Question 1

Sumitomo Bank's risk manager has estimated that the DEARs of two of its major assets in its trading portfolio, foreign exchange and bonds, are -$150,000 and -$250,000, respectively
-What is the total DEAR of Sumitomo's trading portfolio if the correlation among assets is assumed to be 0.80?

Accepted Answer

Total DEAR = (DEAR of FX)^2 + (DEAR of bonds)^2 + 2 x Correlation x DEAR of FX x DEAR of bonds

Total DEAR = (-150,000)^2 + (-250,000)^2 + 2 x 0.80 x (-150,000) x (-250,000) = -$380,789

Therefore, the total DEAR of Sumitomo's trading portfolio is -$380,789, and the correct answer is D.

Question 2

On December 31, 2001 Historic Bank had long positions of 200,000,000 Japanese Yen and 50,000,000 Swiss Francs. The closing exchange rates were ¥92/$ and Swf1.89/$.
-What were the respective positions of the two currencies in dollars?

Accepted Answer

To convert the positions to dollars, divide the amount in each currency by its exchange rate: ¥200,000,000 / 92 = $2,173,913 and Swf50,000,000 / 1.89 = $26,455,026.

Question 3

Sumitomo Bank's risk manager has estimated that the DEARs of two of its major assets in its trading portfolio, foreign exchange and bonds, are -$150,000 and -$250,000, respectively
-What is the total DEAR of Sumitomo's trading portfolio if the correlation among assets is assumed to be 1.0?

Accepted Answer

When the correlation among assets is 1.0, the DEARs are perfectly correlated, so the total DEAR is simply the sum of the individual DEARs: -$150,000 + (-$250,000) = -$400,000.

Question 4

On December 31, 2001 Historic Bank had long positions of 200,000,000 Japanese Yen and 50,000,000 Swiss Francs. The closing exchange rates were ¥92/$ and Swf1.89/$.
-What is the value of delta for the respective positions of the two currencies in dollars?

Accepted Answer

To find the delta value in dollars, convert the positions using the given exchange rates. For Yen: 200,000,000 / 92 = $2,173,913.04. For Francs: 50,000,000 / 1.89 = $26,455,026.46. The delta is the change in value for a small change in the exchange rate, so the values are -$21,524 and -$261,930 respectively.

Question 5

Consider the following discrete probability distributions of payoffs for 3 securities that are held in a DI's trading portfolio (payoff amounts shown are in $millions): $$\begin{array} { | l | l | l | } 
\hline \text { SECURITY } & \text { PROBABILITY } & \text { PAYOFF } \
\hline \text { Alpha } & 0.50 & 355 \
\hline & 0.49 & 150 \
\hline & 0.01 & - 300 \
\hline
\end{array}$$ $$\begin{array} { | l | l | l | } 
\hline \text { SECURITY } & \text { PROBABILITY } & \text { PAYOFF } \
\hline \text { Beta } & 0.50 & 400 \
\hline & 0.49 & 150 \
\hline & 0.0025 & - 300 \
\hline & 0.0075 & - 3,300 \
\hline
\end{array}$$ $$\begin{array} { | l | l | l | } 
\hline \text { SECURITY } & \text { PROBABILITY } & \text { PAYOFF } \
\hline \text { Gamma } & 0.49 & 400 \
\hline & 0.49 & 150 \
\hline & 0.01 & - 150 \
\hline & 0.01 & - 2,000 \
\hline
\end{array}$$
-What is the expected payoff, the 99% value at risk (VAR) and the expected shortfall (ES) of security Gamma (in millions)?

Accepted Answer

The expected payoff for Gamma is calculated as (0.49 * 400) + (0.49 * 150) + (0.01 * -150) + (0.01 * -2000) = $248 million. The 99% VAR is the worst loss not exceeded with 99% confidence, which is -$2,000 million. The expected shortfall is the average of losses beyond the VAR, which is also -$2,000 million.

Question 6

Consider the following discrete probability distributions of payoffs for 3 securities that are held in a DI's trading portfolio (payoff amounts shown are in $millions): $$\begin{array} { | l | l | l | } 
\hline \text { SECURITY } & \text { PROBABILITY } & \text { PAYOFF } \
\hline \text { Alpha } & 0.50 & 355 \
\hline & 0.49 & 150 \
\hline & 0.01 & - 300 \
\hline
\end{array}$$ $$\begin{array} { | l | l | l | } 
\hline \text { SECURITY } & \text { PROBABILITY } & \text { PAYOFF } \
\hline \text { Beta } & 0.50 & 400 \
\hline & 0.49 & 150 \
\hline & 0.0025 & - 300 \
\hline & 0.0075 & - 3,300 \
\hline
\end{array}$$ $$\begin{array} { | l | l | l | } 
\hline \text { SECURITY } & \text { PROBABILITY } & \text { PAYOFF } \
\hline \text { Gamma } & 0.49 & 400 \
\hline & 0.49 & 150 \
\hline & 0.01 & - 150 \
\hline & 0.01 & - 2,000 \
\hline
\end{array}$$
-What is the expected shortfall (ES) of securities Alpha and Beta at the 99 percent confidence level, respectively (in millions)?

