Bob Jensen's Working Paper 288 Case on Overhedging Foreign Currencies With a Swap

Working Paper 288

Overhedging Foreign Currencies With a Swap:
The FAS 133 Controversy

Bob Jensen at Trinity University

This case was inspired, in part, by a speaker that I lined up for a module in a FAS 133 workshop that I chaired in New York City in December of 1999. His name is Martin Klein from the Lehman Brothers office in New York City. You can listen to a segment of his presentation by clicking on the hotlink below:

Martin Klein from Lehman Brothers Audio Clip KLEIN10.mp3

This case and answer derivations are best viewed in an Excel workbook file 288wp.xls that can be downloaded from http://www.cs.trinity.edu/~rjensen/

Links to my other online FAS 133 cases are given in http://www.trinity.edu/rjensen/caseans/000index.htm

Definitions and other helpers are given at http://www.trinity.edu/rjensen/acct5341/speakers/133glosf.htm

Questions

This is Bob Jensen's answer file.

Foreign Currency Hedge of Fixed-Rate Interest-Bearing Foreign 8.00% Debt

XYZ Company's existing DM obligation

On July 1, 20X1, XYZ Company has an obligation to make eight remaining interest payments

in German marks at DM600,000 per quarter on a DM20 million outstanding note payable. The

fixed-interest rate is 8.00% per annum or 2.00% per quarter. David Burns, the

the CFO of XYZ, worries that the the German mark will grow stronger against the U.S. dollar,

leading to foreign currency losses in both the DM600,000 payments and the $20 million pay off.

XYZ enters into a currency swap with ABC Bank

On July 1, 20X1, ABC Bank enters into a two-year pay-fixed German DM 10.25%, receive-fixed

US$ 10.22%. The swap dealer that negotiates the swap and guarantees payments

takes 5 basis points (0.05%) such that the ABC receives US$ 10.22% of 10.27% owed by XYZ, and

XYZ receives only DM 10.20% from the 10.25% owed by ABC. Hence, XYZ owes $256,750

on the swap each quarter and receives DM510,000 in return. The swap is actually

net settled using the spot currency exchange rate at the end of each quarter.

One of the purposes of this case is to analyze underhedging versus overhedging of swaps

that are not perfect matches for hedging. This case is does not have a matched hedge,

because the 8% hedged item note rate is not equal to the 10.2% swap receivable leg of

the hedging swap. To be a matched hedge, both interest rates would have to be equal.

Suppose we define the swap receivable rate as (R+U), where R is the rate of the hedged

item and U is the underhedged or overhedged rate. For example, when (R+U)=.1020, then

a note rate of R=0.1020 implies that this is a "matched hedge" with U=0. However, if R=0.0800,

there is an overhedging of U=0.022 or 2.20%. Conversely, if R=0.1200, there the hedged item

the hedged item is underhedged by 0.1020-0.1200 = -0.0180 or -1.80%.

When the hedged item is underhedged, some FX risk remains, because not all of the

hedged item is protected from fluctuations in foreign currency rates. When the hedged

item is overhedged, then there is also foreign exchange risk of receiving too many

German marks relative to the note's interest rate. Under FAS 133, all changes in the

swap value can be charged to Other Comprehensive Income (OCI) only if there is no

overhedging. If there is overhedging the proportion of the changes in value of the swap

must be charged to current earnings rather than OCI. When u>0, that proportion

is u/(r+u).

At the beginning of the swap, notional amounts are exchanged such that ABC receives

DM20 million and pays XYZ $10 million in US dollars. When the swap is terminated,

ABC receives its $10 million back and returns the DM20 million to the XYZ Company. XYZ

in turn, uses this DM20 million to pay off its existing debt in German marks on June 30, 2003.

