1. 1 Topic 6. Measuring Liquidity Risk 6.1 Definition of liquidity risk 6.2Liquidity risk at depository institutions (DIs) 6.3 Measurement of liquidity risk

2. 2 6.1 Definition of liquidity risk  Liquidity risk (more precisely, funding liquidity risk) of a FI refers to risk of running out of cash and/or unable to raise additional funds to meet the financial claims from its liability holders (liability-side of the balance sheet) or to honor the asset purchase agreement (asset- side of the balance sheet).

3. 3 6.2 Liquidity risk at depository institutions (DIs) Liability-Side  A DI usually funds its long-term assets such as mortgage loans, with short-term liabilities such as time deposit accounts.  In general, the DI only keeps small proportion of these short-term financial deposits in cash asset (cash reserve). If the liabilities claims are unusual high, it may cause the liquidity problem to the DI.

4. 4 6.2 Liquidity risk at depository institutions (DIs)  For a given period of time [t 1, t 2 ], where 0 (now) < t 1 < t 2, the net deposit drains over [t 1, t 2 ], NDD(t 1, t 2 ), is defined as NDD(t 1, t 2 ) = DW(t 1, t 2 ) – DA(t 1, t 2 ) (6.1) where DW(t 1, t 2 ) is the deposit withdrawals over [t 1, t 2 ]; DA(t 1, t 2 ) is the deposit additions over [t 1, t 2 ].

5. 5 6.2 Liquidity risk at depository institutions (DIs)  If NDD is abnormally high, it will make the DI which does not have sufficient cash to meet the withdrawal needs. As a result, it needs to raise the fund from liquidating the assets at fire-sale prices or borrowings with high borrowing cost.  The quality of managing the liquidity risk on the liability side is heavily depend on the how accurate to predict the distribution of NDD(t 1, t 2 ) in order to have a good planning to raise up the required funds.

6. 6 6.2 Liquidity risk at depository institutions (DIs)  Three ways to manage the positively of the NDD: Purchased liquidity management:  To fund the positive NDD through the adjustment on the liability side of the balance sheet. This can be done by borrowing funds through issuing additional fixed- maturity wholesale certificates of deposit or selling notes and bonds.  The higher the cost of funding, the less attractive of the purchased liquidity management.  Under purchased liquidity management, the DI can preserves the asset side of its balance sheet.

7. 7 6.2 Liquidity risk at depository institutions (DIs)  Example 6.1 (Purchased liquidity management) All the values in the following table are measured in million of dollars. $5M net deposit drain.

8. 8 6.2 Liquidity risk at depository institutions (DIs) Increase the borrowed funds by $5M. The size of asset side is preserved. All the values in the following table are measured in million of dollars.

9. 9 6.2 Liquidity risk at depository institutions (DIs) Stored liquidity management:  To fund the positive NDD through the adjustment on the asset side of the balance sheet. This can be done by liquidating some of its assets such as using the excess cash reserves or selling its assets.  Decrease the size of its balance sheet.  The cost of using the excess cash reserves is the opportunity cost. The corresponding cash can not be invested in other high-income-earning assets. Combine purchased and stored liquidity management.

10. 10 6.2 Liquidity risk at depository institutions (DIs)  Example 6.2 (Stored liquidity management) All the values in the following table are measured in million of dollars. $5M net deposit drain Use $5M cash to fund $5M net deposit drain. Size of balance sheet decrease by $5M.

11. 11 6.2 Liquidity risk at depository institutions (DIs) Asset-Side  The liquidity risk on asset-side arises from insufficient funds to cover the exercise of the off-balance-sheet loan commitment by borrower.  The loan commitment offers an option to the borrower to take down any amount of the loan up to the contractual amount at any time over the commitment period.

12. 12 6.2 Liquidity risk at depository institutions (DIs)  In a fixed-rate loan commitment, the interest rate to be paid on any takedown is established when the loan commitment contract originates.  In a floating-rate loan commitment, the borrower pays the loan rate in force when the loan is actually taken down.  The liquidity risk on the asset side can also be managed by purchased and stored liquidity management.

13. 13 6.2 Liquidity risk at depository institutions (DIs)  Example 6.3 All the values in the following table are measured in million of dollars. Exercise $5M loan commitment.

14. 14 6.2 Liquidity risk at depository institutions (DIs) Increase the borrowed funds by $5M. Decrease the cash by $5M. All the values in the following table are measured in million of dollars.

15. 15 6.3 Measurement of liquidity risk Peer group ratio comparisons  To compare certain key ratios and balance sheet features of the DI with those of DIs of a similar size and geographic location. The common key ratios include: i. loan to deposits ii. borrowed funds to total assets iii. commitments to lend to assets  A high ratio of (i) and (ii) means that the DI relies heavily on the purchased funds market rather than on core deposits to fund loans. This could mean future liquidity problems if the DI is at or near its borrowing limits in the purchased funds market.

16. 16 6.3 Measurement of liquidity risk  The high value of (iii) indicates the need of a high degree of liquidity to fund any unexpected takedowns of these loans – high-commitment DIs often face more liquidity risk exposure than do low-commitment DIs.  The major weakness of the peer group ratio comparisons is that it can only show the relative risk but not the absolute risk of the DI.

