Commercial Bank Management Midsem Notes 556q21

CBM Final Exam Notes Return on Equity = Net Income/Total Equity Net income = Interest Income – Interest Expense + other income – other expenses – provisions – taxes. Equity = share capital + retained earnings Return on Assets = Net Income/Total Assets Asset Utilization = Total Operating Income/Total Assets Operating income = net interest income + other operating income Equity Multiplier = Total Assets/Total Equity Capital PM = return on assets/asset utilization OR net income/total operating income Interest Expense ratio = Interest expense/total operating income Provision for loan loss ratio = provision for loan loss/total operating income Non-interest expense ratio = Non interest expense/Total operating income Tax expense ratio = Tax expense/Total operating income Return on assets = PM x AU Return on equity = ROA x EM Q: What is the impact over the next 30 days on the net interest income if all interest rates rise by 50 basis points (0.5%)? Note: 1 basis point = 0.01% or 0.0001 Steps: Calculate change in net interest income (by using the formula!) We need to have funding gap over appropriate period (calculated above) and rate change (given). So

∆ NII = funding gap x rate change = -95 million x 0.5% = -$0.475 million

Therefore, net interest income will fall by $475,000 over the next 30 days. Q. Financial Institution XY has assets of $1 million invested in a 30-year, 10 per cent semi-annual coupon Treasury bond selling at par. The duration of this bond has been estimated at 9.94 years. The assets are financed with equity and a $900 000, two-year, 7.25 per cent semi-annual coupon capital note selling at par. What is the leverage adjusted duration gap of Financial Institution XY? Leverage-adjusted duration gap = DA – kDL DA = 9.94 years. We need to calculate D L and k. DL = PV of CF @t / PV of CF The capital note (liabilities) is selling at par = $900,000. Selling at par means the note is trading at its face value = $900,000. Hence, the coupon rate = current market yield (discount factor) Coupon Rate = 7.25%, payable semi-annually --> this is the same as 3.625% every 6 months Therefore, 3.625% is our semi-annual coupon rate AND our semi-annual market yield or discount factor --> it is very important that we discount CF @ semi-annual rates because it has to be the same measurement as the time periods otherwise we get the wrong answer)

Duration of Liabilities = 1707.73/900 = 1.8975 years Time to calculate k! DA = 9.94 years, DL = 1.8975 years K = liability/total assets = 900,000/1,000,000 = 0.9 DGAP = 9.94 – 0.9 x 1.8975 = 8.23225 years Hedging through Forwards & Futures Example: 20 year $1 million face value bond, current price = $970,000 and interest rates expected to increase from 8 per cent to 10 per cent over next 3 months.  From duration model, the change in bond value: ΔP/P = -D x ΔR / (1+R) ΔP/$970 000 = –9 x (0.02/1.08] -- duration value is given!  

ΔP = –$161 666.67 This means if interest rates increase from 8-10%, this means the bond value will fall by $161,666.67. This drop in bond value can be directly hedged by selling a 3 month forward contract at a forward price of $970,000. How does this work? Well, look at the table below! Time Period Now

(Current Market Value of $970,000)

In 3 months (Current Market Value of $808,333)

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Payments Seller (YOU) agrees to sell a 20-year $1 million face value bond in 3 months’ time for $970,000 Buyer (SOMEONE ELSE) agrees to buy a 20-year $1 million face value bond in 3 months for $970,000 Seller (YOU) goes into the open market and purchases a 20year $1 million face value bond for $808,333 – current market price. Then you go and sell it to the buyer for the agreed price of $970,000 (profit of $161,666.67) Buyer (SOMEONE ELSE) buys the 20-year $1 million face value bond for $970,000 (loss of $161,666.67)

Essentially, two things have happened: the bond you held in your portfolio has experienced a drop in value of $161,666.67. However, you made a profit on your forward contract ($161,666.67), so the forward contract has exactly offset/hedged the drop in the value of your bond (that is held in your portfolio) – it has effectively offset the loss exposure!

