Breakage costs: Difference between revisions

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{{a|banking|{{wmc|breakage costs illustration.jpg|Some breakage costs, yesterday.}}}}{{qd|Breakage costs|/ˈbreɪkɪdʒ kɒsts/|n|{{l1}}(''[[Loan]]s'') The opportunity cost to a [[lender]] of a [[borrower]] repaying a [[loan]] before its stated [[maturity]].<li>
{{a|banking|{{wmc|breakage costs illustration.jpg|Some breakage costs, yesterday.}}}}{{qd|Breakage costs|/ˈbreɪkɪdʒ kɒsts/|n|{{l1}}(''[[Loan]]s'') The opportunity cost to a [[lender]] of a [[borrower]] repaying a [[loan]] before its stated [[maturity]].<li>
(''[[Swap]]s'') the net [[present value]] of the remaining cashflows on a [[swap]].}}  
(''[[Swap]]s'') the net [[present value]] of the remaining cashflows on a [[swap]].}}  
{{drop|B|reakage costs arise}} because the [[lender]] must [[unwind]] its [[interest rate]] [[hedge]]s — usually the difference between the rate payable on the loan for the specified period and the overnight rate. The difference between the [[present value]] of the remaining loan repayments at their stated rate and their present value at the prevailing market rate — that is, the difference between [[present value]] of what I would get if we stuck with the original deal and you repaid the loan at term, and how much I could get if I lent that money out today, at today’s rate, for the remaining term on the original [[loan]]
{{drop|B|reakage costs arise}} because a [[lender]] of money for a fixed term is exposed to changes in interest rates over that term. It will have — can be ''assumed'' to have — hedged the interest rate risk of providing those funds to the end of the committed period, so if it has to [[unwind]] its [[interest rate]] [[hedge]]s beforehand to repay the money, it may make a gain or loss.
 
The ''size'' of interest rate [[breakage costs]] will therefore be a function of (i) how far the prevailing market rates have moved since the contract rate was set, and (ii) how much time remains to the end of the present fixed commitment period. There will be often be a “hump”: breakage costs will tend to ''increase'' as the market rate diverges from the fixed rate (on day 1 they will be the same) then ''decrease'' again as the number of days remaining in the fixed term period (by which the increasing differential is multiplied) diminishes to zero.
 
The breakage costs on a 5-year fixed period on a mortgage loan are therefore, potentially large, which is why it is so expensive to repay a fixed mortgage early. The breakage costs on loan that resets its interest every month (a floating rate loan) will be much smaller. The breakage costs on overnight deposits will be, by definition, nil.
====Swap break costs====
{{drop|T|he same principle}} holds for [[swap break costs]], only the comparison will be the prevailing market rate for the reference asset against its value when the swap was executed (its “strike price”).
 
On the [[Trade Date - ISDA Provision|trade date]] an asset’s strike place and its market price are, [[Q.E.D.]], the same. On any other day [[swap break costs]] will generally be simply the breakage cost of the asset leg, payable one way, less the breakage costs of the financing leg, payable the other. The financing leg is explicitly an interest rate breakage cost; the asset break is by analogy one. In each case, the same “time decay” effect and “duration hump” effect should be in play.


On the [[Trade Date - ISDA Provision|trade date]] those values must have been equal and on any other day [[swap break costs]] will generally be simply the uncollateralised [[mark-to-market]] value, or the [[replacement cost]], of the existing transaction. You could also reach that conclusion by going through the motions:
*If I terminated this [[swap]] today, what would its [[MTM]] be? This is the equivalent of “the [[present value]] of the remaining payments".
*If I traded a new [[swap]] at today’s prices, what would its [[MTM]] be? According to the theory of [[homo economicus]], this ought necessarily to be ''zero'' — any other value would mean I was entering into an off-market [[swap]].<ref>Note that upfront [[PV]] of fees — especially on exotic derivatives, [[CPPI]] and that sort of thing, might mean the MTM of a swap immediately drops to factor in that, whatever else the hell happens, the dealer will have its fee for the whole period, capisce?</ref>
{{sa}}
{{sa}}
*[[Present value]]
*[[Present value]]

Revision as of 12:24, 2 November 2024

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Some breakage costs, yesterday.
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Breakage costs
/ˈbreɪkɪdʒ kɒsts/ (n.)

  1. (Loans) The opportunity cost to a lender of a borrower repaying a loan before its stated maturity.
  2. (Swaps) the net present value of the remaining cashflows on a swap.

Breakage costs arise because a lender of money for a fixed term is exposed to changes in interest rates over that term. It will have — can be assumed to have — hedged the interest rate risk of providing those funds to the end of the committed period, so if it has to unwind its interest rate hedges beforehand to repay the money, it may make a gain or loss.

The size of interest rate breakage costs will therefore be a function of (i) how far the prevailing market rates have moved since the contract rate was set, and (ii) how much time remains to the end of the present fixed commitment period. There will be often be a “hump”: breakage costs will tend to increase as the market rate diverges from the fixed rate (on day 1 they will be the same) then decrease again as the number of days remaining in the fixed term period (by which the increasing differential is multiplied) diminishes to zero.

The breakage costs on a 5-year fixed period on a mortgage loan are therefore, potentially large, which is why it is so expensive to repay a fixed mortgage early. The breakage costs on loan that resets its interest every month (a floating rate loan) will be much smaller. The breakage costs on overnight deposits will be, by definition, nil.

Swap break costs

The same principle holds for swap break costs, only the comparison will be the prevailing market rate for the reference asset against its value when the swap was executed (its “strike price”).

On the trade date an asset’s strike place and its market price are, Q.E.D., the same. On any other day swap break costs will generally be simply the breakage cost of the asset leg, payable one way, less the breakage costs of the financing leg, payable the other. The financing leg is explicitly an interest rate breakage cost; the asset break is by analogy one. In each case, the same “time decay” effect and “duration hump” effect should be in play.

See also

References