Banking and Financial Intermediation
Department of Applied Finance
2024-10-02
Liquidity risk is a normal aspect of everyday management of a financial institution (FI).
We focus on the risk exposure of DIs.
Liquidity risk can arise on both sides of the balance sheet: the asset side as well as the liability side
Note
As of June 2021, U.S. commercial banks had total deposits representing 82.19% of total liabilities and capital.
For CBA, cash and liquid assets account for 9.3% of total assets.
Figure 1: Excerpt of CBA’s 2023 balance sheet - assets
For CBA, deposits and other public borrowings account for 73.25% of total liabilities.
Figure 2: Excerpt of CBA’s 2023 balance sheet - liabilities
It’s not that bad.
Most demand deposits are relatively “stable”, acting as consumer core deposits on a daily basis.
The DI manager must monitor and predict the net deposit drains on any given normal banking day.
import matplotlib.pyplot as plt
import numpy as np
# Data for the plot
x = np.linspace(-10, 15, 1000)
y = np.exp(-0.5 * ((x - 5) / 4)**2) / (4 * np.sqrt(2 * np.pi))
# Plotting
plt.figure(figsize=(10, 6))
plt.plot(x, y, color='gray')
# Adding vertical lines for 0 and 5%
plt.axvline(x=0, color='black', linestyle='-', label='0')
plt.axvline(x=5, color='gray', linestyle='--', label='5%')
# Show x-axis
plt.xlabel("% Net deposit drain (cash outflow)")
# Show the plot
plt.show()Consider a probability distribution of net deposit drains that is assumed to be strongly peaked at the 5 percent net deposit withdrawal level, as shown in Figure 3.
As a result, the liability side of the DI’s balance sheet is contracting.
import matplotlib.pyplot as plt
import numpy as np
# Data for the plot
x = np.linspace(-10, 15, 1000)
y = np.exp(-0.5 * ((x + 2) / 2 )**2) / (4 * np.sqrt(2 * 0.1 * np.pi))
# Plotting
plt.figure(figsize=(10, 6))
plt.plot(x, y, color='gray')
# Adding vertical lines for 0 and 5%
plt.axvline(x=0, color='black', linestyle='-', label='0')
plt.axvline(x=-2, color='gray', linestyle='--', label='-2%')
# Show x-axis
plt.xlabel("% Net deposit drain (cash outflow)")
# Show the plot
plt.show()Consider another probability distribution of net deposit drains that is assumed to be strongly peaked at the -2 percent net deposit withdrawal level, as shown in Figure 4.
As a result, this DI is expected to grow with an expanding balance sheet.
Generally a drain on deposits at DIs can be managed by
Traditionally, DIs have relied on stored liquidity management. Today, most DIs rely on purchased liquidity management.
Note
We will discuss in greater detail liquidity management in next week.
Panel A: Balance sheet immediately before and after deposit drain
| Assets | Deposits | Borrowed funds | Other liabilities | Total Liabilities | |
|---|---|---|---|---|---|
| Before the drain | 100 | 70 | 10 | 20 | 100 |
| After the drain | 100 | 65 | 10 | 20 | 95 |
Panel B: Adjusting to a deposit drain through purchased liquidity management
| Assets | Deposits | Borrowed funds | Other liabilities | Total Liabilities | |
|---|---|---|---|---|---|
| After liquidity management | 100 | 65 | 15 | 20 | 100 |
A DI manager could also liquidate some of its assets, utilizing its stored liquidity.
Traditionally, U.S. DIs hold cash reserves at the Federal Reserve and in their vaults to meet liquidity needs.
The Federal Reserve sets minimum reserve requirements for banks’ cash reserves.
Despite these requirements, DIs often hold cash reserves above the minimum to manage liquidity drains.
Note
Panel A: Balance sheet immediately before deposit drain
| Assets | Liabilities | |||
|---|---|---|---|---|
| Cash | 9 | Deposits | 70 | |
| Borrowed funds | 10 | |||
| Other asset | 91 | Other liabilities | 20 | |
| Total | 100 | Total | 100 |
Panel B: Adjusting to a deposit drain through stored liquidity management
| Assets | Liabilities | |||
|---|---|---|---|---|
| Cash | 4 | Deposits | 65 | |
| Borrowed funds | 10 | |||
| Other assets | 91 | Other liabilities | 20 | |
| Total | 95 | Total | 95 |
This far we have discussed the liability-side liquidity risk due to net deposit drains.
On the asset side, liquidity problems can arise due to
See for example Acharya et al. (2024).
