Chapter 11 Credit risk II: loan portfolio and concentration risk Solutions for end-of-chapter questions Questions and problems How do loan portfolio risks differ from individual loan risks? Loan portfolio risks refer to the risks of a portfolio of loans as opposed to the risks of a single loan. Inherent in the distinction is the elimination of some of the risks of individual loans because of benefits from diversification. What is migration analysis? How do FIs use it to measure credit risk concentration? What are its shortcomings? Migration analysis uses information from the market to determine the credit risk of an individual loan or sectoral loans. For example, bankers can use S&P and Moody’s ratings to determine whether firms in a particular sector are experiencing repayment problems. This information can be used to either curtail lending in that sector or to reduce maturity and/or increase interest rates. A problem with migration analysis is that the information may be too late, because ratings agencies often downgrade issues only after the firm or industry has experienced a downturn. What does ‘loan concentration risk’ mean? Loan concentration risk refers to the extra risk borne by having too many loans concentrated with one firm, industry, geographical or economic sector. To the extent that a portfolio of loans represents loans made to a diverse cross-section of the economy, concentration risk is minimised. A manager decides not to lend to any firm in sectors that generate losses on that part of the loan portfolio in excess of 5 per cent of equity. (a) If the average historical losses in the car sector total 8 per cent, what is the maximum loan a manager can lend to a firm in this sector as a percentage of total capital? Maximum limit = (Maximum loss as a % of capital) × (1/Loss rate) = 0.05 × 1/0.08 = 62.5 per cent is the maximum limit that can be lent to a firm in the automobile sector. (b) If the average historical losses in the mining sector total 15 per cent, what is the maximum loan a manager can lend to a firm in this sector as a percentage of total capital? Maximum limit = (Maximum loss as a % of capital) × (1/Loss rate) = 0.05 × 1/0.15 = 33.3 per cent is the maximum limit that can be lent to a firm in the mining sector. An FI has set a maximum loss of 12 per cent of total capital as a basis for setting concentration limits on loans to individual firms. If it has set a concentration limit of 25 per cent to a firm, what is the expected loss rate for that firm? Maximum limit = (Maximum loss as a % of capital) × (1/Loss rate) 25 per cent = 12 per cent × 1/Loss rate Loss rate = 0.12/0.25 = 48 per cent Explain how modern portfolio theory can be applied to lower the credit risk of an FI’s portfolio. Modern portfolio theory has demonstrated that a well-diversified portfolio can provide opportunities for individuals to invest in a set of efficient frontier portfolios, defined as those portfolios that provide the maximum returns for a given level of risk or the lowest risk for a given level of returns. By choosing portfolios on the efficient frontier, a banker may be able to reduce credit risk to the fullest extent. As shown in Figure 9.1 in the textbook, a manager’s selection of a particular portfolio on the efficient frontier is determined by his or her risk–return trade-off. The Bank of Tiny town has two $20 000 loans that have the following characteristics: Loan A has an expected return of 10 per cent and a standard deviation of returns of 10 per cent. The expected return and standard deviation of returns for loan B are 12 per cent and 20 per cent, respectively. (a) If the covariance between A and B is 0.015 (1.5 per cent), what are the expected return and standard deviation of this portfolio? Expected return = 0.5(10%) + 0.5(12%) = 11 per cent Standard deviation = [0.52(0.102) + 0.52(0.202) + 2(0.5)(0.5)(0.015)]½ = 14.14 per cent (b) What is the standard deviation of the portfolio if the covariance is –0.015 (–1.5 per cent)? Standard deviation = [0.52(0.102) + 0.52(0.202) + 2(0.5)(0.5)(–0.015)]½ = 7.07 per cent (c) What role does the covariance, or correlation, play in the risk reduction attributes of modern portfolio theory? The risk of the portfolio as measured by the standard deviation is reduced when the covariance is reduced. If the correlation is less than perfectly positively correlated, that is, +1.0, the standard deviation of the portfolio always will be less than the weighted average standard deviations of the individual assets. Why is it difficult for small banks, credit unions and building societies to measure credit risk using modern portfolio theory? The basic premise behind modern portfolio theory is the ability to diversify and reduce risk by eliminating diversifiable risk. Small banks and thrifts may not have the ability to diversify their asset base, especially if the local markets in which they serve have a limited number of