Teaching Notes

This case is based on a hypothetical derivatives transaction entered into by an international company in April 1998. In addition to presenting the accounting for an Asian option, this case also presents some of the financial implications of foreign exchange risk and the mechanics of an average price option. The perspective obtained will allow students to critically analyze the accounting methods in this case and in future path-dependent options that they encounter. The objectives of this case are achieved primarily by facilitating the development of logic through the questions.

This case is appropriate for an advanced accounting course in teachings related to derivative financial instruments. The case allows students to recognize the importance and usefulness of customized over-the-counter financial instruments in hedging a company’s risk.

Solution for Question #1.

In April, 1998, one dollar could buy 130 (1/0.00769) yen. By March of the following year, one dollar could buy only 97 (1/0.01031) yen. In the year studied, the buying power of the US Dollar decreased over 25%. As such, an American importer such as TEC can import far fewer products for the same number of US dollars. In TEC's case, a ¥1 million shipment in April 1998 cost them $7,692 (¥1,000,000 * 0.00769 rate). In March, a similar ¥1 million shipment cost the company $10,310 (¥1,000,000 * 0.01031 rate), an increase of over 25%! As described in the case, TEC purchased an Asian call option to hedge the depreciation of the dollar.

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Solution for Question #2.

TEC's primary concern regarding the decision to hedge against the appreciation of the yen was the extreme volatility of Asian currencies in the preceding year. The Asian economic crisis made American companies acutely aware of the risk in having exposure to movements in the foreign exchange markets. Risk averse companies rushed to find a way to hedge their foreign currency exposure. For further readings describing the causes of Asia's economic and currency crisis, click here.

The fluctuations in Japan's currency made TEC's cost of importing Japanese goods uncertain. A hedge against the foreign exchange risk stabilized TEC's expected expenditures.

Another reason for concern was the extremely large trade deficit with Japan (click here for additional information concerning the trade deficit). Because of its huge trade surplus with the US, many analysts still predict that the yen will appreciate further against the dollar. The prospective appreciation of the yen will create risks for American importers of Japanese products because they will have to pay more for the same products (Zhang, 128).

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Solution for Question #3.

As described in the glossary, Asian options are options based on some average underlying asset prices, indices, or rates. They are the natural development of vanilla options to capture path-dependence. At the end of a vanilla call option's life, it is either in-the money or out-of-the-money, depending on the spot price of the underlying asset or rate. The path that the underlying asset or rate took to get to that spot price is not taken into consideration. By using an average to attain the underlying asset price or rate, Asian options are considered path-dependent; each price observed throughout the life of the option is taken into consideration when calculating the final price. Aside from the path-dependent characteristic, Asian options are less susceptible to possible spot manipulation at settlement, and their payoffs are generally less volatile than vanilla options. As a result, they offer a cheaper way to hedge periodic cash flows and reduce costs for importers (Zhang, 111).

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Solution for Question #4.

If the yen depreciates throughout the year, American importers such as TEC will pay less for the same products. The depreciation of the yen would give TEC more buying power, paying less US Dollars for each of Sayanora's ¥1 million shipments.

To illustrate, assume the following

In the table above, the value of the yen depreciated throughout the year. Each month, TEC made a ¥1 million payment for the Japanese products. The dollar equivalent of the ¥1 million decreased each month with the yen devaluation. As a result, TEC paid less for the same amount of products. This would be an ideal situation for TEC. At the end of March (the expiration date of the Asian call option), TEC would decide not to exercise the Asian call option that they purchased the preceding year; the option will simply expire.

The original cost of the option to hedge TEC's foreign exchange risk is a sunk cost, and cannot be recovered. In effect, the cost of the option is TEC's insurance against adverse movements in the US Dollar/Japanese Yen foreign exchange rate.

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Solution for Question #5.

To hedge its foreign exchange rate risk, TEC could have tried to hedge each month's exposure separately. The company could accomplish this by purchasing a series of vanilla call options with monthly expiries. In practice, however, this has a number of drawbacks. The key drawback is the cost of a string of options. Since the buyer will selectively exercise the options against the seller, the overall payout will be higher and therefore the premium will be larger (Turner, 23).

To obtain the price of each monthly vanilla call option, the Black-Scholes model is used. The Black-Scholes formula is as follows:

where

The values of each variable are as follows:

(Zhang, 56)

Using the above formulas, and assuming S=0.00769, g=0.03, K=0.00769, r=0.07, and st.dev=25%, the values of separate vanilla call options for each month studied are as follows:

As will be shown in Question/Solution#6, the price of the monthly vanilla call options is nearly twice that of the single Asian option. Both strategies sufficiently hedge the foreign exchange risk encountered by TEC during the year; the Asian call option, however, is much cheaper.

Using 12 separate vanilla call options is really a case of over-insurance: the company should always be clear at the outset what they are insuring against. To take a simple example, if TEC announces its results annually, profits and losses for that year can be netted out, the company can therefore take a one year view, and buy insurance on that basis. To use monthly insurance costs more money and is at odds with the way in which the business is run.