Q: Given: Assets = $950. Duration = 10 years. Liabilities = $860. Duration = 2 years. Equity = $90. a) What is the FI’s duration gap? DGAP = D A – kDL = 10 – (86/95 x 2) = 8.19 years The financial institution has a positive duration gap which means that the firm’s DA > DL. This means that the firm’s liabilities will mature faster than the firm’s assets, so the firm will need to refinance their liabilities (deposits). By refinancing their deposits, they will be exposed to interest rate increases because if interest rates go up, it means that they will have to pay out a higher amount of interest to their depositors.

b) From (a), we note the FI has a positive duration gap so it is exposed to interest rate increases. Now what does this mean for the FI? An increase in interest rates means that the firm’s market value of equity will decrease. So, the FI will want to offset this decrease by macrohedging its balance sheet – the FI will sell (“go short on”) forward or futures contracts. Why? Because the FI will make a profit on the forward contracts if the value of the contracts go down – i.e. buy the forward contract, lock in the price – if the price goes down, then you can sell it at the higher agreed price. c) If interest rates increase by 1%, the firm’s equity value will change by: ΔE = - D x A x ΔR / (1 + R) = - 8.19 x $950,000 x +0.01 = -$77,805. An increase in interest rates by 1% will decrease firm equity by $77,805. To macrohedge the firm’s balance sheet, the FI must sell futures contracts that will offset the decrease in equity. With a 1% increase in interest rates, the firm’s futures position will fall by: ΔF = - D x F x ΔR / (1 + R) = -9 x 96,000 x 0.01 = -$8,640 per futures contract. Note: The 96,000 is the value of one futures contract. For treasury notes, one futures contract covers 1000 bonds, so if each bond trades at $96, then one futures contract = $96,000. So if interest rates increase by 1%, the firm’s futures position will fall by $8,640 per contract. However, since this macrohedge is a short hedge – meaning that, since the firm has sold futures contracts and locked in the forward price - this will offset the fall in value by $8,640 per contract To fully hedge a 1% increase, 77,805/8,640 = 9.005 futures contracts or 10 contracts. Q: An FI is planning the purchase of a $5 million loan to raise the existing average duration of its assets from 3.5 years to 5 years. It currently has total assets worth $20 million, $5 million in cash (0 duration) and $15 million in loans. All the loans are fairly priced. a) Assuming it uses the cash to purchase the loan, should it purchase the loan if its duration is seven years? The duration of the existing loan is: 0 + $15m/$20m (X) = 3.5 years Existing loan duration = 4.667 years If it purchases $5 million of loans with an average duration of 7 years, its portfolio duration will increase to $5m/$20m (7) + $15m/$20m (4.667) = 5.25 years. In this case, the average duration will be above 5 years (of its liabilities). The FI may be better off seeking another loan with a slightly lower duration. b) What asset duration loans should it purchase in order to raise its average duration to five years? The FI should seek to purchase a loan of the following duration: $5m/$20m(X) + $15m/$20m (4.667 years) = 5 years  X = duration = 6 years. The Risk Metrics model: Fixed Income Securities  Market risk measures the estimated potential loss under adverse circumstances.  

Daily earnings at risk (DEAR) = dollar market value of the position x price volatility Price volatility can be stated as: (–MD) x adverse daily yield move

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Where MD = D / (1+R) and Adverse daily yield move = standard deviation x z-score value of confidence interval

The Risk Metrics model: Foreign Exchange  In the case of foreign exchange, DEAR is computed in the same way as interest rate risk. 

Dollar equivalent value of position = FX position x spot exchange rate

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DEAR = dollar value of position x FX volatility

The Risk Metrics model: Equities  For equities, if the portfolio is well diversified then:  DEAR = dollar value of position x stock market return volatility, where the market return volatility is calculated as the standard deviation of the market  M x z-score value. 

For less well diversified FIs, the effect of unsystematic risk on the value of the trading position would need to be added.

