FRM Level 2 Formulas – Liquidity and Treasury Risk Measurement

Estimated reading time: 4 minutes



We present the formulas for the Liquidity and Treasury Risk Measurement segment.

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Bid-Offer Spread

One measure of the market liquidity of an asset is its bid–offer spread.

This can be measured either as a dollar amount or as a proportion of the asset price


The dollar bid–offer spread

p = Offer price – Bid price


The proportional bid–offer spread

s = ( Offer price – Bid price ) /  Mid-market price


Cost of liquidation (normal market)

 Σi ( si * α/ 2 )


si is an estimate of the proportional bid–offer spread in normal market conditions for the ith financial instrument held by a financial institution

αi   is the dollar value of the position in the instrument


Liquidity-Adjusted VaR (normal market)

VaR  +   Σi ( si * α/ 2 )


Liquidity-Adjusted VaR (stressed market)

VaR  +    Σi  [ [ ( mi +  lσi  ) αi  ] / 2  ]    


Cost of liquidation (stressed market)

 Σi  [ [ ( mi +  lσi  ) αi  ] / 2  ]                    

Define mi and σi as the mean and standard deviation of the proportional bid–offer spread for the ith financial instrument held.

The parameter l  gives the required confidence level for the spread.

For example, if we are interested in considering “worst case” spreads that are exceeded only 1% of the time, and if it is assumed that spreads are normally distributed, then l = 2.326


The liquidity coverage ratio (LCR) requirement

( High-quality liquid assets / Net cash outflows in a 30-day period )  ≥  100%


The net stable funding ratio (NSFR) requirement

( Amount of stable funding / Required amount of stable funding )  ≥  100%


The Leverage Ratio

1 + ( D/E )


D = Debt

E = Equity


After-tax gross yield

Before-tax gross yield * ( 1 – Firm’s marginal income tax rate )


The Tax Equivalent Yield ( TEY )

TEY = After-tax return on a tax-exempt investment / (1 – Investing firm’s marginal tax rate)


Net after-tax return on municipals (in % )

[ Nominal return on municipals after taxes (in %) – Interest expense incurred in acquiring the municipals (in %) ]  +  Tax advantage of a qualified bond


Percentage change in Investment Price

– Duration * [  (Change in interest rate) /  ( 1 + (1/m)*(Initial Rate)  ]

Where m is the number of times during the year that the security pays interest


Financial Firm’s Net Liquidity Position, Lt

= Supplies of Liquidity Flowing into the Firm – Demands of the Firm for Liquidity


Supplies of Liquidity Flowing into the Firm

= Incoming Deposits + Revenues from Services + Customer Loan Repayments + Sale of Assets + Borrowings


Demands of the Firm for Liquidity

= Deposit Withdrawals – Loan Requests – Borrowing Repayments – Operating Expenses – Dividend Payments to Stockholders


Expected Liquidity Requirement

Probability of Outcome A * (Estimated liquidity surplus of deficit in Outcome A)


Probability of Outcome B * (Estimated liquidity surplus of deficit in Outcome B)


Probability of Outcome C * (Estimated liquidity surplus of deficit in Outcome C)




Cash position indicator

Cash and deposits due from depository institutions / total assets


Liquid securities indicator

U.S. government securities / total assets


Net federal funds and repurchase agreements position

(Federal funds sold and reverse repurchase agreements – Federal funds purchased and repurchase agreements) / total assets


Capacity ratio

Net loans and leases / total assets


Pledged securities ratio

Pledged securities / total security holdings


Hot money ratio

Money market (short-term) assets / volatile liabilities

= (Cash and due from deposits held at other depository institutions + holdings of short-term securities + Federal funds loans + reverse repurchase agreements) / (large CDs + Eurocurrency deposits + Federal funds borrowings + repurchase agreements)


Deposit brokerage index

Brokered deposits / total deposits


Core deposit ratio

Core deposits / total assets


Deposit composition ratio

Demand deposits / time deposits


Loan commitments ratio

Unused loan commitments / total assets


Marginal cost rate

Change in total cost / Additional funds raised


Annual Percentage Yield (APY)

APY earned = 100 [ ( 1 + Interest earned/Average account balance )(365/Days in period) – 1 ]


Available Funds Gap (AFG)

AFG = [ Current and projected loans and investments the lending institution desires to make ] – [ Current and expected deposit inflows and other available funds ]


Effective cost rate on deposit and non-deposit sources of funds

= [ Current interest cost on amounts borrowed + Non-interest costs incurred to access these funds ]  /  Net investable funds raised from this source


Current interest cost on amounts borrowed = Prevailing interest rate in the money market * Amounts of funds borrowed

Non-interest costs incurred to access these funds = Estimated cost rate representing staff time, facilities, transaction costs * Amounts of funds borrowed

Net investable funds raised = Total amount borrowed – legal reserve requirements (if any), deposit insurance assessments (if any), and funds placed in non-earning assets


Pooled deposit and non-deposit funds expense

All expected operating expenses / All new funds expected


Hurdle rate of return over all earning assets

All expected operating costs / Dollars available to place in earning assets


Weighted Average Life ( WAL )

=  ∑ ( pi / P ) ti


Pi = principal amount in distribution i,

P = amount of loan

ti = time (in years) of payment i


Funds Transfer Price ( FTP )

= Base Rate + Term Liquidity Premium + Liquidity Premium


Base Rate = rate depicted from the swap curve corresponding to the asset’s contractual / behavioral maturity or repricing term, whichever is less

Term Liquidity Premium = spread between the swap curve and the bank’s marginal cost of funds curve based on the contractual/ behavioral maturity of the asset

Liquidity Premium = cost of carrying liquidity cushion averaged over total assets of the bank


Bank Discount Rate

= [ ( 100 – Purchase Price on Security or Loan ) / 100 ] * (  360 / # days to Maturity )


YTM Equivalent Yield

= [ ( 100 – Purchase Price ) / Purchase Price ] * (  365 / Days to Maturity )


Nominal (Published) Market Interest Rate on a Risky Security or Loan

= Risk Free Rate + Risk Premiums to Compensate Lenders


Net Interest Margin ( NIM ) =  Net Interest Income / Total Earning Assets

=  ( Interest from Loans and Investments – Interest Expense on deposits or borrowed funds )  / ( Total Earning Assets )


Interest Sensitive Gap

= Interest Sensitive Assets – Interest Sensitive Liabilities


Relative IS GAP

= IS GAP / Size of Financial Institution


Net Interest Income

= Total Interest Income – Total Interest Cost


Change in Net Interest Income

= Overall change in Interest Rate (in percentage points) * Size of the Cumulative Gap (in dollars)


Duration Gap

= Dollar Weighted Duration of Asset Portfolio – Dollar Weighted Duration of Liability Portfolio


Leverage Adjusted Duration Gap

= Duration Gap * (Total Liabilities / Total Assets)

= (Dollar Weighted Duration of Asset Portfolio – Dollar Weighted Duration of Liability Portfolio) * (Total Liabilities / Total Assets)


Dollar Weighted Asset Portfolio Duration

= ∑( Duration of Each Asset in Portfolio ) * Market Value of Each Asset in Portfolio  /  ( Total Market Value of all Assets )


Current Leverage-Adjusted Position

= Average Asset Duration – [ Average Liability Duration * ( Total Liabilities / Total Assets ) ]



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