single adjustment to the portfolio midway between Day 1 and the end of the taxable year six months later. The interim adjustment comes from the hypothetical purchase of 0.1682 new shares, reflecting the increase in delta from 0.5675 to 0.7357. Hasen deems this purchase to have been made at a share price of $32.54 (i.e., the midway point between $35.08 and $30). (64)

Professor Hasen would tax the initial stock purchase and the interim purchase on a mark-to-market basis. This system, which he calls a "quasi-mark-to-market approach," produces gains as follows. There are gains of $2.88 on the initial purchase (65) and $0.43 on the interim purchase. (66) As a result, Hasen would subject A to short-term capital gains of $3.31. Professor Hasen appears also to allow A an interest deduction of $0.77 on the imputed debt. (67) The net income would be $2.54.

This result obviously deviates from the realization rule. Under the realization rule, A would have no gain at all for year one, because she has only bought nondividend-paying stock and borrowed money. Indeed, A might even be entitled to an interest deduction. Professor Hasen justifies deviation from the realization rule by addressing the "policy question of whether it is appropriate to tax the gain on the value of the underlying asset during the pendency of the option or to wait until some future date." (68) The realization rule gives one, rather clear, answer to this policy question, although there is no reason Hasen should not argue for a better answer. (69)

But his answer points to full (not quasi) mark-to-market treatment of the option itself. In Hasen's example, the option price has increased only $1.36 (from $3.64 to $5.00), although he would impute income of $2.54. Hasen wants to avoid marking the option to market to "avoid the difficulty of actually computing the spot prices of the option on a daily basis (or in principle even more frequently)." (70) Yet, taxing the option on a mark-to-market basis would typically require only a single year-end valuation of the option. (71) In fact, valuing the option is no more difficult than calculating delta, as the formula for both have the same dependent variables. (72) Marking the option to market is no more difficult than performing the delta calculations that Hasen proposes.

At a conceptual level, this article approaches the taxation of options in a manner similar to Hasen's. Delta hedging gives us a way to break options down into more fundamental transactions. However, this article accepts as a reality the fact that these fundamental transactions have clear tax treatments that are rather uncontroversial outside the academy. Modeling this reality--including the realization rule--is the goal of this article.

3. Professor Shuldiner's Formula Interest

The spirit of this article is most in line with the framework given by Professor Warren and the bifurcation models of Professors Strnad and Hasen. There are, however, other noteworthy proposals to reform the taxation of options. Professor Reed Shuldiner has proposed tax consequences for options based on implicit interest. Professor Shuldiner would impute interest income to the holder of puts and calls, based on the amount of premium paid. (73) Shuldiner gives the following example (subject to an interest rate of 10%):

Diva enters into a cash-settlement call option with David to purchase

10,000 ounces of silver in two years at $12 per ounce. Diva pays David

$10,000 for the option....

Diva has purchased an asset for $10,000 which she is presumed to

expect to increase in value to $11,000 by the end of the first year

and to $12,100 by the end of the second year. Diva should accordingly

have income of $1000 in the first year and $1100 in the second

year. (74)

Shuldiner's approach actually imputes interest income in the opposite direction from a delta-hedging approach. Shuldiner does not supply a current price of silver nor its volatility in his example. Nevertheless, a current price of $9 per ounce and a volatility of 26.02% are consistent with the example. (75) With these parameters, delta is 47.84%. (76) Rather than buying an option over 10,000 ounces of silver for $10,000, Diva could alternatively buy 4784 ounces of silver. The cost would be $43,056, (77) which would be financed with $10,000 out of pocket (representing the premium) and $33,056 of debt. If we simply project this debt over the next two years, Diva would have year one interest expense of $3306 (78) and year two interest expense of $3636. (79)

Recall that Professor Warren had identified two basic tax regimes: fixed return and contingent return. Current law treats options as contingent-return transactions, whereas Professor Shuldiner would treat them as fixed-return transactions. Option theory shows that an option is neither fixed- nor contingent-return in its entirety. Instead, it is a hybrid of the two. (80)

4. Proposals for Covered Calls

Professor Calvin Johnson has argued that the premium received on a short call should be taxable as ordinary income if the call writer owns the underlying asset (i.e., writes a covered call). (81) The amount of income would be equal to the lesser of (1) the premium received or (2) the unrealized appreciation in the underlying property. This approach relies on an accounting concept of income, focusing on the cash received rather than the elimination of risk in the underlying asset. Thus, this approach fails to reach a protective put, which an investor pays for, even though a protective put can eliminate risk as well as a covered call. Also, the approach would not reach an equity collar either, even though it yields a relatively certain cash return but at a future date.

Professors Cunningham and Schenk would treat the sale of a covered call as the sale of part of the underlying asset. (82) Bruce Kayle has a similar approach. He used an example in which a taxpayer owns 1000 shares of stock with fair market value of $100 and adjusted basis of $40 per share. (83) Rather than selling a covered call with a strike price of $100, the taxpayer might create an economically equivalent partnership. The partnership has two classes of ownership. Class 1--analogous to the covered call--entitles the owner to all proceeds from the pre-established sale over $100. Class 2--analogous to the retained rights--entitles the owner to all dividends until the sale, plus all sale proceeds up to $100 per share. In Mr. Kayle's example, the taxpayer sells Class 1 for $5000, retaining Class 2. Mr. Kayle concludes that the taxpayer would have gain of $3000 from the sale. Because Class 2 replicates a covered call, Mr. Kayle suggests that the covered call could have similar tax treatment.

Mr. Kayle's approach would determine the taxation of the covered call by analogy to a more complicated transaction (classes of a partnership or trust). The approach of this article, in contrast, is to determine the taxation of options by their financial equivalence to more fundamental transactions (stock ownership, short selling, borrowing, and lending). Once a consistent system for taxing options is found, we could possibly invert Mr. Kayle's approach, applying the option-tax rules to partnership interests like Class 2.