# FRM Level 2 Formulas – Liquidity and Treasury Risk Measurement

## Introduction

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

Note that this information may be downloaded this free of charge in PDF format.

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

p = Offer price – Bid price

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

VaR  +   Σi ( si * α/ 2 )

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%

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 )

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

= 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 )

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