17. 17 6.3 Measurement of liquidity risk  Example 6.4 From Table 17-7, we observe that the three ratios ((i), (ii) and (iii)) of Bank of America (BOA) are higher than Northern Trust Bank (NTB). So, BOA exposes higher liquidity risk than NTB. Further, the ratio of core deposits to total assets of NTB is higher than that of BOA shows that NTB relies more on the stable core deposits to fund its asset than BOA.

18. 18 6.3 Measurement of liquidity risk Liquidity index  The liquidity index, I, is defined as where w i is the percent of asset i in the portfolio; P i and P i * are the fire-sale asset price and fair market price of asset i respectively.  From Eq. (6.2), it is obvious that 0  I  1.

19. 19 6.3 Measurement of liquidity risk  The 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 – which might take a lengthy period of time as a result of a careful search and bidding process. The closer of I to 0, the higher the liquidity risk of the FI.

20. 20 6.3 Measurement of liquidity risk  Example 6.5 Consider a portfolio which consists of: $20 million in Treasury bills (T-bills). $50 million in Mortgage loans. If the assets in the portfolio need to be liquidated at short notice, the DI will receive only 99% of the fair market value of the T-bills and 90% of the fair market value of the mortgage loans.

21. 21 6.3 Measurement of liquidity risk Let w 1 and w 2 be the weight of T-bills and mortgage loans respectively. From Eq. (6.2), the liquidity index is given by

22. 22 6.3 Measurement of liquidity risk Financing gap  Classification of Payments: Scheduled payments are those which have previously been agreed on by the counterparties. For example, scheduled loan disbursements to customers (cash outflow) and scheduled loan repayment from the customers (cash inflow). Unscheduled payments arise from customer behavior. For example, unscheduled loan disbursements to customers through credit cards (cash outflow) and unscheduled checking-account deposits by customers (cash inflow).

23. 23 6.3 Measurement of liquidity risk  Classification of Payments (cont.): Semidiscretionary payments occur as part of the bank’s normal trading operations but can be quickly changed if necessary. For example, semidiscretionary payments for the purchase of securities by bank (cash outflow) and semidiscretionary payments from the sale of normal trading securities (cash inflow). Discretionary transactions are those carried out by the bank’s funding unit to balance the net cash flow each day. For example, discretionary lending to other banks in the short-term interbank market (cash outflow) and discretionary borrowing from other banks in the interbank market (cash inflow).

24. 24 6.3 Measurement of liquidity risk  The daily financing gap I D is defined as where O S : daily scheduled cash outflow; O U : daily unscheduled cash outflow; O SD : daily semidiscretionary cash outflow; I S : daily scheduled cash inflow; I U : daily unscheduled cash inflow; I SD : daily semidiscretionary cash inflow;

25. 25 6.3 Measurement of liquidity risk  In fact, I D is the daily amount of the discretionary fund to be raised in order to balance the net daily cash outflow. Further, I D is similar to NDD in Eq. (6.1).  Define R = (O U + O SD ) – (I U + I SD )(6.4)  Since the unscheduled and semidiscretionary flows evolve randomly according to the behavior of customers and the bank’s normal operation, R is a random variable.  From Eqs. (6.3) and (6.4), we have I D = O S – I S + R(6.5)

26. 26 6.3 Measurement of liquidity risk  Assume, then  and  R can be estimated by collecting historical data for O U, O SD, I U and I SD to calculate R for each past day.  The larger the  R, the higher the liquidity risk of the DI.

27. 27 6.3 Measurement of liquidity risk  Define I  as the solution of the following equation  It is clear than I  is the level of the discretionary fund to be raised daily in order to make the DI has  % (confidence level) chance to meet the daily net cash outflow.  With the normality condition of I D in (6.6), we have

28. 28 6.3 Measurement of liquidity risk  Example 6.6 Suppose  = 95, O S = $2M, I S = $1.5M,  = $3M and  R = 20%. From Eq. (6.8),

29. 29 6.3 Measurement of liquidity risk  With (6.6) holds and R from one day to the next are uncorrelated, the required level of discretionary fund over a period of T days for the confidence level  % is given by where O S,T and I S,T are the scheduled cash outflow and inflow over a period of T days.

30. 30 6.3 Measurement of liquidity risk BIS approach  Maturity ladder For each maturity, assess all cash inflows versus outflows. Daily and cumulative net funding requirements can be determined in this manner.

31. 31 6.3 Measurement of liquidity risk  Example 6.7 Net funding requirement Using BIS Maturity Laddering Model (in millions of dollars)

32. 32 6.3 Measurement of liquidity risk One-day: $4 million in excess. One-month: Cumulative net cash shortfall of $46 million. Six-month: Cumulative excess cash of $1,104 million. Therefore, the corresponding DI will need to start planning to obtain additional funding to fill this net funding requirement in the one-month period.

33. 33 6.3 Measurement of liquidity risk  Scenario analysis Under the BIS scenario analysis, a DI needs to assign timing of cash flows for each type of asset and liability by assessing the probability of the behavior of those cash flows under the scenario being examined.

34. 34 6.3 Measurement of liquidity risk