In summary, XYZ company declares the swap with ABC Bank as a foreign currency hedge

against its existing obligation. Since only DM510,000 is received each quarter under the swap, the swap

leaves XYZ DM90,000 short of a matched hedge needed for DM600,000 payments

Assume the following ex post outcomes with respect to XYZ Company's books:

Ex Post

Loan

XZY Net

Swap's

XYZ

Spot DM/$

Payment

Swap

Estimated

Accrued

Quarter

Rate

in DM

Cash Flow

Value

Interest

07/01/01

2.0000

09/30/01

2.0225

600000

($4,587)

($3,891)

12/31/01

2.0150

600000

($3,648)

$4,996

($100)

03/31/02

1.9875

600000

($146)

$5,972

$128

06/30/02

1.9750

600000

$1,478

$9,770

$153

09/30/02

1.9685

600000

$2,331

$16,782

$251

12/31/02

1.9480

600000

$5,057

$11,737

$431

03/31/03

1.9325

600000

$7,157

$7,646

$301

06/30/03

1.9300

600000

$7,499

Assume that the FX hedge is perfectly effective for whatever portion

of the loan is being hedged.

= Question Number

If XYZ Company does not enter into the swap with ABC Bank, what

interest rate risk and foreign currency risks are faced by XYZ?

There is no interest rate risk, because its DM20 million outstanding loan has a

fixed 8.00% rate of interest. However, since the interest is payable in German

marks, there is a foreign currency risk in that the amount of dollars needed to

acquire the German marks for each payment may vary with the DM/$ FX rate.

Also there is a huge foreign exchange risk on the DM20 million that must be

repaid at maturity of the loan.

Since the DM20 million note is at a fixed rate, there is a fair value risk in that

the value of the note will vary inversely with movements in interest rates. XYZ

did not hedge fair value with this swap since all legs of the swap are at fixed

interest rates.

= Question Number

If XYZ Company swaps with ABC Bank, is this a cross-currency hedge for XYZ Company?

No! Both legs of the hedge have a fixed rate of interest. For a cross-currency

hedge, one of the legs must have a variable (floating) rate. You can read

about cross-currency hedges under "Foreign Currency Hedges" in Bob Jensen's

FAS 133 and IAS 39 Glossary at the website shown below:

http://www.trinity.edu/ACCT5341/speakers/133glosf.htm#F-Terms

= Question Number

ABC Bank is taking on a FX risk by by agreeing to send an uncertain amount of

German marks to XYZ Company each quarter. Why might ABC Bank want to

enter into such a swap?

ABC Bank might be hedging an investment that returns quarterly cash flows

in German marks. The swap, thereby, hedges some or all of the FX risk of

investment.

ABC Bank may have better credit standing in Germany than in the U.S. As a

result of the swap, ABC Bank may have obtained its best possible

loan in U.S. dollars.

Of course ABC Bank might also be speculating that the German mark is

going to weaken against the dollar. It is more likely, however, that ABC

Bank has one of the other reasons mentioned above.

= Question Number

If the DM20 million debt has a fixed rate of 8.00%, has XYZ Company underhedged

or overhedged its FX risk with the specified swap with ABC Bank? How much

was lost or gained by not having a matched hedge (assuming no added speculation)?

Make a table showing the extent of underhedging or overhedging each quarter

ex post after the incurred DM/$ foreign exchange rates are know for certain.

Recall that there are two types of FX risk involved. The huge FX risk of having

DM20 million marks available at the debt's maturity date is perfectly hedged by

the swap. The quarterly interest payments of DM600,000 under the 8.00% loan

rate, however, are overhedged since the swap returns DM510,000 to XYZ when

only DM400,000 are needed for the quarterly interest payments on the 8.00% note.

The amount of overhedging is -DM110,000 = DM400,000-DM510,000. This translates

into a $7,715 opportunity loss from not having a matched hedge of $22,855.

