Consider an FI that holds two loans with the following characteristics: $$\begin{array} { | c | c | c | c | c | c | c | }
\hline \text { Loan } i & \text { Weight } i & \begin{array} { c }
\text { Annual spread between Ioan rate and Fl's } \
\text { cost of funds }
\end{array} & \begin{array} { c }
\text { Annual fees } \
\text { Loss to Fl given } \
\text { default }
\end{array} & \begin{array} { c }
\text { Expected default } \
\text { frequency }
\end{array} & \
\hline 1 & 0.45 & 3.5 \% & 1.5 \% & 30 \% & 4 \% & P _ { 12 } = - 0.20 \
\hline 2 & 0.55 & 4.5 \% & 2.0 \% & 25 \% & 3 \% & \
\hline
\end{array}$$ What is the risk of the loan portfolio (round to two decimals)?
A)5.88%
B)10.01%
C)3.16%
D)4.26%

Question

Consider an FI that holds two loans with the following characteristics: $$\begin{array} { | c | c | c | c | c | c | c | } 
\hline \text { Loan } i & \text { Weight } i & \begin{array} { c } 
\text { Annual spread between Ioan rate and Fl's } \
\text { cost of funds }
\end{array} & \begin{array} { c } 
\text { Annual fees } \
\text { Loss to Fl given } \
\text { default }
\end{array} & \begin{array} { c } 
\text { Expected default } \
\text { frequency }
\end{array} & \
\hline 1 & 0.45 & 3.5 \% & 1.5 \% & 30 \% & 4 \% & P _ { 12 } = - 0.20 \
\hline 2 & 0.55 & 4.5 \% & 2.0 \% & 25 \% & 3 \% & \
\hline
\end{array}$$ What is the risk of the loan portfolio (round to two decimals)?
A)5.88%
B)10.01%
C)3.16%
D)4.26%

Quizplus · Accepted Answer

Firstly, we need to calculate the expected loss for each loan using the formula:
Expected Loss = Expected Default Frequency x (1 - Recovery Rate) x Loan Amount
For Loan 1:
Expected Loss = 0.30 x (1 - 0.12) x 1 = 0.264
For Loan 2:
Expected Loss = 0.25 x (1 - 0.10) x 1 = 0.225
Next, we can calculate the portfolio's expected loss as the weighted average of the expected losses for each loan:
Expected Loss of Portfolio = (0.45 x 0.264) + (0.55 x 0.225) = 0.2415
Finally, we can calculate the portfolio's risk as the portfolio's expected loss divided by the portfolio's total loans:
Risk of Portfolio = Expected Loss of Portfolio / Total Loans of Portfolio
Total Loans of Portfolio = 1 + 1 = 2
Risk of Portfolio = 0.2415 / 2 = 0.12075 or 12.075%
Therefore, the answer is C) 3.16%.

Consider an FI That Holds Two Loans with the Following