Ch9Q4. A bank has a $1 million position in a five-year, zero-coupon bond with a face value of $1,402,552. The bond is trading at a yield to maturity of 7 per cent. The historical mean change in daily yields is 0.0 per cent, and the standard deviation is 12 basis points. a) What is the modified duration of the bond? Maturity of the bond is 5 years. It is a zero coupon bond so its duration is also 5 years. Modified duration = Macaulay duration / 1 + yield to maturity = 5 / (1+0.07) = 4.6729 years b) What is the maximum adverse daily yield move given that we desire no more than a 5 per cent chance that yield changes will be greater than this maximum? If we assume yield changes are distributed normally, 90% of the time, yield changes will be within 1.65 standard deviations from the mean. Potential adverse move in yield at 5% = 1.65 standard deviations = 1.65 x (0.0012) = 0.001980 or 0.1980% c) What is the price volatility of this bond? Price volatility = -MD x potential adverse move in yield = - 4.6729 x 0.001980 = -0.009252 or -0.9252% d) What are the daily earnings at risk for this bond? DEAR = dollar value of position x price volatility = $1,000,000 x 0.009252 = $9252 (no minus sign) Ch9Q12. Bank of Ayers Rock's stock portfolio has a market value of $10,000,000. The beta of the portfolio approximates the market portfolio, whose standard deviation of returns has been estimated at 1.5%. What is the 5-day VAR of this portfolio, using adverse rate changes in the 99th percentile? At a 98% confidence interval (same as 99th percentile), the Z-score is 2.33. Assuming that the volatility of stock market returns are normally distributed, it means that 98 per cent of the time, the volatility of the market will not exceed 2.33 standard deviations from the mean. With a 1.5% standard

deviation, this corresponds to a 3.495% (volatility in returns). This means there is a 1% chance that the stock market returns will exceed 3.495% on any given day. DEAR = dollar value of position x stock market return volatility DEAR = dollar value of position x (z-score x standard deviation of returns for the stock portfolio) = $10,000,000 x (2.33 x 0.015) = $349,500 5 day VaR = amount of VaR over the next 5 days = $349,500 x

√5

)=

349,500 x 2.2351 = $781,505.76     Linear discriminant models o Altman's Z score model for manufacturing firms Z = 1.2X1 + 1.4X2 + 3.3X3 + 0.6X4 + 1.0X5 o Z gives you a probability of the borrower defaulting  X1 = Working capital/total assets  X2 = Retained earnings/total assets  X3 = EBIT/total assets  X4 = Market value equity/book value long-term debt  X5 = Sales/total assets o Critical values of Z = 1.81 and Z = 2.99 -> if Z-value <1.91, high credit risk (high probability of defaulting/bankruptcy), if Z-value is >2.99, low credit risk (low probability of defaulting, most likely a financially stable company), if Z-value is in the range of 1.81 and 2.99, borrower is said to have (indeterminant credit risk)  

Assume: 1 – P1 = 0.04 = marginal default probability in year 1. 1 – P2 = 0.06 = marginal default probability in year 2.

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Survival probability = 0.96 × 0.94 = 0.9024 = 90.24%.

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Cumulative default probability: o = 1 – [(p1) (p2)] where p1 and p2 are the probabilities of non-default o Thus: 1 – (0.96 × 0.94) = 9.76%.

Tutorial 7: Credit risk I: individual loan risk Ch20Q10. MNO Inc., a publicly traded manufacturing firm, has provided the following financial information in its application for a loan. Assets $ Liabilities and equity $ Cash 20 s payable 30 s 90 Notes payable 90 receivables Inventory 90 Accruals 30 Long-term debt 150 Plant and 50 Equity 400 equipment 0 Total assets 70 Total liabilities and 700 0 equity Also assume sales = $500, cost of goods sold = $360, taxes = $56, interest payments = $40 and net income = $44; the dividend payout ratio is 50 per cent and the market value of equity is equal to the book value. Assume prior retained earnings are zero.

