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FRM Level 2 Formulas – Liquidity and Treasury Risk Measurement

Estimated reading time: 4 minutes

 

Introduction

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 )

Where:

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 )

Where:

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

Where:

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

Where:

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

Where:

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

Where:

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 ) ]

 

Conclusion

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