Formula for Expected Return on a Loan Portfolio with Default Risk
The expected return on a loan from a diversified portfolio is calculated by weighting the potential outcomes by their probabilities. For a loan with a repayment probability of at an interest rate of , and a default probability of with zero recovery, the expected return is: . For instance, with a 90% repayment probability and a 20% interest rate, the calculation is , yielding an expected return of 8% on the loan.
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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.
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Inverse Relationship Between Default Probability and Expected Return
Calculating Expected Return on a Startup Loan Portfolio
A commercial bank issues a $50,000 loan to a company at an annual interest rate of 10%. The bank's analysts determine that there is a 92% probability the company will repay the loan in full, but an 8% probability of a complete default where nothing is recovered. What is the bank's expected percentage return on this loan?
Determining Minimum Interest Rate Based on Default Risk
A bank is considering two loans of the same principal amount. Loan A has a 15% interest rate and a 90% probability of full repayment. Loan B has a 10% interest rate and a 95% probability of full repayment. Assuming zero recovery in case of default, the bank's expected return is higher for Loan A than for Loan B.
A financial institution is evaluating a portfolio of similar loans. Each loan has a principal amount of $50,000, an interest rate of 12%, and a 90% probability of being fully repaid. In the event of non-repayment, the institution recovers nothing. Match each calculated value below to the concept it represents in the expected return analysis for a single loan.
Implied Repayment Probability from Expected Return
Critique of the Expected Loan Return Model
A bank's loan portfolio has an average interest rate of 10% and an average repayment probability of 95%, with zero recovery on defaulted loans. To improve profitability, management is debating two proposals. Proposal 1 is to increase the average interest rate to 11%. Proposal 2 is to implement a new screening process that increases the average repayment probability to 96%. Which proposal would lead to a higher expected return for the bank?
Evaluating Loan Viability
Calculating Expected Return with Collateral