P2.T8.25.4 Deterministic vs. Stochastic Cash Flows and Their Term Structures

[Derrick.Roslanic]

Learning Objectives: Differentiate between deterministic and stochastic cash flows and provide examples of each. Interpret the term structure of expected cash flows and cumulative cash flows.

Questions:

25.4.1. A commercial bank is managing its liquidity risk and needs to classify its cash flows to assess potential liquidity shortfalls. The bank has the following obligations and inflows over the next year:

1. Fixed-rate bond coupon payments: $10 million due every six months.
   
   
2. Floating-rate loan repayments: $5 million per quarter, indexed to 3-month SOFR.
   
   
3. Customer deposit withdrawals: Historically, customers withdraw an average of $20 million per month, but withdrawals fluctuate between $15 million and $30 million depending on economic conditions.
   
   
4. Corporate credit line usage: The bank has extended $100 million in committed credit lines, with an estimated drawdown rate of 25%–50% during periods of economic stress.

Which of the above cashflows is Deterministic?

a. 1
b. 2
c. 3
d. 4


25.4.2. A commercial bank is assessing its liquidity risk under stress conditions. The bank has the following cash flows over the next year:

• Fixed-rate bond coupon payments: $15 million due every six months.
  
  
• Floating-rate loan repayments: $6 million per quarter.
  
  
• Customer deposit withdrawals: Historically, withdrawals average $25 million per month but range between $20 million and $35 million.
  
  
• Corporate credit line usage: The bank has extended $120 million in committed credit lines, with a drawdown rate of 30%–55% during periods of stress.
  
  
• New mortgage loan originations: Expected to generate between $60 million and $110 million in inflows over the next year, depending on market conditions.

Stress Scenario Assumptions:

• Deposit withdrawals increase to $35 million per month.
• Credit line drawdowns rise to 55%.
• New mortgage loan originations decline to $60 million for the year.
• All other cash flows remain unchanged.

What is the expected net liquidity impact under these stress conditions?

a. -$530 million
b. -$460 million
c. -$432 million
d. -$620 million


25.4.3. A bank is stress testing its liquidity risk and wants to determine whether it has sufficient liquidity to cover expected cash flow shortfalls over the next year using The Term Structure of Expected Liquidity (TSLe) framework. The bank's normal and stress scenario cash flows are as follows:

• Normal Conditions:
  • Expected inflows: $795M per year
  • Expected outflows: $230M per year
  • Starting cash reserves: $50M
• Stress Scenario Adjustments:
  • Inflows decline by 25%
  • Outflows increase by 40%
  • The bank has a liquidity buffer of $100M that it can deploy to meet shortfalls

Using TSLe, what is the bank’s expected liquidity balance at the end of the year under stress conditions?

a. -191M
b. -424.25M
c. -91M
d. -9M

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