SEEM 3580 Risk Analysis for Financial Engineering YANG Chen, Spring 2024
Homework Set 4
(Due on April 10, 2024 at 23:59)
Assignment
Please provide adequate explanation to support your answers. Unless otherwise men-
tioned, all quoted yields, interest rates and coupon rates are annualized. You may need
the following percentiles of standard normal distribution: z99% = 2.326, z95% = 1.645.
1. (Liquidity Management during Deposit Drain) A DI with the following balance
sheet (in millions) expects a net deposit drain of $20 million.
Assets Liabilities and Equity
Cash $40 Deposits $30
Loans 30 Borrowed Fund 20
Securities 20 Equity 40
Total assets $90 Total liabilities and equity $90
Assume that the DI uses either one of the following methods to fund the net
deposit drain:
I. Purchased Liquidity Method via borrowing funds;
II. Stored Liquidity Management Method.
(a) Write out the DI’s balance sheets right after adjusting to the liquidity
drain using method I and method II, respectively.
(b) Suppose the DI can only receive 70% and 80% of the fair market values
of the loans and the securities respectively under the situation of fire sale.
What is the liquidity index of the bank asset portfolio (including cash,
loans and securities) after the adjustment by each of the methods? (Note
that the DI receives 100% of the fair market values of cash under fire sale.)
2. (Financing Gap) The daily scheduled cash inflow and cash outflow of Bank XYZ
at the end of the next day are $2.7 million and $2 million, respectively. Suppose
the daily unscheduled net cash flow OU−IU and the daily semidiscretionary net
cash flow OSD − ISD both follow a normal distribution, and have a correlation
ρ = 0.2. Their means and standard deviations are given as follows:
Mean Standard Deviation
OU − IU 1.5 million 1.2 million
OSD − ISD −0.4 million 1.0 million
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SEEM 3580 Risk Analysis for Financial Engineering YANG Chen, Spring 2024
(a) Given that R = (OU + OSD) − (IU + ISD) follows a normal distribution
N (R¯, σ2R) with mean R¯ and standard deviation σR, what are R¯ and σR?
Hint: Recall that if both X and Y follow a normal distribution with mean
µ1 and µ2, standard deviations σ1 and σ2 respectively, and X and Y has
correlation ρ, we have that X+Y follows a normal distribution with mean
µ1 + µ2 and standard deviation
√
σ21 + 2ρσ1σ2 + σ
2
2.
(b) How much discretionary fund should Bank XYZ raise in order to have 95%
chance to meet the daily net cash outflow in the next one day?
3. (Capital Adequacy under Basel I) National Bank has the following balance sheet
(amount in millions).
Assets Liabilities and Equity
Cash $40 Deposits $450
Treasury bills 50 Cumulative preferred stock 90
Residential mortgages* 400 Common stock 140
Corporate bonds 300 Retained earnings 110
Total assets $790 Total liabilities and equity $790
*uninsured mortgage.
The bank also has off-balance sheet items including $40 million of Amazon
performance bonds, $30 million bankers’ acceptance from an OECD bank and
$20 million forward purchase of crude oil from OECD public sector entity.
Under Basel I Accord:
(a) What is the risk-weighted on-balance-sheet asset? What is the risk-weighted
off-balance-sheet asset?
(b) What is the minimum level of total regulatory capital and Tier 1 capital
required, respectively?
(c) What are the amounts of Tier 1 and Tier 2 capitals available from National
Bank, respectively? Does the bank have adequate total regulatory capital
and Tier 1 capital?
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