Net working capital = current assets minus current liabilities Current assets = cash + s receivable + inventories Current liabilities = s payable + accruals + notes payable EBIT = revenues – cost of goods sold – depreciation Taxes = (EBIT – interest)(tax rate) Net income = EBIT – interest – taxes Retained earnings = net income (1 – dividend payout ratio) (a) What is the Altman discriminant function value for MNO Inc.? Z = 1.2X1 + 1.4X2 + 3.3X3 + 0.6X4 + 1.0X5 X1 = working capital / total assets = 0.0714 X2 = retained earnings / total assets = 0.0314 X3 = EBIT / total assets = 0.20 X4 = market value of equity / long term debt = 2.67 X5 = sales / total assets = 0.7143 Therefore: Z = 1.2(0.0714) + 1.4(0.0314) + 3.3(0.20) + 0.6(2.67) + 1(0.7143) = 3.204 23. A bank has made a loan charging a base lending rate of 10 per cent. It expects a probability of default of 5 per cent. If the loan is defaulted, it expects to recover 50 per cent of its money through sale of its collateral. What is the expected return on this loan? Expected return on loan: p(1 + k) + (1 – p)(α) Where p is the probability of non-default; and α is the % recovered when the loan is defaulted Therefore: E(r) = 0.95(1+0.10) + 0.05 (1+0.10)(0.50) = 1.0450 + 0.0275 = 1.0725 – 1 = 7.25% Q12. CountrySide Bank uses the Moody's KMV Portfolio Manager Model to evaluate the risk–return characteristics of the loans in its portfolio. A specific $10 million loan earns 2 per cent per year in fees, and the loan is priced at a 4 per cent spread over the cost of funds for the bank. For collateral considerations, the loss to the bank if the borrower defaults, will be 20 per cent of the loans face value. The expected probability of default is 3 per cent. What is the anticipated return on this loan? What is the risk of the loan? The expected return on a loan is measured by the all-in-spread (AIS) which measures annual fees earned on the loan plus the annual spread between the loan rate paid by the borrowers and the FI’s cost of funds. The expected loss is equal to the expected probability of the borrower defaulting over the next year – that is, the expected default frequency (EDF) – multiplied by the amount of the loss by the FI if the borrower defaults – that is, the loss given default (LGD) Expected return (R) = AIS – E(L) = (fees + spread) – (EDF x LGD) = (0.02 + 0.04) – (0.03 x 0.20) = 0.054 or 5.4% Risk of the loan = σD x LGD = =

√ [(EDF) x (1 – EDF) x LGD √ [(0.03 x (1 – 0.03)] x 0.20 = 0.0341 or 3.41%

The risk of the loan reflects the volatility of the loan’s default rate (σD) around its expected value times the amount loss given default (LGD). The product of the volatility of the default rate and the LGD is called the unexpected loss on the loan (UL) and is a measure of the loan’s risk. To measure the volatility of the default rate, assume the loan can either default or repay (that is, not default), then the defaults are binomially distributed and the standard deviation of the default rate for the ith borrower (σD) is

√ [(EDF) x (1 – EDF) x LGD.