Balance Sheet Immediately Before and After Exercise
| Amount | Amount | ||
|---|---|---|---|
| Cash | 12 | Deposits | 100 |
| Other assets | 138 | Borrowed funds | 20 |
| Other liabilities | 5 | ||
| Equity | 25 | ||
| Total | 150 | Total | 150 |
| Amount | Amount | ||
|---|---|---|---|
| Cash | 12 | Deposits | 100 |
| Other assets | 143 | Borrowed funds | 20 |
| Other liabilities | 5 | ||
| Equity | 25 | ||
| Total | 155 | Total | 150 |
Adjusting the Balance Sheet to a Loan Commitment Exercise
| Amount | Amount | ||
|---|---|---|---|
| Cash | 12 | Deposits | 100 |
| Other assets | 143 | Borrowed funds | 25 |
| Other liabilities | 5 | Other liabilities | 5 |
| Equity | 25 | ||
| Total | 155 | Total | 155 |
| Amount | Amount | ||
|---|---|---|---|
| Cash | 7 | Deposits | 100 |
| Other assets | 143 | Borrowed funds | 20 |
| Other liabilities | 5 | ||
| Equity | 25 | ||
| Total | 150 | Total | 150 |
Another type of asset-side liquidity risk arises from the investment portfolio.
Technological development is claimed to have improved the liquidity of financial markets. But given the herding hebaviour in the market, liquidity could still dry up and investment securities only sold at fire-sale prices.
Balance Sheet Immediately Before and After Drop in Investment Portfolio Value
| Amount | Amount | ||
|---|---|---|---|
| Cash | 12 | Deposits | 100 |
| Investment portfolio | 50 | Borrowed funds | 20 |
| Other assets | 88 | Other liabilities | 5 |
| Equity | 25 | ||
| Total | 150 | Total | 150 |
| Amount | Amount | ||
|---|---|---|---|
| Cash | 12 | Deposits | 100 |
| Investment portfolio | 45 | Borrowed funds | 20 |
| Other assets | 88 | Other liabilities | 5 |
| Equity | 20 | ||
| Total | 145 | Total | 145 |
Adjusting the Balance Sheet for a Drop in Investment Portfolio Value
| Amount | Amount | ||
|---|---|---|---|
| Cash | 12 | Deposits | 105 |
| Investment portfolio | 50 | Borrowed funds | 20 |
| Other assets | 88 | Other liabilities | 5 |
| Equity | 20 | ||
| Total | 150 | Total | 150 |
| Amount | Amount | ||
|---|---|---|---|
| Cash | 7 | Deposits | 100 |
| Investment portfolio | 50 | Borrowed funds | 20 |
| Other assets | 88 | Other liabilities | 5 |
| Equity | 20 | ||
| Total | 145 | Total | 145 |
\[ \text{Financing gap} = \text{Average loans} - \text{Average deposits} \]
A positive financing gap implies that the DI must fund it using its cash and liquid assets and/or borrowing funds in the money market. Therefore,
\[ \text{Financing gap} = -\text{Liquid assets} + \text{Borrowerd funds} \]
We thus have the following relationship:
\[ \text{Financing gap} + \text{Liquid assets} = \text{Financing requirement (borrowed funds)} \]
Comparison of certain key ratios and balance sheet features of the DI with similar DIs, for example,
Developed by Jim Pierce at the Federal Reserve, liquidity index measures the potential losses an FI could suffer from a sudden or fire-sale disposal of assets compared with the amount it would receive at a fair market value established under normal market (sale) conditions.
\[ I = \sum_{i=1}^N \left(W_i \times \frac{P_i}{P^*_i}\right) \]
where
The liquidity index should lie between 0 and 1.
\[ \text{Minimum LCR} = \frac{\text{Stock of HQLAs}}{\text{Total net cash outflows over next 30 calendar days}} \ge 100\% \]
The stock of HQLAs is defined as follows:
The total net cash outflows is defined as:
\[ \text{Total net cash outflows over next 30 calendar days} = Out - \min(In, 75\% \times Out) \]
where
Cash inflows and outflows are computed based on the type of assets/liabilities and associated draw-down factors.
Note
For a detailed calculation of cash outflows and inflows, refer to textbook Saunders, Cornett, and Erhemjamts (2023) or to the suggested readings.
Consider the following balance sheet (in million of dollars) of a bank. Calculate the bank’s LCR.
| Assets | $ | Liquidity Level | Liabilities and Equity | $ | Run-Off Factor |
|---|---|---|---|---|---|
| Cash | 5 | Level 1 | Stable retail deposits | 95 | 3% |
| Deposits at the Fed | 15 | Level 1 | Less Stable retail deposits | 40 | 10 |
| Treasury securities | 100 | Level 1 | Unsecured wholesale funding from: | ||
| GNMA securities | 75 | Level 2A | - Stable small business deposits | 100 | 5 |
| Loans to A-rated corporations | 110 | Level 2A | - Less Stable small business deposits | 80 | 10 |
| Loans to B-rated corporations | 85 | Level 2B | - Nonfinancial corporates | 50 | 75 |
| Premises | 20 | Equity | 45 | ||
| Total | 410 | Total | 410 |
The LCR is calculated as follows:
First, calculate the amount of HQLA.
