Creating Instruments Using Derivatives

The ability of derivatives to blur the demarcations between instruments is best appreciated from the put-call parity relationship derived in the appendix. For simplicity, this relationship is reproduced here for a nondividend-paying stock (S) with the subscript on S removed:

which shows that there is a fundamental relationship among the four instruments: two derivatives (a call option (C) and a put option (P)), a stock, and a bond (B). Any one of the four instruments could be synthesized by a suitable combination of the other three. For example, a bond, in conjunction with a long call and a short put, would produce a synthetic stock. Furthermore, since a long forward contract (F) is no more than a combined right and obligation to purchase an underlying asset at a certain price at some future date, it can be replicated by a long call (representing the right to purchase the asset) combined with a short put (representing the obligation to purchase the asset) at the same price and date. Hence,

Together with equation (1), it implies that a synthetic stock can also be created by combining a bond with a long forward contract:

Likewise, a synthetic bond is created by combining a stock with a short forward contract. Though derived partly from the put-call parity relationship (1), one can, in fact, arrive at equation (3) directly from intuitive reasoning: holding a bond with the intention of using its proceeds to purchase a stock at the delivery date and price under the forward contract is equivalent to holding the stock.

Instruments created by derivatives could be grouped under two broad categories: hybrids and synthetics. Each category, either by itself or in combination with the other category, would provide taxpayers with virtually limitless tax arbitrage opportunities under traditional income tax systems.

Hybrids

A hybrid is a new instrument created by combining debt, equity, and, possibly, other derivatives. The new instrument may not be recognized by existing tax laws and, hence, its tax treatment could be uncertain. Many hybrids are available, but contingent debt (or structured notes) and swaps are probably the most popular.

Synthetics

A synthetic instrument is one constructed from a combination of different instruments (which could themselves include hybrids and other synthetics) in such a way as to replicate the cash flows of another instrument. As described earlier, options and forward contracts can be used to create synthetics of varying degrees of complexity.

Tax rules that are applied differentially on the basis of how instruments are classified—as is the case with traditional income tax systems—will clearly have problems dealing with synthetics, since, by implication, taxpayers would have the ability to transform one instrument into another to maximize tax benefits. For example, an individual owning a substantially appreciated stock who is interested in selling the stock for a bond could defer the realization of the capital gain by creating a synthetic bond with a short forward contract (see equation (3)). The contract’s delivery price, which would be equal to the stock’s current appreciated value compounded over the life of the contract, once set, would not change regardless of the future movements in the stock price; thus, the price of the contract takes on the character of the principal of a bond. In this way, investors are able to achieve their objectives and defer tax on both the capital gain (from selling a stock) and the interest income (from acquiring a real bond) until the forward contract matures.

Synthetics constructed from multiple components also allow taxpayers to selectively realize losses of some components without realizing offsetting gains in other components at any given point in time. Continuing with the above example, suppose the stock appreciated further after the short forward contract had been struck by the individual, in which case the value of the contract would have gone down.² Instead of waiting for the contract to mature, the individual could now choose to close out the contract and hold on to the stock.³ In this way, a loss is realized (on the forward transaction) without realizing the accrued gain (on the stock) at the same time, which would allow the individual to reap substantial tax benefits stemming from the deferred recognition of the gain.

Marking to Market

Marking to market for tax purposes means that, at the end of each tax period, the gain or loss on an instrument—calculated as the difference between its market value and cost basis—would be recognized by the holder as if it were sold (and repurchased). The cost basis would be adjusted upward (downward) for any cash payment paid (received) during the period. If implemented comprehensively, this approach overcomes the temporal asymmetry by applying the same rate of tax to market-determined gains and losses and overcomes the intertemporal asymmetry by eliminating the timing consideration for income recognition.

Marking broadly traded instruments to market is straightforward and, in fact, is already widely practiced (futures, for example). However, many derivatives are not traded or are traded thinly, so that a reliable market price cannot be established. For these “off-market” derivatives, marking to market would present significant valuation difficulties, even if their underlying assets are themselves broadly traded. If marking to market is applied only to some instruments but not to others because of the valuation problem, then tax arbitrage opportunities would remain and taxpayers could reengineer their portfolios so that marking to market would, in effect, be applied only at their discretion.

Another difficulty with marking to market is that taxing unrealized gains imposes a cash-flow burden on taxpayers that could become real if the gains are not eventually realized. For example, suppose an instrument is held not for speculative purposes but solely because it is a perfect hedge for an underlying asset. Then, by assumption, no net gain would materialize when the position on the underlying asset is closed out. Yet tax liabilities could be incurred if the hedging instrument is marked to market but the hedged asset is not.

