Use the following information for questions
Consider a bank with federally insured deposits maturing in one year.The bank's asset value changes monthly and you have the following data on asset value for the past five months.Assume that the probability distribution of asset value changes remains stationary over time.The bank's current deposit to asset value ratio is 0.85. $$\begin{array} { | l | l | }
\hline \text { Month } & \text { Bank Asset Value } \
\hline 1 & \$ 110 \text { million } \
\hline 2 & \$ 104 \text { million } \
\hline 3 & \$ 95 \text { million } \
\hline 4 & \$ 102 \text { million } \
\hline 5 & \text { \$ } 100 \text { million } \
\hline
\end{array}$$
-What is the cost of deposit insurance per dollar of insured deposits?

Question

Use the following information for questions 
Consider a bank with federally insured deposits maturing in one year.The bank's asset value changes monthly and you have the following data on asset value for the past five months.Assume that the probability distribution of asset value changes remains stationary over time.The bank's current deposit to asset value ratio is 0.85. $$\begin{array} { | l | l | } 
\hline \text { Month } & \text { Bank Asset Value } \
\hline 1 & \$ 110 \text { million } \
\hline 2 & \$ 104 \text { million } \
\hline 3 & \$ 95 \text { million } \
\hline 4 & \$ 102 \text { million } \
\hline 5 & \text { \$ } 100 \text { million } \
\hline
\end{array}$$
-What is the cost of deposit insurance per dollar of insured deposits?

Quizplus · Accepted Answer

The cost of deposit insurance per dollar of insured deposits is the expected loss divided by the amount of insured deposits. The expected loss is the probability of a loss times the amount of the loss. The probability of a loss is the probability that the asset value falls below the deposit value. The amount of the loss is the difference between the deposit value and the asset value. The amount of insured deposits is $100 million.The probability of a loss is the probability that the asset value falls below $85 million. The asset value has fallen below $85 million in 2 of the 5 months, so the probability of a loss is 2/5 = 0.4.The amount of the loss is the difference between the deposit value and the asset value. The deposit value is $100 million. The asset value has fallen below $100 million in 3 of the 5 months, so the expected loss is (2/5) * ($100 million - $95 million) + (1/5) * ($100 million - $100 million) + (2/5) * ($100 million - $102 million) = $10 million.The cost of deposit insurance per dollar of insured deposits is the expected loss divided by the amount of insured deposits, which is $10 million / $100 million = 0.1.Therefore, the correct answer is A.

Use the Following Information for Questions Consider a Bank

Use the Following Information for Questions
Consider a Bank