Suppose that the current market interest rate is 12% for non-fraudulent bonds, and that one in six bonds are fraudulent in a given market.What would the interest rate be if a fraud premium is introduced, assuming (1)a one-year investment horizon and (2)the market does not require a risk premium?

Question

Quizplus · Accepted Answer

1 in 6 bonds are fraudulent, so the probability of a bond being non-fraudulent is 5/6. If the market interest rate for non-fraudulent bonds is 12%, then the expected return on a non-fraudulent bond is:

Expected return = probability of non-fraudulent bond x market interest rate
Expected return = (5/6) x 12%
Expected return = 10%

If a fraud premium is introduced, this means that investors require a higher return for investing in bonds due to the risk of fraud. Let's say the fraud premium is x%. Then, the expected return on a fraudulent bond is:

Expected return = probability of fraudulent bond x (market interest rate + fraud premium)
Expected return = (1/6) x (12% + x%)

Since investors are risk averse, they will only invest in a fraudulent bond if the expected return is greater than or equal to the expected return on a non-fraudulent bond. Therefore, we can set these two expressions equal to each other and solve for x:

(1/6) x (12% + x%) = 10%
x^2 + 72x - 720 = 0
Solving using the quadratic formula, we get:
x = (-72 ± sqrt(72^2 + 4(1)(720))) / (2(1))
x = (-72 ± sqrt(53504)) / 2
x = (-72 ± 231.22) / 2

Since we're only interested in the positive solution, we get:
x = (-72 + 231.22) / 2
x = 79.61%

Therefore, the interest rate with the fraud premium would be:
Interest rate = 12% + 79.61%
Interest rate = 91.61%
To the nearest tenth of a percent, this is equal to 34.4%.

Suppose That the Current Market Interest Rate Is 12% for Non-Fraudulent