Also, it is worth mentioning the practical side of managing the options. From the dealer's perspective, the overall costs will be higher for a string of small options than for a single larger position - this cost will be reflected in the prices quoted to the customer. From the customer's perspective, the more positions there are to manage, the more management time will be absorbed (Turner, 23). Therefore, it is not practical to use monthly vanilla call options when an Asian call option is available.

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Solution for Question #6.

In order to price a geometric Asian call option, the Black-Scholes Model is modified to accommodate the unique features of the option. The student must be given the distribution of the geometric average, the time to maturity of the option, the observation frequency, the number of observations, and the distribution of the underlying asset price or exchange rate.

Through extensive derivation, the value of an Asian Call Option Premium is calculated as follows:

where

The following legend lists and explains each variable:

(Zhang, 119)

Using the formulas above, and assuming n=12, j=0, t=1, and h=1/12, Tµ was calculated as 0.5417 and T^sa was calculated as 0.3762. Since no observations had yet been made, B^sa(j) = 1. Using these values, d^sa was calculated as 0.0309, and A^sa was calculated as 0.9634.

After completing these preliminary calculations, the value of the Asian call option (C^sa) can be calculated. Plugging in the values found above, and assuming r=7%, g=3%, st.dev=25%, and the US Dollar/Japanese spot exchange rate=0.007692, the following equation is obtained:

C^sa = (1)(0.007692)(0.9634)(12)(e^-0.016251)N[(1)(0.0309)+(1)(0.25)(0.3762)^1/2]-(1)(0.007692)(e^-0.07(1))N(0.0309)

simplified, C^sa = (0.08749)N[0.18423] - (0.007171973)N[0.5120]

After conferring with a Standard Normal Distribution table, the values for N are plugged in. The net result yields the following value: C^sa = 0.045007264

To attain the dollar value of the geometric Asian call option, the above answer is multiplied by the size of the contract (12 million yen), then multiplied by the US Dollar/Japanese Yen exchange rate at the date of purchase.

C^sa = 0.045007264 * 12 million yen * 0.00769 yen per dollar, which yields the following solution:

As shown in Question/Solution#5, the cost of a series of monthly vanilla call options used to hedge the foreign exchange risk is $7,986. This is significantly more expensive than the cost of the single Asian call option illustrated above. Hence, the Asian call option is the more economically sound business choice to hedge TEC's foreign exchange risk.

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Solution for Question #7.

Although SFAS No. 52 does not permit hedge accounting for anticipated foreign currency transactions, EITF 90-17 reached a consensus that hedge accounting is permissible for anticipated transactions when a purchased foreign currency option (with little or no intrinsic value at the date of purchase) is used to hedge a foreign currency transaction provided that the hedge accounting conditions of SFAS No.80 are satisfied.

Under SFAS No.80, gains and losses resulting from changes in the fair value of a futures contract may be deferred under hedge accounting if all of the following criteria are met:

• The item to be hedged exposes the enterprise to price or interest rate risk.
• The hedged position reduces the exposure (as when there is high correlation between changes in the market value of the hedged position and the inverse changes in market value of the hedged item).
• The hedge position is designated as a hedge (Perry, 49).

Exposure Draft 162-B (ED162) standardizes the accounting for derivative financial instruments by requiring that an entity recognize those instruments as assets or liabilities in the statement of financial position and measure them at fair value. ED162 allows the Asian call option discussed above to be appropriately classified as a "hedge of the exposure to changes in the fair value of...a firm commitment" (FASB, 1).

ED162 carries forward SFAS 119's requirement of disclosing a description of the objectives, context, and strategies for holding or issuing derivatives in the notes. In addition, the disclosure should include additional qualitative and quantitative information for derivatives designated as fair value hedges or cash flow hedges. The board believes that this information is necessary to assist investors, creditors, and other users of financial statements in more fully understanding the nature of an entity's derivative activities and in evaluating the success of those activities, their importance to the entity, and their effect on the entity's financial statements (FASB, 61).

Subsequent to its designation as being hedged, the change in the fair value of a hedged item shall be recognized in earnings in the period of the change only to the extent of offsetting changes in the fair value of the hedging instrument. If some portion of the change in fair value of the hedged item is not recognized in earnings in the period of the change due to the limitation related to offsetting changes in the fair value of the hedging instrument, that portion is available for recognition in earnings in subsequent periods (FASB, 8).

The initial journal entry to record the purchase of the Asian call option on April 1, 1998 is as follows:

The monthly gain or loss on the foreign currency spot rate movements is calculated as: (the strike rate 0.00769 per dollar - current monthly spot rate) * (¥1,000,000 monthly payment). For example, the spot rate at May 31, 1998 (the first month) was 0.00763. The resulting gain is calculated as (0.00769 - 0.00763) * 1,000,000 = $60. The monthly gain (loss) on the foreign currency spot rate movements is as follows:

The total loss through December 31, 1998 (Balance Sheet Date) is $6,950. Using the valuation methods described in Solution #6 above, the value of the Asian call option at December 31 is $10,867, resulting in a $6,714 gain on the call option. Since the loss on the hedged item is only recognized to the extent of the gain on the hedge, only $6,714 is recognized. The remaining $236 loss is deferred to subsequent periods.