Sensitivity Analysis: You can change the value in blue Cell G68 from the original 8.00%:

Actual

Interest Expense

You can change XYZ's original unhedged note rate to R in Cell G68 =

0.0800

8.00%

Under or

Ex Post

Unhedged

Hedged

Note

Swap Hedge

Received

Matched

Overhedged

Underhedged

(Over)

Spot DM/$

Interest

Rec. Leg

0.1027

Swap

Due to

Hedged

Quarter

Rate

in DM

Fixed Rate

Swap Rec. Leg

Swap in $

Amount

07/01/01

2.0000

09/30/01

2.0225

(110000)

400000

400,000

0.1020

$252,163

$197,775

($54,388)

12/31/01

2.0150

(110000)

400000

400,000

0.1020

$253,102

$198,511

($54,591)

03/31/02

1.9875

(110000)

400000

400,000

0.1020

$256,604

$201,258

($55,346)

06/30/02

1.9750

(110000)

400000

400,000

0.1020

$258,228

$202,532

($55,696)

09/30/02

1.9685

(110000)

400000

400,000

0.1020

$259,081

$203,200

($55,880)

12/31/02

1.9480

(110000)

400000

400,000

0.1020

$261,807

$205,339

($56,468)

03/31/03

1.9325

(110000)

400000

400,000

0.1020

$263,907

$206,986

($56,921)

06/30/03

1.9300

(110000)

400000

400,000

0.1020

$264,249

$207,254

($56,995)

$2,069,140

$1,622,855

($446,285)

Case Hedge

Hypothetical

Overhedging

0.0800

8.00%

Interest Expense

8.00%

Matched Hedge

Proportion

Change in

Swap Value

8.00%

0.00%

10.20%

8.00%

Under or

Ex Post

With a

10.20%

Overhedged

Swap's

(Overhedged)

With a

Without

Amount

(Over)

Spot DM/$

10.20%

8.00%

Versus

Due to

Estimated

Due to

10.20%

The

Saved by

Hedged

Quarter

Rate

Swap Rec. Leg

0.0800

Swap in %

Value

Swap in $

Swap Rec. Leg

Swap

Matched Swap

Amount

07/01/01

2.0000

09/30/01

2.0225

10.20%

8.00%

2.20%

0.2750

($3,891)

$1,070

$197,775

($4,587)

($58,975)

($54,388)

12/31/01

2.0150

10.20%

8.00%

2.20%

0.2750

$8,887

($2,445)

$198,511

($3,648)

($58,239)

($54,591)

03/31/02

1.9875

10.20%

8.00%

2.20%

0.2750

$976

($268)

$201,258

($146)

($55,492)

($55,346)

06/30/02

1.9750

10.20%

8.00%

2.20%

0.2750

$3,799

($1,044)

$202,532

$1,478

($54,218)

($55,696)

09/30/02

1.9685

10.20%

8.00%

2.20%

0.2750

$4,020

($1,106)

$203,200

$2,331

($53,550)

($55,880)

12/31/02

1.9480

10.20%

8.00%

2.20%

0.2750

($2,054)

$565

$205,339

$5,057

($51,411)

($56,468)

03/31/03

1.9325

10.20%

8.00%

2.20%

0.2750

($4,090)

$1,125

$206,986

$7,157

($49,764)

($56,921)

06/30/03

1.9300

10.20%

8.00%

2.20%

0.2750

($7,646)

$2,103

$207,254

$7,499

($49,496)

($56,995)

Interest on note =

$1,622,855

$15,140

($431,145)

($446,285)

Swap loss (gain) =

($15,140)

$431,145

($446,285)

Change in RE =

$1,607,715

$2,054,000

($431,145)

Deviation of the actual hedge from matched hedge =

$446,285

Matched hedge outcome =

$2,054,000

if the hedged note rate =

10.20%

instead of

(Note that just because the hedge is not matched, does not make it ineffective under FAS 133 definitions of ineffectiveness.)

The value of the swap each quarter is not affected directly by interest rate movements
unless the swap has at least one variable rate leg.

Thus, in hind sight the German mark strengthened against the dollar, and

the hedge saved XYZ Company $15,140. A matched swap would have

generated another $7,715 to fully hedge all DM600,000 per quarter.

Of course, if the German mark had weakened, XYZ Company would have

lost on the swap.