industries. The ability to diversify is even more acute if these loans cannot be traded easily. What is the minimum risk portfolio? Why is this portfolio usually not the portfolio chosen by FIs to optimise the return–risk trade-off? The minimum risk portfolio is the combination of assets that reduces the portfolio risk as measured by the standard deviation or variance of returns to the lowest possible level. This portfolio usually is not the optimal portfolio choice because the returns on this portfolio are very low relative to other alternative portfolio selections. By accepting some additional risk, portfolio managers are able to realise a higher level of return relative to the risk of the portfolio. The obvious benefit to holding a diversified portfolio of loans is to spread risk exposures so that a single event does not result in a great loss to the bank. Are there any benefits to not being diversified? One benefit to not being diversified is that a bank that lends to a certain industrial or geographic sector is likely to gain expertise about that sector. This may allow the FI to deliver substantially higher profits from its chosen specialisation. Being diversified requires that the bank becomes familiar with many more areas of business and so lending into areas they do not know as well as they possibly should or where risks are more accurately priced by their competitors in that sector. This may pose problems in some FIs, particularly relatively smaller institutions. A bank’s risk management director is attempting to rank, in terms of the risk–reward trade-off, the loan portfolios of three loan officers. How would you rank the three portfolios? The portfolios have the following information:
Portfolio Expected return % Standard deviation %
A 10 8
B 12 9
C 11 10
Portfolio B dominates portfolio C because B has a higher expected return and a lower standard deviation. Thus, C is clearly inferior. A comparison of portfolios A and B indicates that they represent a risk–return trade-off in that B has a higher expected return, but B also has a higher risk measure. A crude comparison may use the coefficient of variation, that is, CV = standard deviation/expected return, or the Sharpe ratio, that is, SR = [expected return – risk-free rate]/standard deviation. However, a judgement regarding which portfolio is ‘better’ would be based on the risk preference of the judge and the goals of the portfolio, such as greater stability versus a manager seeking higher returns. Country Side Bank uses the Moody’s Analytics 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 loan’s 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? Expected return = AISi – E(Li) = (0.02 + 0.04) – (0.03 × 0.20) = 0.054 or 5.4 per cent Risk of the loan = Di × LGDi = [0.03(0.97)]½ × 0.20 = 0.0341 or 3.41 per cent Information concerning the allocation of loan portfolios to different market sectors is given below:
Allocation of loan portfolios in different sectors (%)
Sectors National Bank A Bank B
Business 30 50 10
Consumer 40 30 40
Real estate 30 20 50
Bank A and Bank B would like to estimate how much their portfolios deviate from the national average. (a) Which bank is further away from the national average? Using Xs to represent portfolio holdings:
Bank A Bank B
(X1j – X1)2 (0.50 – 0.30)2 = 0.04 (0.10 – 0.30)2 = 0.04
(X2j – X2)2 (0.30 – 0.40)2 = 0.01 (0.40 – 0.40)2 = 0.00 Bank B deviates from the national average more than Bank A. (b) Is a large standard deviation necessarily bad for a bank using this model? No, a higher standard deviation is not necessarily bad for an FI because it could have comparative advantages that are not required or available to a national well-diversified bank. For example, a bank could generate high returns by serving specialised markets or product niches that are not well diversified. Or, a bank could specialise in only one product, such as mortgages, but be well diversified within this product line by investing in several different types of mortgages that are distributed both nationally and internationally. This would still enable it to obtain portfolio diversification benefits that are similar to the national average. Using regression analysis on historical loan losses, a bank has estimated the following: XC = 0.002 + 0.8XL and XH = 0.003 + 1.8XL where XC = loss rate in the business sector XH = loss rate in the consumer (household) sector XL = loss rate for its total loan portfolio. (a) If the bank’s total loan loss rates increase by 10 per cent, what are the increases in the expected loss rates in the business and consumer sectors? Business loan loss rates will increase by 0.002 + 0.8(0.10) = 8.20 per cent. Consumer loan loss rates will increase by 0.003 + 1.8(0.10) = 18.30 per cent. (b) In which sector should the bank limit its loans, and why? The bank should limit its loans to the consumer sector because the loss rates are systematically higher than the loss rates