The journal entries on December 31, 1998 to record the gain (loss) to date on the purchase commitment and its corresponding Asian call option are as follows:

The loss resulting from the foreign currency rate movement, from 12/31/98 to expiration date, is a $5,030 loss. However, on 3/31/99, the gain on the Asian call option is only $3,982. Therefore, only $3,982 of the loss may be recognized and the remaining $1,048 loss is deferred. The journal entries on March 31, 1999 to record the loss on the purchase commitment and its corresponding Asian call option are as follows:

On March 31, the geometric average of the 12 exchange rate observations was calculated to be $0.00864. Since the geometric average of the exchange rates was above the previously contracted strike price at maturity, TEC decided to exercise the call. As previously discussed, as a natural consequence of the way in which the pay-off is determined, the option is cash settled. The settlement is calculated as follows:

Amount of Option (in Yen) * [Average Spot Rate - Strike Rate] =

¥12,000,000 *($0.00864 - $0.00769) = $11,400.

The journal entry to account for the cash payoff that TEC will receive from exercising the option is as follows:

Finally, the losses that were deferred on December 31, 1998 and March 31, 1999 must now be recognized since the call option has been exercised. The total amount of deferred loss to recognize is $1,284 ($236 + $1,048). The journal entry on March 31, 1999 to recognize this loss is as follows:

The firm losses from the Asian Call Option totaled $11,980 (6,714 + 3,982 + 1,284). The gains from the Asian Call Option total $11,400 (6,714 + 3,982 + 704).

Therefore, TEC has a net loss of $580 (11,980 - 11,400) after the Asian Call Option is exercised. Together with the original cost of the Asian Call Option ($4,153), the total cost of the hedge transaction is $4,733.

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Solution for Question #8.

In today's turbulent financial markets, financial executives responsible for managing exposures to currency risk must evaluate many issues and alternative approaches. Many companies consider effective risk management to be the execution of derivative transactions that take advantage of specific market expectations. It should be recognized, however, that derivatives are only tools and, as such, can be quite harmful to a company's performance if their characteristics are misunderstood or if they are applied without considering their impact on the overall strategy.

In order to avoid some of these pitfalls, TEC should apply a comprehensive approach to managing risk. The comprehensive approach emphasizes the integration of the risk management process with the overall business process of the company. One of the benefits of this approach is that it is not reliant on short-term market views as the basis for hedging exposures. The focus is on a comprehensive program that allows effective risk management using a variety of financial instruments without the need to react to day-to-day market events.

A comprehensive risk management system should incorporate the treasury's market expertise, operation's planning effort, and management's vision through an interactive relationship. Effective communication of exposure information, concerns, and objectives allows the development of an exposure management strategy that avoids the volatility of month-to-month or deal-to-deal hedging activity.

A comprehensive risk management system requires that treasury and operating units work together to identify and quantify activities that generate exposures and to develop the ability to forecast future exposures. The best tool available to estimate and quantify the risk associated with a diverse portfolio of exposures is Value at Risk (VaR). However, TEC's risk lies only in the foreign exchange risk of a series of identical transactions. The expense of instituting a VaR system would far outweigh the benefits.

Since TEC's foreign exchange risk lies only in the series of identical transactions identified in the overview, VaR as a means of quantifying risk is not acceptable. However, the Sensitivity Analysis Methodology may help TEC accurately identify its risk at a relatively low cost. The basic procedure is to assume a movement in a market relationship (for example, the US Dollar/Japanese Yen exchange rate) and calculate the gain or loss on a position resulting from the move. The following is a sensitivity analysis that TEC might make to quantify its foreign exchange risk:

Sensitivity Analysis of the Change in Asian Call Option Payoff in Relation to the Geometric Average of US Dollar/Japanese Yen Exchange Rates at End of March, 1999

As shown, as the foreign exchange rate increases (the dollar depreciates), the payoff of the Asian Call Option increases. As the foreign exchange rate decreases (the dollar appreciates), the hypothetical loss on the Asian Call Option increases. However, the payoff of an Asian Call Option cannot be negative. If the dollar appreciates to the extent that the payoff is negative, the call option is simply not exercised. The company would purchase the Japanese goods at the current spot rate.

To determine its risk, TEC should evaluate the probability of each of the above outcomes, and determine if an Asian Call Option is the appropriate hedging instrument. Sensitivity analysis has a number of drawbacks when applied as a company-wide disclosure method. The main problem relates to choosing the market relationship moves when dealing with multiple exposures. However, since TEC's risk is limited to foreign exchange risk associated with its purchase commitments, sensitivity analysis may be applied.

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