Measuring Net Duration of a Bank, A practical example

Net duration of bank implies  the gap between duration of its earning assets and duration of liabilities.  A duration gap or net duration of a balance sheet measures the gap or mis-match between timings of cash flows received from assets versus those  payable against liabilities/ deposits. This article is about calculating and measuring Net Duration, i.e. duration gap of a balance sheet. This is explained with the help of practical example along with reference to definitions  of Durations and Duration Gap of Balance Sheet. 

How to define Duration of an asset or deposit.

Duration of asset or liability in its simple form, refers to time period during which an asset or liability travels towards its maturity date or converts into cash flow. 

For assets having multiple cash flows or coupons before maturity, Duration is also defined as  weighted average of the time until  expected maturity/cash flow from  a security or assets.  

Duration Gap of Balance Sheet

Balance sheet comprises of assets and liabilities along with equity. In a banking business, assets and liabilities mostly have time period attached to their maturity or future re-pricing, while equity is of perpetual nature. Therefore, only assets or liabilities are considered for duration analysis. 

Difference of maturity period of assets over liabilities may create a gap, referred to as duration gap. 

Changes in interest rates in financial markets may have an impact on the business of banks. Increase or decrease in market rates are translated into rise or fall in cost of new deposits. Similarly, markup rates on fresh loans issued near or after this change will also vary accordingly. However, the existing portfolios of liabilities and assets/loans carry the same prices until their respective contractual tenures are completed.  Banks therefore are exposed to consequential change in the value of these existing asset/liabilities in comparison to the prevailing market parameters. 

The impact of  changes in market interest rates on the bank's portfolios is dependent upon the quantum of mis-match or duration gaps in assets and liabilities of the bank. Higher the gap, higher the resultant impact of any variation in the market rates.

Measuring Duration Gap

Typically business model of commercial banks are based on such loans and investments, which carry higher duration  in comparison to their deposits. Most of the Deposits (demand deposits or saving deposits) mature earlier than loans or investments. For such banks, net duration will mostly be positive  In order to manage or quantify the extent of risks, which ultimately translates into upward or downward change in the value of their net equity, duration analysis provides a useful direction for working out a remedial strategy. Duration analysis is carried out on the following lines:

 

·         Duration of all the assets in the balance sheet items is calculated by

i)     working out average time to contractual maturity (or re-pricing) of each class of asset

ii)    Calculate proportion to its respective weightage with respect to total assets 

·       Similarly duration of deposits and liabilities is worked out along with weightage of each type of liability with respect to total liabilities. 

     Weighted duration of each class of asst or liability is summed up.

·     Difference of the two sums is called Duration gap of the balance sheet or Net duration.

 

Calculation:

Consider a Balance Sheet of a Bank with total assets of Rs. 7,000 million and Liabilities of Rs. 6,300 million. Lets work out Net Duration of the bank (or Duration Gap).

Before reaching out the detail working, duration of each item under asset or liability in the balance sheet is measured in terms of time period left to its maturity or re-pricing.

For understanding and simplicity of calculations, duration is  assumed to be based on contractual maturity or re-pricing of asset or liability. Months or days are reported in ‘years’ for calculation purpose. (however,  more elaborative models work out Duration on the basis of time value of money/ cash flows.) 

 

Each asset or liability group is then tabulated in the respective rows of the tables below, with their respective proportion  to total assets or total liabilities.  

Average Duration of respective assets and liabilities of Balance Sheet as of December 31, xxxx has been worked out on proportionate weight basis in the last column. For more clarity last column is worked out as per following equation:

 

Duration of Assets        =  D1*P1/100 + D2*P2/10+…....….+D7*P7/100

 

Duration of Assets as of December 31, xxxx

	Asset Type	Amount (Rs. in Millions)      ( A)	Weight in percentage        (P)	Duration (Years)     (D)	Weighted Duration (years)      (D*P/100)
1	Cash and Treasury Accounts	700	(700/7000)*100	0	0.0
2	Receivables	350	5%	0.3*	0.02
3	Investments in liquid Instruments	1,400	20	0.2*	0.04
4	Short Term Lending/ placements	700	10	1.0	0.01
5	Loans, floating rates	700	10	0.5*	0.05
6	Medium Term Securities	2000	29	2.0	0.58
7	Long Term Securities, investments	1150	16	5.0	0.8
	Total /sum	7,000	100		1.5
	Total weighted Duration of Assets is 1.5 Years

*Explainer: Receivables are assumed to have average turnover of 4 months (0.33 years)

                       Bank assumes that it can hold liquid investments for 60-90 days (average duration 75 days or 0.2 year)

                      Floating rate assets are re-priced after every 6 months, hence duration is ½ years.

 

Now apply the same method on Liabilities of the Bank

Duration of Liabilities      =  D1*P1/100 + D2*P2/100……….D6*P6/100

 

Liabilities as of December 31, xxxx

	Liability Type	Amount (Rs. in Millions)      ( L)	Weight in percentage       (P)	Duration(Years)      (D)	Weighted Duration (years)    (D*P/100)
1	Sundry Creditors/Payables	300	(300/6300)*100= 5%	0	0.0
2	Demand Deposit*	2400	38%	0.29*	0.11
3	Time Deposits 6 Months	1,200	19	0.5	0.095
4	Time Deposits 1 year	1,200	19	1.0	0.19
5	Time Deposits over 1 years*	600	9.5	3.5*	0.33
6	Long Term Liabilities floating Rate	600	9.5	0.5*	0.05
	Total /sum	6,300	100		0.775
	Total weighted Duration of Liabilities is 0.8 Years (rounded off)

*Explainer

In view of no fixed time for demand deposits, a turnover is assumed from 1 to 6 months (i.e. avg. 3.5 months or 0.29 years).

Average is worked out by clubbing assumed duration range of 2 to 5 years of various time deposits of over 1 Year .

Floating rate liabilities are re-priced after 6 months.

 

 

Net  Duration  of Balance Sheet          =          1.5   –   0.8      =          0.7 Years

                              Net Duration =  Asset Duration – Liabilities Duration      

 

Duration of assets is longer than liabilities. Therefore Net Duration or Duration Gap in this case is positive.