for the total loan portfolio. Loss rates are lower for the business sector. For a 10 per cent increase in the total loan portfolio, the consumer loss rate is expected to increase by 18.30 per cent, as opposed to only 8.2 per cent for the business sector. Suppose management is unwilling to permit losses exceeding 20 per cent of an FI’s capital to a particular sector. If management estimates that the amount lost per dollar of defaulted loans in this sector is 50 cents, find the concentration limit. The concentration limit is the maximum loans to a single sector as a per cent of capital, and is found as: Concentration limit = [maximum loss as a per cent of capital] × 1/Loss rate = 20% × [1/.5] = 40% What is the gain on the purchase of a $20 million credit forward contract with a modified duration of seven years if the credit spread between a benchmark Treasury Bond and a borrowing firm’s debt decreases by 50 basis points? The gain would be (CST – CSF) MD$20 million = 0.005 × 7 × $20 million = $700 000. How is selling a credit forward similar to buying a put option? After the loan is made, the FI sells a credit forward. If the credit risk of the borrower decreases sufficiently that the spread over the benchmark bond increases, the forward seller (the FI) will realise a gain at the maturity of the forward contract that will offset the decrease in value of the loan. Thus, the FI benefits as the credit risk of the borrower decreases. This is the exact same situation as a put option buyer when the stock price goes down. If the credit risk improves, the lender FI will pay the forward buyer because the benchmark spread will have decreased. However, since the spread can only decrease to zero, the FI has limited loss exposure. This is similar to paying a premium on a put option. A property-casualty (PC or general) insurance company has purchased catastrophe futures contracts to hedge against losses during the hurricane season. At the time of purchase, the market expected a loss ratio of 0.75. After processing claims from a severe hurricane, the PC actually incurred a loss ratio of 1.35. What amount of profit did the PC make on each $25 000 futures contract? The payoff = actual loss ratio × $25 000 = 1.35 × $25 000 = $33 750. What is a credit spread call option? A credit spread call option has a payoff that increases as the yield spread against some specified benchmark bond increases above the exercise spread. The increased payoff compensates the lender for decreases in value caused by an increase in the credit risk of the borrower. What is a digital default option? This option pays a stated amount in the event of a loan default. If the loan is repaid in its entirety, the option expires unexercised. How do the cash flows to the lender differ for a credit spread call option hedge from the cash flows for a digital default option spread? In both cases, the maximum loss to the call option purchaser is the amount of the premium paid for the option. The digital default option has a one-time, lump-sum cash payment at the time the loan defaults. The payoff for the credit spread option increases as the default risk increases. See Figures 23.17 and 23.18 in the textbook for a visual illustration of the payoff profiles. What is a catastrophe call spread option? How do the cash flows of this option affect the buyer of the option? For a premium the purchaser of this option receives a hedge against a range of loss ratios that may occur, where the loss ratio is the amount of losses divided by the insurance premiums. For loss ratios below the minimum in the option, the option expires out of the money. For loss ratios between the minimum and the maximum stated ratios, the option holder receives an increasing payoff as the loss ratio increases. For loss ratios in excess of the maximum ratio in the option, the holder of the option receives a maximum payoff equal to the maximum ratio in the option coverage. Thus, there is a cap or ceiling to the amount of payoff or benefit that can be received from this option. How does a pure credit swap differ from a total return swap? How does it differ from a digital default option? The total return swap includes an element of interest rate risk, while the pure credit swap has stripped this risk from the contract. In a pure credit swap, the lender makes a fixed fee or payment premium to the counterparty in exchange for the potential coverage of any loss due to a specific borrower defaulting on a loan. The swap is not tied to interest rate changes. The pure credit swap is similar in payoff to a digital default option with the exception that the premium is paid over the life of the swap rather than at the initiation of the risk coverage as with the option. Why is the credit risk on a swap lower than the credit risk on a loan? The credit risk on a swap is lower than that of a loan for the following reasons: (a) Swaps do not involve the exchange of principal