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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 * αi / 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 * αi / 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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