Accepted Answer

The expected shortfall (ES) at the 99% confidence level for Alpha is the average of the worst 1% of outcomes, which is -$300. For Beta, the worst 1% includes both -$300 and -$3,300, weighted by their probabilities, resulting in an ES of -$25.50.

Question 7

Sumitomo Bank's risk manager has estimated that the DEARs of two of its major assets in its trading portfolio, foreign exchange and bonds, are -$150,000 and -$250,000, respectively
-What is the total DEAR of Sumitomo's trading portfolio if the correlation among assets is assumed to be 0.0?

Accepted Answer

The answer of Sumitomo Bank's risk manager has estimated that...

Question 8

Sumitomo Bank's risk manager has estimated that the DEARs of two of its major assets in its trading portfolio, foreign exchange and bonds, are -$150,000 and -$250,000, respectively
-What is the total DEAR of Sumitomo's trading portfolio if the correlation among assets is assumed to be -1.0?

Accepted Answer

The answer of Sumitomo Bank's risk manager has estimated that...

Question 9

Sumitomo Bank's risk manager has estimated that the DEARs of two of its major assets in its trading portfolio, foreign exchange and bonds, are -$150,000 and -$250,000, respectively
-What is the 10-day VAR of Sumitomo's trading portfolio if the correlation among assets is assumed to be -1.0?

Accepted Answer

The formula for calculating 10-day VAR with two assets with a correlation of -1.0 is:
VAR = (DEAR1^2 + DEAR2^2 - 2*correlation*DEAR1*DEAR2)^0.5 * (10)^0.5
Substituting the given values:
VAR = [(150,000)^2 + (250,000)^2 - 2*(-1.0)*150,000*250,000]^0.5 * (10)^0.5
VAR = $316,228 (approx.)

Question 10

City bank has six-year zero coupon bonds with a total face value of $20 million. The current market yield on the bonds is 10 percent.
-What is the 10-day VAR assuming the daily returns are independently distributed?

Accepted Answer

The answer of City bank has six-year zero coupon bonds...

Question 11

City bank has six-year zero coupon bonds with a total face value of $20 million. The current market yield on the bonds is 10 percent.
-What is the daily earnings at risk (DEAR) of this bond portfolio?

Accepted Answer

The DEAR is calculated using the formula: DEAR = (Dollar Duration) x (Yield Volatility). First, calculate the present value of the bonds using the formula: PV = FV / (1 + yield)^n, where FV = $20 million, yield = 10%, and n = 6 years. Then, calculate the dollar duration and apply the yield volatility to find the DEAR. The correct calculation results in option B.

Question 12

On December 31, 2001 Historic Bank had long positions of 200,000,000 Japanese Yen and 50,000,000 Swiss Francs. The closing exchange rates were ¥92/$ and Swf1.89/$. -Over the past 500 days, the 25^th worst day for adverse exchange rate changes saw a change in the exchange rates of 0.78 percent for the Yen and 0.30 percent for the Swiss Franc. What is the expected VAR exposure on December 31?

Accepted Answer

The VAR exposure is calculated by determining the potential loss from adverse exchange rate changes. For the Yen: 200,000,000 * 0.0078 / 92 = $169,565. For the Swiss Franc: 50,000,000 * 0.0030 / 1.89 = $79,233. The total VAR exposure is $169,565 + $79,233 = $248,798. However, the closest option is A) -$96,332, indicating a possible error in the calculation or assumptions.

Question 13

Consider the following discrete probability distributions of payoffs for 3 securities that are held in a DI's trading portfolio (payoff amounts shown are in $millions): $$\begin{array} { | l | l | l | } 
\hline \text { SECURITY } & \text { PROBABILITY } & \text { PAYOFF } \
\hline \text { Alpha } & 0.50 & 355 \
\hline & 0.49 & 150 \
\hline & 0.01 & - 300 \
\hline
\end{array}$$ $$\begin{array} { | l | l | l | } 
\hline \text { SECURITY } & \text { PROBABILITY } & \text { PAYOFF } \
\hline \text { Beta } & 0.50 & 400 \
\hline & 0.49 & 150 \
\hline & 0.0025 & - 300 \
\hline & 0.0075 & - 3,300 \
\hline
\end{array}$$ $$\begin{array} { | l | l | l | } 
\hline \text { SECURITY } & \text { PROBABILITY } & \text { PAYOFF } \
\hline \text { Gamma } & 0.49 & 400 \
\hline & 0.49 & 150 \
\hline & 0.01 & - 150 \
\hline & 0.01 & - 2,000 \
\hline
\end{array}$$
-Based on your answers to the previous three question, which of the following is true?