payments. They only involve the swapping of interest payments, so the most a counterparty can lose is the difference in the interest payments. (b) In most cases, payments are made through netting by novation, which nets all payments with one counterparty, further reducing the possibility of default. (c) Swaps made by parties with poor credit ratings are usually backed by lines of credit, effectively making them collateralised loans, and further reducing their risks. What is netting by novation? Netting by novation involves the process of combining all contracts between two parties to determine the differential amount that must be forwarded from one party to another. Thus, all fixed-rate and variable-rate contracts are combined for a net payment. This reduces the potential for loss when some contracts are in the money and some contracts are out of the money. What role did the swap market play in the financial crisis of 2008–2009? The financial crisis showed just how much risk the swap market can present to FIs and the global financial system. Specifically, as the sub-prime mortgage market began to fail in the summer of 2008, sub-prime mortgage pools that FIs bought were overrated and ended up falling precipitously in value as foreclosures rose on the underlying mortgage pools. Many of the credit default swaps were written on these sub-prime mortgage securities. Thus, as mortgage securities started to fail, buyers of the CDS contracts wanted to be paid for these losses. AIG was a major writer of these CDS securities. As of 30 June 2008, AIG had written $441 billion worth of swaps on corporate bonds and mortgage-backed securities. And when mortgage-backed securities started going bad, AIG had to make good on billions of dollars of credit default swaps. The problem was exacerbated by the fact that so many FIs were tied to one another through these deals. Lehman Brothers alone had made more than $700 billion worth of swaps, and many of them were backed by AIG. As the value of these insured-referenced entities fell, AIG had massive write-downs and additionally had to post more collateral. Soon it became clear that AIG was not going to be able to cover its losses. The result was massive write-downs at banks, investment banks and insurance companies that had purchased the CDS contracts. Indeed, the reason the federal government stepped in and bailed out AIG was that the insurer was something of a last backstop in the CDS market. While banks and hedge funds were playing both sides of the CDS business—buying and trading them and thus offsetting whatever losses they took—AIG was simply providing the swaps and holding on to them. Had AIG been allowed to default, every FI that had bought a CDS contract from the company would have suffered huge losses in the value of the insurance contracts they had purchased, causing them their own credit problems. Global funding market pressures were also evident in the virtual shutdown of the FX swap market during the financial crisis. This risk was driven by demand for dollar funding from global financial institutions, particularly European financial institutions. As many of these institutions increasingly struggled to obtain funding in the unsecured cash markets, they turned to the FX swap market as a primary channel for raising dollar funding. This extreme demand for dollar funding led a sizable shift in FX forward prices, with the implied dollar funding rate observed in FX swaps on many major currencies rising sharply above that suggested by the other relative interest measures such as the dollar OIS (overnight index swap) rate and the dollar LIBOR. Dealers reported that bid-ask spreads on FX swaps increased to as much as 10 times the levels that had prevailed before August 2007. During the quarter, the spread of the three-month FX swap-implied dollar rate from euro and sterling—US dollar FX forward points—over the dollar LIBOR fixing rate widened to around 330 and 260 basis points, respectively, in early October after the Lehman failure. An FI has a concentration of home mortgages and is feeling exposed to increasing interest rates and the impact that this may have on the default characteristics of the mortgage portfolio. How may loan sales and/or securitisation assist the FI to diversify their portfolio? The FI has a number of options. It could sell mortgages outright to other FIs. Alternatively, it could sell mortgages to a securitisation special purpose vehicle. The proceeds of the sale of the mortgages could be used to purchase business loans. The following questions and problems relate to material in Appendixes 11A and 11B. From Table 8A.1, what is the probability of a loan upgrade? A loan downgrade? The probability of an upgrade is 5.95% + 0.33% + 0.02% = 6.30%. The probability of a downgrade is 5.30% + 1.17% + 0.12% = 5.59%. (a) What is the impact of a rating upgrade or downgrade? The effect of a rating upgrade or downgrade