Editing Duration gap

{{Short description|Financial institutions duration gap}}
{{refimprove|date=July 2008}}

In [[Finance]], and [[accounting]], and particularly in [[asset and liability management]] (ALM), the '''duration gap''' measures how well matched are the timings of [[Cash flow|cash inflows]] (from assets) and cash outflows (from liabilities), and is then one of the primary [[asset–liability mismatch]]es considered in the ALM process<!-- and {{slink|Fractional-reserve banking#Hypothetical example of a bank balance sheet and financial ratios}} -->.
The term is typically used by banks, [[pension fund]]s, or other [[financial institution]]s to measure, and manage, their risk due to changes in the interest rate: by duration matching, that is creating a "zero duration gap", the firm becomes [[immunization (finance)|immunized]] against [[interest rate risk]]. 
See {{slink|Financial risk management#Investment management}}. 
<ref name="Mishkin">Frederic S. Mishkin and Apostolos Serletis (2004). [https://www.pearsoned.ca/highered/divisions/text/mishkin_2/data/appendices/09_ch09_mishkin_append1.pdf Duration Gap Analysis] </ref>
<ref name="analystprep">Staff (2020). [https://analystprep.com/study-notes/frm/risk-management-for-changing-interest-rates-asset-liability-management-and-duration-techniques/ Risk Management for Changing Interest Rates: Asset-Liability Management and Duration Techniques], analystprep.com </ref>

==Measurement ==
Formally, the duration gap is the difference between the [[Bond duration|duration]] - i.e. the [[Bond_duration#Modified_duration|average ''maturity'']] - of [[asset]]s and [[liability (financial accounting)|liabilities]] held by a financial entity.<ref name="LeeLee2006">{{cite book|last1=Lee|first1=Cheng-Few|last2=Lee|first2=Alice C.|title=Encyclopedia of Finance|url=https://books.google.com/books?id=I6BH-RKYVG4C&pg=PA423|accessdate=15 February 2013|date=2006-05-05|publisher=Springer|isbn=9780387262840|pages=423–}}</ref> 
A [[Bond_duration#Modified_duration|related approach]] is to see the "duration gap" as the difference in the [[PV01|price sensitivity]] of interest-yielding assets and the price sensitivity of liabilities (of the organization) to a change in market interest rates (yields).<ref name="Skinner2004">{{cite book|last=Skinner|first=Frank|title=Pricing and Hedging Interest and Credit Risk Sensitive Instruments|url=https://books.google.com/books?id=2OAkxj2hAkgC&pg=PA218|accessdate=15 February 2013|date=2004-10-29|publisher=Butterworth-Heinemann|isbn=9780080473956|pages=218–}}</ref>

Under either, a gap can be beneficial or harmful, depending on where interest rates are headed.
*When the duration of assets is larger than the duration of liabilities, the duration gap is positive. In this situation, if [[Interest|interest rates]] rise, assets will lose more value than liabilities, thus reducing the value of the firm's equity. If interest rates fall, assets will gain more value than liabilities, thus increasing the value of the firm's equity.
*Conversely, when the duration of assets is less than the duration of liabilities, the duration gap is negative. If interest rates rise, liabilities will lose more value than assets, thus increasing the value of the firm's equity. If interest rates decline, liabilities will gain more value than assets, thus decreasing the value of the firm's equity.

==Management==
{{also|Financial risk management#Banking}}
As outlined, a key objective of ALM is to measure and then manage the direction and extent of any asset-liability mismatch - i.e. a funding or "maturity gap" - so as to maintain adequate profitability. <ref name="analystprep"/><ref name="Mishkin"/>
This exercise will have the joint objectives of balancing maturities, cash-flows and / or interest rates, for a particular time horizon. The management thus takes the form of:
*matching the maturities of loans and investments with the maturities of deposits, equity, and external credit; the techniques commonly employed are [[Immunization (finance)|immunization]] and [[cashflow matching]].
*managing the spread between interest rate sensitive assets and interest rate sensitive liabilities; see {{slink|Corporate bond#Risk_analysis}} and {{slink|Yield spread#Yield spread analysis}}.

A formula sometimes applied is:
<math>Duration \ gap = duration \ of \ earning \ assets \ - \ duration \ of \ paying \ liabilities \ \times \ \frac{paying \ liabilities}{earning \ assets}</math>

Implied here, is that even if the duration gap is zero, the firm is immunized only if the size of the liabilities equals the size of the assets. Thus as an example, with a two-year loan of one million and a one-year asset of two millions, the firm is still exposed to [[Deposit_risk#Types_of_deposit_risk|rollover risk]] after one year when the remaining year of the two-year loan has to be financed.

<math>0 = 1 - 2 \times \frac{1,000,000}{2,000,000}</math>

Further limitations of the duration gap approach to risk-management include the following:
* the difficulty in finding assets and liabilities of the same duration
* some assets and liabilities may have patterns of cash flows that are [[Embedded option|not well defined]]
* [[Prepayment of loan|customer prepayments]] may distort the expected cash flows in duration
* [[default (finance)|customer defaults]] may distort the expected cash flows in duration
* [[bond convexity|convexity]], the extent to which duration is non-linear, can cause problems in estimation.

==Scope==
The outlined "static" approach considers any future gaps due to ''current'', i.e. existing, exposures, and any related [[Exercise (options)|exercise]] of ([[embedded option|embedded]]) options - usually [[Prepayment of loan|prepayments]] - at different points in time.
"Dynamic gap analysis" enlarges the scope by including "what if" scenarios, testing potential changes in business activity (new volumes, additional prepayment transactions, potential [[hedge (finance)|hedging transactions]]), and [[Fixed_income_analysis#Analysis|considering]] unusual interest rate scenarios, with their associated [[Yield_curve#Significance_of_slope_and_shape|shape of the yield curve]] and resultant [[Bond_valuation#Present_value_approach|changes in pricing]].
Depending on deal-stage and likelihood, [[Financial_analyst#Financial_planning_and_analysis |analysts]] will incorporate expected [[capital investment]]s and their [[Corporate_finance#Sources_of_capital|required funding]] under either approach, as appropriate.

==See also==
* [[Bond convexity]]
* [[Bond duration]]
* [[Cashflow matching]]
* [[Debt sculpting]]
* [[Embedded option]]
* [[Fixed income analysis]]
* [[Immunization (finance)]]
* [[Maturity transformation]]
* [[Interest rate risk in the banking book]]

==References==
{{Reflist}}
[[Category:Banking]]
[[Category:Insurance]]
[[Category:Liability (financial accounting)]]
[[Category:Asset management]]
[[Category:Fixed income analysis]]
[[Category:Financial risk management]]
[[Category:Interest rates]]