Before adjustment for capps,
However, Level 2 assets is capped at 40% of HQLA!
Therefore, the HQLA is 200 million.
Next, calculate the total net cash outflows over next 30 days.
Cash outflows are:
Therefore,
Lastly, calculate LCR:
\[ \text{LCR} = \frac{\text{Stock of HQLAs}}{\text{Total net cash outflows over next 30 calendar days}} = \frac{200}{52.35} = 382.04\% \ge 100\% \]
\[ \text{NSFR} = \frac{\text{Available amount of stable funding}}{\text{Required amount of stable funding}} \ge 100\% \]
Available stable funding (ASF) includes:
These equity and liabilities are assigned to one of five categories, each with a specific ASF factor.
ASF is calculated as the sum of the weighted amounts.
Required stable funding (RSF) is calculated as the sum of
| CBA | NAB | ANZ | Westpac | |
|---|---|---|---|---|
| Cash Outflows | ||||
| Retail And Counterparties Deposits Outflow | 37,416 | 29,947 | 25,517 | 29,304 |
| Stable Deposits | 12,700 | 5,843 | 5,879 | 7,969 |
| Less Stable Deposits | 24,716 | 24,104 | 19,638 | 21,335 |
| Unsecured Wholesale Funding Outflow | 82,444 | 82,299 | 146,698 | 76,953 |
| Operational Deposit Outflow | 22,219 | 21,540 | 22,553 | 18,631 |
| Non Operational Deposits Outflow | 49,236 | 47,619 | 111,549 | 47,073 |
| Unsecured Debt Outflow | 10,989 | 13,140 | 12,596 | 11,249 |
| Secured Wholesale Funding Outflow | 6,839 | 10,701 | 5,405 | 3,891 |
| Additional Outflow Requirements | 26,186 | 38,693 | 70,639 | 30,463 |
| Derivative Expo And Other Collateral Requirement | 7,557 | 8,154 | 48,206 | 12,462 |
| Loss of Funding on Debt Products | 0 | 0 | 0 | 136 |
| Credit And Liquidity Facilities | 18,629 | 30,539 | 22,433 | 17,865 |
| Other Contractual Funding Obligation | 0 | 81 | 0 | 4,515 |
| Other Contingent Funding Obligation | 10,373 | 5,219 | 8,024 | 4,082 |
| Total Cash Outflow | 163,258 | 166,940 | 256,283 | 149,208 |
| CBA | NAB | ANZ | Westpac | |
|---|---|---|---|---|
| Cash Inflows | ||||
| Secured Lending | 2,328 | 3,898 | 1,549 | 0 |
| Inflows From Fully Performing Exposures | 9,520 | 11,788 | 17,190 | 5,020 |
| Other Cash Inflows | 6,753 | 1,589 | 36,016 | 7,988 |
| Total Cash Inflow | 18,601 | 17,275 | 54,755 | 13,008 |
| CBA | NAB | ANZ | Westpac | |
|---|---|---|---|---|
| Liquidity Coverage Ratio (LCR) | ||||
| Average High Quality Liquid Assets | 189,419 | 209,561 | 267,905 | 181,882 |
| Average Net Cash Outflows | 144,657 | 149,665 | 201,528 | 136,200 |
| Average Liquidity Coverage Ratio | 131.00 | 140.00 | 132.90 | 134.00 |
| Net Stable Funding Ratio (NSFR) | ||||
| Available Stable Funding | 860,999 | 646,508 | 625,285 | 707,893 |
| Required Stable Funding | 693,453 | 556,016 | 537,430 | 615,341 |
| Net Stable Funding Ratio | 124.00 | 116.00 | 116.35 | 115.00 |
Major liquidity problems can arise, however, if deposit drains are abnormally large and unexpected, which may occur for a number of reasons, including:
In these cases, unexpected deposit drains could trigger a bank run that may eventually force a bank into insolvency.
In the worst case, a bank panic may occur - systemic or contagious bank run on deposits of banking industry.
The two major liquidity risk insulation devices are deposit insurance and the discount window.
Not without economic costs
Note
An example is the case of Equitable Life. Increase in surrenders after it received an adverse legal ruling contributed to its failing. Its 256-year history ended in June 2018, after an 18-year-long winding-down process.
AFIN8003 Banking and Financial Intermediation
