Working Paper 287

Underhedging 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 287wp.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 

 

This is Bob Jensen's answer file.
Foreign Currency Hedge of Fixed-Rate Interest-Bearing Foreign 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 12.00% per annum or 3.00% 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   $0 $0 $0
09/30/01 2.0225 600000 ($4,587) ($3,891) $0
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 $0 $0
 
Assume that the FX hedge is perfectly effective for whatever portion
of the loan is being hedged.
1 = Question Number
1 If XYZ Company does not enter into the swap with ABC Bank, what
1 interest rate risk and foreign currency risks are faced by XYZ?
1
1 There is no interest rate risk, because its DM20 million outstanding loan has a
1 fixed 12.00% rate of interest.   However, since the interest is payable in German
1 marks, there is a foreign currency risk in that the amount of dollars needed to
1 acquire the German marks for each payment may vary with the DM/$ FX rate.
1 Also there is a huge foreign exchange risk on the DM20 million that must be
1 repaid at maturity of the loan.
1
1 Since the DM20 million note is at a fixed rate, there is a fair value risk in that
1 the value of the note will vary inversely with movements in interest rates.  
1 XYZdid not hedge fair value with this swap since all legs of the swap are at fixed
1 interest rates.
2
2 = Question Number
2
2 If XYZ Company swaps with ABC Bank, is this a cross-currency hedge for XYZ Company?
2
2 No!  Both legs of the hedge have a fixed rate of interest.  For a cross-currency
2 hedge, one of the legs must have a variable (floating) rate.  You can read
2 about cross-currency hedges under "Foreign Currency Hedges" in Bob Jensen's
2 FAS 133 and IAS 39 Glossary at the website shown below:
2 http://www.trinity.edu/ACCT5341/speakers/133glosf.htm#F-Terms
2  
3
3 = Question Number
3 ABC Bank is taking on a FX risk by by agreeing to send an uncertain amount of
3 German marks to XYZ Company each quarter.  Why might ABC Bank want to
3 enter into such a swap?
3
3 ABC Bank might be hedging an investment that returns quarterly cash flows
3 in German marks.  The swap, thereby, hedges some or all of the FX risk of
3 investment.
3
3 ABC Bank may have better credit standing in Germany than in the U.S.  As a
3 result of the swap, ABC Bank may have obtained its best possible
3 loan in U.S. dollars.
3
3 Of course ABC Bank might also be speculating that the German mark is
3 going to weaken against the dollar.  It is more likely, however, that ABC
3 Bank has one of the other reasons mentioned above.
4
4 = Question Number
4 If the DM20 million debt has a fixed rate of 12.00%, has XYZ Company underhedged
4 or overhedged its FX risk with the specified swap with ABC Bank?  How much
4 was lost or gained by not having a matched hedge (assuming no added speculation)?
4
4 Make a table showing the extent of underhedging or overhedging each quarter
4 ex post after the incurred DM/$ foreign exchange rates are know for certain.
4  
4 Recall that there are two types of FX risk involved.  The huge FX risk of having
4 DM20 million marks available at the debt's maturity date is perfectly hedged by
4 the swap.  The quarterly interest payments of DM600,000 under the 12.00% loan
4 rate, however, are underhedged since the swap only returns DM510,000 to XYZ.
4 That leaves DM90,000 German marks in the payment that are subject to FX
4 risk.
4
4 The amount of underhedging is DM90,000 = DM600,000-DM510,000.  This translates
4 into a$19,142 opportunity loss from not having a matched hedge of $34,282.
4
4
4 Actual Interest Expense      
4 0.1200 0.1200 12.00% 12.00% Under or
4   Ex Post Unhedged Hedged Note Swap Hedge Received Matched Overhedged Underhedged (Over)
4   Spot DM/$ Interest Interest Interest Rec. Leg 0.1027 Swap Due to Due to Hedged
4 Quarter Rate in DM in DM in DM Fixed Rate Swap Rec. Leg Swap Rec. Leg Swap in $ Swap in $ Amount
4 07/01/01 2.0000                  
4 09/30/01 2.0225 90000 510000 600,000 0.1020 $252,163 $252,163 $0 $44,499 $44,499
4 12/31/01 2.0150 90000 510000 600,000 0.1020 $253,102 $253,102 $0 $44,665 $44,665
4 03/31/02 1.9875 90000 510000 600,000 0.1020 $256,604 $256,604 $0 $45,283 $45,283
4 06/30/02 1.9750 90000 510000 600,000 0.1020 $258,228 $258,228 $0 $45,570 $45,570
4 09/30/02 1.9685 90000 510000 600,000 0.1020 $259,081 $259,081 $0 $45,720 $45,720
4 12/31/02 1.9480 90000 510000 600,000 0.1020 $261,807 $261,807 $0 $46,201 $46,201
4 03/31/03 1.9325 90000 510000 600,000 0.1020 $263,907 $263,907 $0 $46,572 $46,572
4 06/30/03 1.9300 90000 510000 600,000 0.1020 $264,249 $264,249 $0 $46,632 $46,632
4       $2,069,140 $2,069,140 $0 $365,142 #######
4      
4     Case Hedge Hypothetical Overhedging 0.1200   12.00% Interest Expense        
4     12.00% Matched Hedge of Proportion Change in Swap Value 12.00% 0.00% 10.20% 12.00% Under or
4   Ex Post With a With a 10.20% Overhedged Swap's (Overhedged) With a Without Amount Amount (Over)
4   Spot DM/$ 10.20% 12.00% Versus Due to Estimated Due to 10.20% The Saved by Saved by Hedged
4 Quarter Rate Swap Rec. Leg Swap Rec. Leg 0.1200 Swap in % Value Swap in $ Swap Rec. Leg Swap Swap Matched Swap Amount
4 07/01/01 2.0000         $0            
4 09/30/01 2.0225 10.20% 12.00% 0.00% 0.0000 ($3,891) $0 $296,663 $296,663 ($4,587) $39,913 $44,499
4 12/31/01 2.0150 10.20% 12.00% 0.00% 0.0000 $8,887 $0 $297,767 $297,767 ($3,648) $41,017 $44,665
4 03/31/02 1.9875 10.20% 12.00% 0.00% 0.0000 $976 $0 $301,887 $301,887 ($146) $45,137 $45,283
4 06/30/02 1.9750 10.20% 12.00% 0.00% 0.0000 $3,799 $0 $303,797 $303,797 $1,478 $47,047 $45,570
4 09/30/02 1.9685 10.20% 12.00% 0.00% 0.0000 $4,020 $0 $304,801 $304,801 $2,331 $48,051 $45,720
4 12/31/02 1.9480 10.20% 12.00% 0.00% 0.0000 ($2,054) $0 $308,008 $308,008 $5,057 $51,258 $46,201
4 03/31/03 1.9325 10.20% 12.00% 0.00% 0.0000 ($4,090) $0 $310,479 $310,479 $7,157 $53,729 $46,572
4 06/30/03 1.9300 10.20% 12.00% 0.00% 0.0000 ($7,646) $0 $310,881 $310,881 $7,499 $54,131 $46,632
4 Interest on note = $2,434,282 $2,434,282 $15,140 $380,282 $365,142
4   Swap loss (gain) = ($15,140) ($380,282) #######  
4 Change in RE = $2,419,142 $2,054,000 #######
4 Deviation of  the actual hedge from matched hedge = ($365,142)
4 Matched hedge outcome = $2,054,000 if the hedged note rate = 10.20% instead of 12.00%
4 (Note that just because the hedge i