Example of a Bank's Expected Return Calculation with Default Probability
To illustrate how a bank manages risk, consider a scenario where it lends to many similar borrowers. The bank projects that 90% of these borrowers will repay their loans in full, but the remaining 10% will default and repay nothing. To compensate for the defaults, the bank sets a relatively high interest rate of 20%. Based on these probabilities, the bank can calculate its expected return across the entire portfolio, anticipating full repayment plus interest from the majority of loans and a total loss on the rest.
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Example of Bank Diversification with Multiple Borrowers
Example of a Bank's Expected Return Calculation with Default Probability
How Bank Diversification Reduces Return Variability Compared to Bilateral Loans
Principle of Uncorrelated Risks in Portfolio Diversification
Residual Risk in Diversified Loan Portfolios
A bank has $50 million available for lending and is evaluating two strategies. Strategy A involves lending the entire $50 million to a single, large, well-established corporation. Strategy B involves lending $500,000 to each of 100 different small businesses across various unrelated industries. From a risk-management perspective, which statement best analyzes the two strategies?
Evaluating a Bank's Lending Strategy
A bank that successfully diversifies its loan portfolio by lending to a large number of different borrowers across various industries can guarantee it will not suffer a financial loss from its lending operations.
Analyzing the Effectiveness of Diversification Strategies
The Principle of Diversification in Banking
A bank shifts its lending strategy from providing a few very large loans to a handful of clients in the technology sector to providing thousands of small loans to borrowers across many different, unrelated industries (e.g., agriculture, retail, manufacturing, healthcare). Which statement best explains the primary risk management benefit of this new strategy?
Match each lending scenario with its most accurate risk profile description.
A bank provides loans to 1,000 different startup companies. All of these companies operate exclusively within the emerging 'smart home' technology sector. A financial analyst claims the bank's loan portfolio is poorly diversified, despite the large number of borrowers. Which of the following statements best supports the analyst's claim?
A commercial bank aims to minimize its overall lending risk by applying the principle of diversification. It has $100 million to lend. Which of the following lending strategies best achieves this goal?
Evaluating Competing Diversification Strategies
Learn After
Formula for Expected Return on a Loan Portfolio with Default Risk
A financial institution provides 200 separate small business loans, each for $5,000. The institution charges an interest rate of 15% on each loan. Based on its risk assessment model, the institution projects that 6% of these businesses will fail and be unable to repay any portion of their loan. The remaining businesses are expected to repay their loans in full, including interest. What is the total amount of money the institution can expect to receive back from this entire portfolio of 200 loans?
Loan Portfolio Profitability Analysis
Calculating Required Interest Rate with Default Risk
A commercial bank issues 1,000 identical loans of $10,000 each. The bank charges an annual interest rate of 12% on these loans. Based on historical data, the bank anticipates that 8% of the borrowers will be unable to repay any amount, while the remaining borrowers will repay their loans in full with interest. Which statement best analyzes the financial outcome for the bank from this portfolio?
A bank has a large, diversified portfolio of loans. It currently charges an 18% interest rate and anticipates that 5% of its borrowers will default, repaying nothing. The remaining 95% are expected to repay in full. Which of the following independent changes to its lending model would result in the largest increase in the bank's expected return per dollar loaned?
A bank issues a large number of identical loans. It expects 5% of these loans to default, with the borrowers paying back nothing. To break even on its entire loan portfolio (i.e., to have an expected return of 0%), the bank must charge an interest rate of exactly 5% on the loans that are repaid.
A financial institution is deciding between two strategies for a loan portfolio valued at $100,000.
- Strategy A: Offer loans at a 20% interest rate, anticipating that 10% of borrowers will default and repay nothing.
- Strategy B: Offer loans at a 15% interest rate, anticipating that only 5% of borrowers will default and repay nothing.
By calculating the total expected monetary return for each strategy, determine which one is more profitable and by how much.
A bank issues a portfolio of 100 loans, each for $1,000, at an interest rate of 22%. The bank projects that 10% of the loans will default, with nothing being repaid. The remaining 90% of loans will be repaid in full with interest. Which of the following statements accurately breaks down the bank's expected net profit from this entire portfolio?
Bank Lending Strategy Evaluation
A bank has a loan portfolio totaling $1,000,000. The bank charges a 15% interest rate on all loans. Based on its analysis, the bank anticipates that 95% of the loans will be repaid in full (principal plus interest), while the remaining 5% will default, resulting in a complete loss of the principal for those loans. Match each financial component with its correct calculated value based on this scenario.