Finally, marking to market is incompatible with many features of a traditional income tax system, such as the differentiation of debt from equity and of ordinary income from capital gains. To the extent that such features are maintained for other tax policy reasons, ad hoc rules would be required to resolve this incompatibility. For example, in the United States, all gains and losses from trading futures are considered capital in nature. However, for noncorporate taxpayers, they are considered 60 percent long term and 40 percent short term (the so-called “60/40 rule,”—the application of which does not depend on the length of the period the traded futures are actually held), the latter being taxed in the same way as ordinary income. For hedging transactions, gains and losses are recognized only when the associated positions on the hedged assets are closed out.

Retrospective Taxation

An alternative approach to marking to market, first proposed by Auerbach⁴ and later generalized by Bradford⁵, involves taxing gains and losses retrospectively. This approach is equally effective in neutralizing both the temporal and intertemporal dimensions of tax arbitrage engendered by the use of derivatives. The basic idea is best illustrated with a simple example. Suppose an asset bought exactly two years ago is sold today at $121, and the risk-free interest rate during this period was 10 percent per year. Under the Auerbach proposal, the asset’s acquisition price would be presumed to be $100, and the tax liability in the two years would be the applicable tax rate (say, 30 percent) on the gains calculated on the basis of the risk-free interest rate, that is, $3 in the first year and $3.3 in the second year. However, since the tax for the first year is not paid until the second year, the taxpayer would owe $0.3 in interest on the deferred tax payment, making a total gross payment in tax and interest of $6.6. If the interest payment is tax deductible, it would generate a tax deduction of $0.09. The net tax and interest payment would thus be $6.51.⁶

In essence, the Auerbach proposal taxes only the risk-free rate of return from holding an asset. The actual gain or loss net of the risk-free rate—which represents the risk premium—is left untaxed and is, therefore, inconsequential for tax purposes. Hence, there is no incentive for taxpayers to engage in temporal or intertemporal tax arbitrage. Implementing the Auerbach proposal requires neither information on the actual acquisition cost of the asset nor adjustments to the asset’s cost basis (as would be required under the mark-to-market approach). Of course, under this approach, a tax liability may arise even if a capital loss is incurred.

The conceptual validity of the proposal is based on the theoretical consideration that, since an income tax reduces both net-of-tax gains and net-of-tax losses (assuming losses are tax deductible), the risk-adjusted tax liability on the risk premium should be zero. The Bradford proposal generalizes the Auerbach proposal by taxing the risk premium at an artificial rate⁷ and becomes identical to the latter when this rate is chosen to be zero. It thus captures some income in the tax net that is left out by the Auerbach proposal but provides no opportunity—like the Auerbach proposal—for tax arbitrage.

Bifurcation

The bifurcation approach to taxing derivatives is based on the straightforward logic that, since a derivative is constructed from different components, these components should be taxed separately. Under this approach, for example, the second portfolio discussed in the contingent debt section earlier would be taxed just like the first portfolio, a fixed-interest debt and a long forward contract on the stock. In theory, bifurcation would remove the incentive to enter into derivative positions for tax reasons. Moreover, it would preserve the different tax treatments accorded to certain types of assets under traditional income tax systems.

The most serious argument against bifurcation is that there is no unique way of bifurcating a derivative, since it can be constructed from a multitude of different combinations of underlying components. Returning again to the contingent debt example above, the fixed-debt and long-forward contract components could themselves be further bifurcated into different instruments, potentially producing different tax consequences.⁸ Similarly, a swap between streams of fixed and variable cash flows could also result in different tax consequences, depending on whether the swap is bifurcated into fixed- and floating-rate bonds or into a series of forward contracts. Bifurcation has also been criticized on the grounds that the very act of constructing a derivative creates additional economic value (arising from synergy) that its components lack by themselves. If valid, this criticism would render bifurcation conceptually suspect.

Integration

In contrast with bifurcation, the integration approach links a derivative to other instruments with which it has some associative attributes and taxes them as a combined unit. Obviously, integration could differ in degree. Some integration rules are partial, in that the tax system identifies only specified transactions for combined taxation. A “straddle”—a combination of a long call with a long put on the same underlying asset at the same strike price and expiration date—is a classic example. While gains and losses on the call and put are always offsetting, taxpayers would benefit if they were allowed to electively realize losses. An integration rule in this case could deny such elective realization of losses until both the call and the put positions are closed out. An integration rule that specifies that gains and losses on a hedging transaction are deferred until the hedge instrument is closed out is also partial, because a fuller integration rule could, instead, defer all gains and losses on the hedge instrument until the underlying hedged asset is closed out.

Just like bifurcation, however, where the extent to which a derivative should be bifurcated for tax purposes is unclear, integration can be criticized in that the degree to which transactions should be integrated is ambiguous. Moreover, regardless of degree, integration requires the identification of linked transactions, which, in many cases, is administratively difficult to achieve, since the intent of the taxpayer would need to be ascertained. For example, the linked transactions, if any, to many hybrids (such as swaps) are almost impossible to verify.