Net Exposure of a FI  Net exposure of an FI = (FX Assetsi – FX liabilitiesi) + (FX boughti – FX soldi) = Net foreign assetsi + Net FX boughti  Net long in a currency: asset holding > liabilities in that currency  Net short in a currency: asset holding < liabilities in that currency  FX exposure = Dollar loss/gain in currency i = Net exposure in foreign currency i measured in Australian dollars x shock (volatility) to the $/foreign currency i exchange rate Tutorial 9: Sovereign risk Ch12Q17. Chase Bank holds a $200 million loan to Argentina. The loans are being traded at bid-offer (buy/sell) prices of 91–93 per 100 in the London secondary market. Note: this means someone else will BUY the loan from you for $0.91 and will SELL the loan to you for $0.93. We only look at the $0.91 value, since we (the bank) are the owner of the $200m loan. (a) If Chase has an opportunity to sell this loan to an investment bank at a 7 per cent discount, what are the savings after taxes compared to selling the loan in the secondary market? Assume the tax rate is 40 per cent. Sell to investment bank: Sell in secondary market: Amount received = $200m x (1 – 0.07) = Amount received = 0.91 x $200m = $186m $182m Tax loss benefit = ($200m – $186m) x Tax loss benefit = ($200m – $182m) x 0.40 = $5.6m 0.40 = $7.2m Net price received = $186m + $5.6m = Net price received = $182m + $7.2m = $191.6m $189.2m So selling to an investment bank would generate an extra $2.4m (b) The investment bank in turn sells the debt at a 6 per cent discount to a real estate company planning to build apartment complexes in Argentina. What is the profit after taxes to the investment bank? The investment bank purchased the loan for $186m. It sells the loans for $200m x (1 – 0.06) = $188m The profit before taxes is $188m - $186m = $2m The tax rate is 40%, so the profit after taxes is $1.2m (c) The real estate company converts this loan into pesos under a debt-equity swap organised by the Argentinean Government. The official rate for dollar to peso conversion is P1.05/$1. The free market rate is P1.10/$1. How much did the real estate company save by investing in Argentina through the debt-equity

swap program as opposed to directly investing $200 million using the free market rates? If the real estate company had invested directly (if they did not buy the loans), it would have received $200m × 1.10 = 220 million pesos. By purchasing through the debt-equity swap, the company pays $188 million and receives $200m × 1.05 = 210 million pesos, for an equivalent rate of 210/188 = P1.117/$1. Thus, it still saves by purchasing through the debt-for-equity swap (P1.117/$1 > P1.10/$1). (d) How much would Chase benefit from doing a local currency debt-equity swap itself? Why doesn't the bank do this swap? Assuming the bank could convert the loan at $118 million into pesos at P1.05/$1, the after tax effect would be $188 million plus the tax loss benefit, which equals: $188m + ($200m - $188m) x 0.40 = $192.8 million The actual benefit was $191.6 million, the net price from part (a). So the bank would gain $1.2 million. However, the bank doesn’t do this swap because the Federal Reserve Regulation K does not allow Chase to participate in debt-equity purchases in other countries. Chase is also not allowed to engage in commerce in other countries. Furthermore, a long term pesos denominated position on the balance sheet may create more credit, liquidity, and foreign exchange risk problems than the benefits are worth. Ch13Q30. An FI has assets denominated in UK pound sterling of AUD$125 million and sterling liabilities of AUD$100 million. (a) What is the FI's net exposure? The net exposure is $125 million - $100 million = $25 million (b) Is the FI exposed to an A$ appreciation or depreciation? The financial institution is exposed to an appreciation in AUD, or declines in the value of the pounds sterling relative to the AUD. (c) How can the FI use futures or forward contracts to hedge its FX rate risk? The financial institution can hedge its FX rate risk by selling forward contracts in pound sterling, assuming the contracts are quoted as AUD/STG. (d) What is the number of futures contracts to be utilised to hedge fully the FI's currency risk exposure? Assuming that the contract size for STG is £62,500, the FI must sell: Nf = 25,000,000 / 62,500 = 400 pound sterling future contracts. (e) If the British pound falls from $1.60/£ to $1.50/£, what will be the impact on the FI's cash position? The cash position will see a loss if the STG depreciated in of the USD. The loss will be equal to the net exposure (in AUD) multiplied by the FX rate shock ΔS. AUD 25 million x (1.50 – 1.60) = 25 x -0.1 = -2.5 million (f) If the British pound futures price falls from $1.55/£ to $1.45/£, what will be the impact on the FI's futures position? The gain on the short futures hedge is: Nf x 62,500 x Δft = -400 x (62,500) x (1.45 – 1.55) = +2.5 million Liquidity index