will be reflected in the credit-risk spreads or premiums on loans, and thus on the implied market value of the loan. A downgrade should cause this credit spread premium to rise. (b) How is the discount rate determined after a credit event has occurred? The discount rate for each year in the future in which cash flows are expected to be received includes the forward rates from the current Treasury yield curve plus the annual credit spreads for loans of a particular rating class for each year. These credit spreads are determined by observing the spreads of the corporate bond market over Treasury securities. (c) Why does the probability distribution of possible loan values have a negative skew? The negative skew occurs because the probability distribution is non-normal. The potential downside change in a loan’s value is greater than the possible upside change in value. (d) How do the capital requirements of the Credit Metrics approach differ from those of the BIS? The Fed and the BIS require the capital reserve to be 8 per cent of the book value of the loan. Under Credit Metrics each loan is likely to have a different VaR and thus a different implied capital requirement. Further, this required capital is likely to be greater than 8 per cent of book value because of the non-normality of the probability distributions. A five-year fixed-rate loan of $100 million carries a 7 per cent annual interest rate. The borrower is rated BB. Based on hypothetical historical data, the probability distribution given below has been determined for various ratings upgrades, downgrades, status quo and default possibilities over the next year. Information is also presented reflecting the forward rates of the current government bond yield curve and the annual credit spreads of the various maturities of BBB bonds over Treasuries.
Forward rate spreads at time t
Rating Probability distribution % New loan value plus coupon $ t rt% st%
AAA 0.01 114.82 1 3.00 0.72
AA 0.31 114.60 2 3.40 0.96
A 1.45 114.03 3 3.75 1.16
BBB 6.05 4 4.00 1.30
BB 85.48 108.55
B 5.60 98.43
CCC 0.90 86.82
Default 0.20 54.12
(a) What is the present value of the loan at the end of the one-year risk horizon for the case where the borrower has been upgraded from BB to BBB? (b) What is the mean (expected) value of the loan at the end of year 1? The solution table on the following page reveals a value of $108.06. (c) What is the volatility of the loan value at the end of year 1? The volatility or standard deviation of the loan value is $4.19. (d) Calculate the 5 per cent and 1 per cent VaRs for this loan assuming a normal distribution of values. The 5 per cent VaR is 1.65 × $4.19 = $6.91. The 1 per cent VaR is 2.33 × $4.19 = $9.76.
Year-end rating Probability Value Probability × value Deviation Probability × deviation squared
AAA 0.0001 $114.82 $0.01 6.76 0.0046
AA 0.0031 $114.60 $0.36 6.54 0.1325
A 0.0145 $114.03 $1.65 5.97 0.5162
BBB 0.0605 $113.27 $6.85 5.21 1.6402
BB 0.8548 $108.55 $92.79 0.49 0.2025
B 0.0560 $98.43 $5.51 –9.63 5.1968
CCC 0.0090 $86.82 $0.78 –21.24 4.0615
Default 0.0020 $54.12 $0.11 –53.94 5.8197
1.0000 Mean = $108.06 Variance = 17.5740
Standard deviation = $4.19
(e) Estimate the ‘approximate’ 5 per cent and 1 per cent VaRs using the actual distribution of loan values and probabilities. 5% VaR = 95% of actual distribution = $108.06 – $102.02 = $6.04 1% VaR = 99% of actual distribution = $108.06 – $86.82 = $21.24 where: 5% VaR is approximated by 0.056 + 0.009 + 0.002 = 0.067 or 6.7 per cent, and 1% VaR is approximated by 0.009 + 0.002 = 0.011 or 1.1 per cent. Using linear interpolation, the 5% VaR = $10.65 million and the 1% VaR = $19.31 million. For the 1% VaR, $19.31 = (1 – 0.1/1.1) × $21.24. (f) How do the capital requirements of the 1 per cent VaRs calculated in parts (d) and (e) compare with the capital requirements of the BIS? The BIS system would require 8 per cent of the loan value, or $8 million. The 1 per cent VaR would require $19.31 million under the approximate method, and $9.76 million in capital under the normal distribution assumption. In each case, the amounts exceed the BIS amount. How does the Credit Risk3 model of Credit Suisse Financial Products differ from the Credit Metrics model of JPMorgan Chase? Credit Risk attempts to estimate the expected loss of loans and the distribution of these losses with the focus on calculating the required capital reserves necessary to meet these losses. The method assumes that the probability of any individual loan defaulting is random, and that the correlation between the defaults on any pair of loan defaults is zero. Credit Metrics is focused on estimating a complete VaR framework. An FI has a loan portfolio of 10 000 loans of $10 000 each. The loans have a historical default rate of 4 per cent, and the severity of loss is 40 cents per $1. (a) Over the next year, what are the probabilities of having default rates of 2, 3, 4, 5 and 8 per cent?