= Question Number

How come the gain on the swap is the same $15,140 when the note's interest

rate is 12.00% or 8.00%? Shouldn't the XYX Company earn higher profits on

as a result of having a lower note interest?

Actually the XYZ Company has less interest expense when the note's interest

is 8.00% instead of 12.00%. However, the net swap cash flows depend upon the

fixed rates of interest on the swap legs. This rate does not change with the

hedged item (DM 10 million note) rate.

= Question Number

Record the DM 20 million loan as if it commenced on July 1, 20X1, and then

record all interest payments, swap payments, interest accruals, and the adjustment

of the swap to fair value each quarter. For the interest accruals, simply multiply

the swap balance (value) at the end of the previous period by 2.55% = 10.2%/4.

Hint: If the loan interest payments are underhedged, assume all the change in

the swap's value can be charged to Other Comprehensive Income (OCI). However,

if there is an overhedge, the overhedged proportion of changed swap value must

be charged to current earnings (Interest Expense and Revenue) rather than OCI.

Be able to reason why this is the case.

= Question Number

Does the earnings impact differ with respect to overhedging versus underhedging

in this illustration? Explain the importance to XYZ Company.

With underhedging, all changes in XYX's swap value were debited or credited

to Other Comprehensive Income (OCI). Hence, changes in swap value did not

impact upon the level or variability or earnings per share.

With overhedging, it is a different matter. When XYZ Company has more German

marks coming in than are needed to make the hedged item's payments, a portion of the change in the swap value providing those excess marks must be debited

or credited to current earnings rather than OCI. Those portions of swap value

change impact both upon the amount and variability of net income. Furthermore,

those "excess" value changes do not affect cash flows. In other words, a large

increase in swap value due to overhedging will not increase the amount of cash

in the till beyond what the net swap cash flows themselves. You can see this by

examining the journal entries in this case.

= Question Number

Show the impact of under hedging versus overhedging on quarterly earnings,

assuming a 10.2% swap receivable leg that is specified in this case. In other words,

keep the swap receivable rate constant, but vary the DM20 million note's interest rate

across 6%, 7%, 8%, 9%, 10.2%, 11%, and 12$.

Hint: The 8% and 12% outcomes are shown below:

10.2% Swap Receivable

XZY Net

Swap's

Loss (Gain)

Swap

Estimated

From

Cash Flow

Value

Overhedge

07/01/01

($4,587)

($3,891)

$839

09/30/01

($3,648)

$4,996

($1,917)

12/31/01

($146)

$5,972

($211)

03/31/02

$1,478

$9,770

($819)

06/30/02

$2,331

$13,791

($867)

09/30/02

$5,057

$11,737

$443

12/31/02

$7,157

$7,646

$882

03/31/03

$7,499

$1,649

Overhedging Total =

XYZ Loan Rate on DM20 Million Note =

8.00%

12.00%

= Question Number

Show the underhedging or overhedging dollar amount portions of a 10.2% hedging

swap receivable leg used to hedge the $20 million note at interest rates varying

across 6%, 7%, 8%, 9%, 10.2%, 11%, and 12$.

Hint: The 8%, 10.2%, and 12% outcomes are shown below:

10.2% Swap

Under or

XZY Net

(Over)

Swap

Hedged

Cash Flow

Amount

07/01/01

($4,587)

(54,388)

44,499

09/30/01

($3,648)

(54,591)

44,665

12/31/01

($146)

(55,346)

45,283

03/31/02

$1,478

(55,696)

45,570

06/30/02

$2,331

(55,880)

45,720

09/30/02

$5,057

(56,468)

46,201

12/31/02

$7,157

(56,921)

46,572

03/31/03

$7,499

(56,995)

46,632

($446,285)

$365,142

XYZ Loan Rate =

8.00%

10.20%

12.00%

This case and answer derivations are best viewed in an Excel workbook file 288wp.xls that can be downloaded from http://www.cs.trinity.edu/~rjensen/