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Developed by James Pierce, it measures the potential loss a DI could suffer from a sudden disposal of assets, compared to the amount it would receive under normal market conditions Where: Wi = weighting % of each asset in the DI's portfolio Pi = the immediate sales price Pi* = the fair market price The liquidity index always lies between 0 and 1 Example: Assume a DI has two assets: 40 per cent in one-month Treasury bonds and the remaining 60 per cent in personal loans. If the DI liquidates the Treasury bonds today, it receives $98 per $100 face value, but it would receive the full face value on maturity (in one month's time). If the DI liquidates its loans today, it receives $82 per $100 face value, whereas liquidation closer to maturity that is in one month’s time would lead to $93 per $100 of face value. What is the one-month liquidity index? Answer: P1 = 0.98 P*2 = 0.93

P*1 = 1.00 W1 = 0.4

P2 = 0.82 W2 = 0.6

Tutorial 10: Liquidity Risk Ch15Q13. An FI has estimated the following annual costs for its demand deposits: management cost per = $140, average size = $1500, average number of cheques processed per per month = 75, cost of clearing a cheque = $0.10, fees charged to customer per cheque = $0.05, and average fee charged per customer per month = $8. (a) What is the implicit interest cost of demand deposits for the FI? Cost of clearing cheques = $0.10 × 75 × 12 = $90 Cost of managing each = $140 Per cheque fee per = $0.05 × 75 × 12 = –$45 Fee received per = $8 × 12 = –$96 Total cost per = $89 The average (implicit) interest cost of demand deposits = $89/1500 = 5.93 per cent. (b) If the FI has to keep an average of 8 per cent of demand deposits as required reserves with the RBA paying no interest, what is the implicit interest cost of demand deposits for the FI? If the bank has to keep 8 per cent as reserves, its use of funds is limited to 0.92 × $1500 per or $1380. The average (imputed) interest cost = $89/$1380 = 6.45 per cent. (c) What should be the per-cheque fee charged to customers to reduce the implicit interest costs to 3 per cent? Ignore the reserve requirements. For an average imputed interest cost of 3 per cent, the total cost per = 1500 × 0.03 = $45. This means that the total cost per should be decreased by $44 ($89 – $45) and the per-cheque fee charged to customers

should be increased to $89 ($45 + $44). Thus, the fee per-cheque should be raised to $89/(75 × 12) = $0.0989 per cheque.

Tutorial 11: Off balance sheet Risk Q10) Suburb Bank has issued a one-year loan commitment of $10,000,000 for an up-front fee of 50 basis points. The back-end fee on the unused portion of the commitment is 20 basis points. The bank requires a compensating balance of 10 per cent of the loan drawn down to be placed in demand deposits. In addition, it has a cost of funds of 7 per cent, will charge an interest rate on the loan of 9 per cent, and must maintain reserve requirements on demand deposits of 10 per cent. The customer is expected to draw down 60 per cent of the commitment at the beginning of the year. (a) What is the expected return on this loan? Up-front fee = 0.0050 x $10,000,000 = $50,000 Interest Income = 0.09 x $10,000,000 x (0.6) = $540,000 Back-end fee = 0.002 x $10,000,000 x (1-0.6) = $8,000 Total revenue for the year = $598,000 Funds committed: Value of the drawn down Loan = $10,000,000 x 0.6 = $6,000,000 Value of the Compensating balance (10% drawn down loan) = $10,000,000 x 0.6 x 0.1 = $600,000 Value of the Reserve requirement (10% CB) = $10,000,000 x 0.6 x 0.1 x 0.1 = $60,000 Total funds committed for the year = $5,460,000 Expected return = $598,000 / $5,460,000 = 0.1095 or 10.95% (b) What is the expected annual return on the loan if borrower delays the drawdown commitment until at the end of six months? If the draw down is in six months, both the up-front and back-end fees remain the same. But the interest earned is for six months only = $540,000/2 = $270,000. So the total revenue will now be $50,000 + $270,000 + $8,000 = $328,000 Funds committed will also be halved = $5,460,000 = $2,730,000. The funds committed is halved because the loan only runs for the remaining half year, and we’re calculating the annual rate of return! The expected annual rate of return = $328,000 / $2,730,000 = 12.0147% The return in (b) is greater than (a), because the fees are dollar sensitive, not time sensitive! Q18. A corporation is planning to issue $1 million of 270-day commercial paper for an effective annual yield of 5 per cent. The corporation expects to save 30 basis points (0.3%) on the interest rate by using either an SLC or a loan commitment as collateral for the issue. Note: the commercial paper borrowing only occurs for 270 days, so interest % charged and interest % saved on using a SLC or loan commitment is applied to the 270/365 portion only! (a) What are the net savings to the corporation if a bank agrees to provide a 270day SLC for an up-front fee of 20 basis points to back the commercial paper issue? Cost of using SLC = 0.0020 (or 0.2%) x $1,000,000 = $2,000