n 2 3 4 5 8
Probability 0.1465 0.1954 0.1954 0.1563 0.0298
(b) What would be the dollar loss on the portfolios with default rates of 4 and 8 per cent? Dollar loss of 4 loans defaulting = 4 × 0.40 × $10 000 = $16 000 Dollar loss of 8 loans defaulting = 8 × 0.40 × $10 000 = $32 000 (c) How much capital would need to be reserved to meet the 1 per cent worst-case loss scenario? What proportion of the portfolio’s value would this capital reserve be? The probability of 8 defaults is ~3 per cent. The probability of 10 defaults is 0.0106 or close to 1 per cent. The dollar loss of 10 loans defaulting is $40 000. Thus, a 1 per cent chance of losing $40 000 exists. A capital reserve should be held to meet the difference between the unexpected 1 per cent loss rate and the expected loss rate of 4 defaults. This difference is $40 000 minus $16 000 or $24 000. This amount is 0.024 per cent of the total portfolio. Web questions Go to the Bank for International Settlements (BIS) website and review any recent papers dealing with the implementation of risk-based models for measuring loan portfolio risk. However, the BIS regularly publishes research papers, reports, and publications on various topics related to banking, financial stability, and risk management. To find recent papers on the implementation of risk-based models for measuring loan portfolio risk from the BIS website, you can follow these general steps: 1. Visit the BIS website: Go to the official website of the Bank for International Settlements at www.bis.org. 2. Navigate to the Research section: Look for a section or tab on the website dedicated to research, publications, or working papers. This is where you're likely to find the latest research papers and reports. 3. Search for relevant papers: Use the search function on the BIS website to look for papers related to risk-based models for measuring loan portfolio risk. You can use keywords such as "loan portfolio risk," "credit risk models," "risk-based modeling," etc. 4. Filter by date: If available, you can filter the search results by date to focus on recent papers published by the BIS. 5. Review abstracts or summaries: Once you've identified relevant papers, review the abstracts or summaries to understand their scope, methodology, and key findings. 6. Access the full papers: If the papers are freely available, you can download and read the full texts directly from the BIS website. Otherwise, you may need to check if access is restricted or if the papers are available through other channels such as academic databases or subscriptions. By following these steps, you should be able to find and review any recent papers from the Bank for International Settlements dealing with the implementation of risk-based models for measuring loan portfolio risk. If you encounter any difficulties or have specific questions, you can also reach out to the BIS directly for assistance or inquire about their research publications. Go to your central bank’s website to see how recommendations from the BIS are being implemented in your country. See the RBA website at: www.rba.gov.au, the New Zealand website at www.rbnz.govt.nz or the central bank homepage in your country. As an AI language model, I don't have access to real-time data or the ability to browse the internet, including central bank websites. Therefore, I can't provide specific information on how recommendations from the Bank for International Settlements (BIS) are being implemented in any particular country. However, central banks often play a crucial role in implementing international standards and recommendations, including those set forth by the BIS. The BIS provides guidelines, frameworks, and best practices for central banks and financial institutions worldwide to promote financial stability, sound risk management, and effective supervision. To see how recommendations from the BIS are being implemented in a specific country, you would typically visit the website of that country's central bank. On the central bank's website, you might find information about regulatory updates, policy initiatives, and supervisory practices that align with BIS recommendations. For example, central banks may adopt Basel Committee on Banking Supervision (BCBS) standards, which are set by the BIS, to strengthen the regulation and supervision of banks in their jurisdictions. These standards cover areas such as capital adequacy, risk management, and liquidity requirements. Additionally, central banks may issue reports, guidelines, or consultative documents that reflect BIS recommendations on various aspects of monetary policy, financial stability, and banking supervision. To find out how recommendations from the BIS are being implemented in your country, you can visit the website of your central bank and look for relevant publications, speeches by central bank officials, or regulatory updates that reference international standards and guidelines from organizations like the BIS. You may also contact your central bank directly for more information or clarification on specific issues. Integrated mini case As a senior loan officer at MC Financial Corp, you have a loan application from a firm in the biotech industry. While the loan has been approved on the basis of an individual loan, you must evaluate the loan based on its impact on the risk of the overall loan portfolio. The FI uses the following three methods to assess its loan portfolio risk. 1 Concentration limits—The FI currently has lent an amount equal to 40 per cent of its capital to the biotech industry and does not lend to a firm in any sector that generates losses in excess of 2 per cent of capital. The average historical losses in the biotech industry total 5 per cent. Concentration limit = (maximum loss as a per cent of capital) × (1/loss rate) = 0.02 × 1/0.05 = 40 per cent of capital is the maximum amount that can be lent to firms in the biotech sector. MC Financial already has 40 per cent of its capital lent out to the biotech industry. To give out this new loan would put the FI over its concentration limit. Thus, MC Financial should not grant this loan. 2 Loan volume-based model—National and MC Financial’s loan portfolio allocations are as follows.
Allocation of loan portfolios in different sectors (%)
Sectors National MC Financial
Business 30 40
Real estate 50 45
Consumer 20 15
MC Financial does not want to deviate from the national average by more than 12.25 per cent. Using Xs to represent portfolio holdings: (X1j – X1)2 (0.40 – 0.30)2 = 0.0100 (X2j – X2)2 (0.45 – 0.50)2 = 0.0025 (X3j – X3)2 (0.15 – 0.20)2 = 0.0025 = 12.25 per cent The FI’s standard deviation in its loan portfolio allocation is 12.25 per cent. To issue another business loan would push MC Financial even further from the national average. Thus, the FI would not want to give out the loan. 3 Loan loss ratio-based model—Based on regression analysis on historical loan losses, the FI estimates the following loan loss ratio models: Xbus = 0.001 + 0.85XL and Xcon = 0.003 + .65XL where Xbus = loss rate in the business sector, Xcon = loss rate in the consumer (household) sector, XL = loss rate for its total loan portfolio. MC Financial’s total increase in the loan loss ratio is expected to be 12 per cent next year. Based on consideration of all three methodologies, should MC Financial Corp. grant this loan? Business loan loss rates will increase by 0.001 + 0.85(0.12) = 10.30 per cent. Consumer loan loss rates will increase by 0.003 + .65(0.12) = 8.10 per cent. MC Financial should limit its loans to the business sector because the loss rates are systematically higher than the loss rates for the total loan portfolio. Loss rates are lower for the consumer sector. For a 12 per cent increase in the total losses in the loan portfolio, the business loss rate is expected to increase by 10.30 per cent, as opposed to only 8.1 per cent for the consumer sector. Thus, MC Financial should not issue this loan. Based on all three models, from an overall loan portfolio perspective, MC Financial would not want to issue this loan to a firm in the biotech sector. Solution Manual for Financial Institutions Management Anthony Saunders, Marcia Cornett, Patricia McGraw 9780070979796, 9780071051590
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