Savings by using SLC = 0.0030 (or 0.3%) x (270/365) x $1,000,000 = $2,219.18 Net savings = $219.18 (b) What are the net savings to the corporation if a bank agrees to provide a 270day loan commitment to back the issue? The bank will charge 10 basis points for an up-front fee and 10 basis points for a back-end fee for any unused portion of the loan. Assume the loan is not needed (unused) and that the fees are on the face value of the loan commitment. Up-front fee of loan commitment = 0.0010 (or 0.1%) x $1,000,000 = $1,000 Back end fee (loan not used) = 0.0010 (or 0.1%) x $1,000,000 = $1,000 Savings by using loan commitment = 0.0030 (or 0.3%) x (270/365) x 1,000,000 = $2,219.18 Net savings = $219.18 Measuring capital adequacy Risk-based capital ratios – APRA requirements  Common Equity Tier 1 must be at least 4.5 per cent of risk-weighted assets at all times; that is o (Common Equity Tier 1 Capital) / (Total Risk Adjusted Assets) ≥ 4.5 per cent  Total Tier 1 capital must be at least 6 per cent of risk-weighted assets at all times; that is o (Total Tier 1 Capital) / (Total Risk Adjusted Assets) ≥ 6 per cent  Total Capital or Total Regulatory Capital (Tier 1 capital plus Tier 2 capital) must be at least 8 per cent of risk-weighted assets at all times; that is o (Total Regulatory Capital) / (Total Risk Adjusted Assets) ≥ 8 per cent Tutorial 12: Capital Adequacy Third Bank has the following balance sheet (in $m) with the risk weights in parentheses.

In addition, the bank has $30 million in performance-related standby letters of credit (SLCs), $40 million in two-year forward FX contracts that are currently in the money by $1 million, and $300 million in six-year interest rate swaps that are currently out of the money by $2 million. Credit conversion factors (taken from Tables 18.6 and 18.7 in the textbook) are:

(a) What are the risk-adjusted on-balance-sheet assets of the bank as defined under the Basel II?

Risk-adjusted assets: Cash 0 × 20 = $0 Interbank deposits 0.20 × 25 = $5 Mortgage loans 0.50 × 70 = $35 Business loans 1.00 × 70 = $70 Total risk-adjusted on-balance sheet assets = $110 = $110 (b) What is the total capital required for both off- and on-balance-sheet assets? Assumption risk weight 100% Standby LCs: $30 × 0.50 × 1.00 = $15 = $15 Foreign exchange contracts: Potential exposure $40 × 0.05 = $2 Current exposure in the money = $1 = $3 × 1.00 = $3 Interest rate swaps: Potential exposure $300 × 0.015 = $4.5 Current exposure out of the money = $0 = $4.5 × 1.00 = $4.5 Total risk-adjusted on- and off-balance-sheet assets = $132.5 × 0.08 Total minimum capital required = $10.66