Accepted Answer

The answer of Consider the following discrete probability distributions of...

Question 14

City bank has six-year zero coupon bonds with a total face value of $20 million. The current market yield on the bonds is 10 percent.
-What is the price volatility if the maximum potential adverse move in yields is estimated at 20 basis points?

Accepted Answer

The answer of City bank has six-year zero coupon bonds...

Question 15

Consider the following discrete probability distributions of payoffs for 3 securities that are held in a DI's trading portfolio (payoff amounts shown are in $millions): $$\begin{array} { | l | l | l | } 
\hline \text { SECURITY } & \text { PROBABILITY } & \text { PAYOFF } \
\hline \text { Alpha } & 0.50 & 355 \
\hline & 0.49 & 150 \
\hline & 0.01 & - 300 \
\hline
\end{array}$$ $$\begin{array} { | l | l | l | } 
\hline \text { SECURITY } & \text { PROBABILITY } & \text { PAYOFF } \
\hline \text { Beta } & 0.50 & 400 \
\hline & 0.49 & 150 \
\hline & 0.0025 & - 300 \
\hline & 0.0075 & - 3,300 \
\hline
\end{array}$$ $$\begin{array} { | l | l | l | } 
\hline \text { SECURITY } & \text { PROBABILITY } & \text { PAYOFF } \
\hline \text { Gamma } & 0.49 & 400 \
\hline & 0.49 & 150 \
\hline & 0.01 & - 150 \
\hline & 0.01 & - 2,000 \
\hline
\end{array}$$
-What are the expected returns for securities Alpha and Beta, respectively (in millions)?

Accepted Answer

The answer of Consider the following discrete probability distributions of...

Question 16

Consider the following discrete probability distributions of payoffs for 3 securities that are held in a DI's trading portfolio (payoff amounts shown are in $millions): $$\begin{array} { | l | l | l | } 
\hline \text { SECURITY } & \text { PROBABILITY } & \text { PAYOFF } \
\hline \text { Alpha } & 0.50 & 355 \
\hline & 0.49 & 150 \
\hline & 0.01 & - 300 \
\hline
\end{array}$$ $$\begin{array} { | l | l | l | } 
\hline \text { SECURITY } & \text { PROBABILITY } & \text { PAYOFF } \
\hline \text { Beta } & 0.50 & 400 \
\hline & 0.49 & 150 \
\hline & 0.0025 & - 300 \
\hline & 0.0075 & - 3,300 \
\hline
\end{array}$$ $$\begin{array} { | l | l | l | } 
\hline \text { SECURITY } & \text { PROBABILITY } & \text { PAYOFF } \
\hline \text { Gamma } & 0.49 & 400 \
\hline & 0.49 & 150 \
\hline & 0.01 & - 150 \
\hline & 0.01 & - 2,000 \
\hline
\end{array}$$
-What is the one-day, 99% confidence level, value at risk (VAR) of securities Alpha and Beta, respectively (in millions)?

Accepted Answer

The answer of Consider the following discrete probability distributions of...

Question 17

Sumitomo Bank's risk manager has estimated that the DEARs of two of its major assets in its trading portfolio, foreign exchange and bonds, are -$150,000 and -$250,000, respectively
-What is the total DEAR of Sumitomo's trading portfolio if the correlations among assets are ignored?

Accepted Answer

When correlations among assets are ignored, the total DEAR is simply the sum of the individual DEARs: -$150,000 + (-$250,000) = -$400,000.

Quiz 15: Market Risk

Sumitomo Bank's risk manager has estimated that the DEARs of two of its major assets in its trading portfolio, foreign exchange and bonds, are -$150,000 and -$250,000, respectively -What is the total DEAR of Sumitomo's trading portfolio if the correlation among assets is assumed to be 0.80?

On December 31, 2001 Historic Bank had long positions of 200,000,000 Japanese Yen and 50,000,000 Swiss Francs. The closing exchange rates were ¥92/$ and Swf1.89/$. -What were the respective positions of the two currencies in dollars?

Sumitomo Bank's risk manager has estimated that the DEARs of two of its major assets in its trading portfolio, foreign exchange and bonds, are -$150,000 and -$250,000, respectively -What is the total DEAR of Sumitomo's trading portfolio if the correlation among assets is assumed to be 1.0?

On December 31, 2001 Historic Bank had long positions of 200,000,000 Japanese Yen and 50,000,000 Swiss Francs. The closing exchange rates were ¥92/$ and Swf1.89/$. -What is the value of delta for the respective positions of the two currencies in dollars?

Sumitomo Bank's risk manager has estimated that the DEARs of two of its major assets in its trading portfolio, foreign exchange and bonds, are -$150,000 and -$250,000, respectively -What is the total DEAR of Sumitomo's trading portfolio if the correlation among assets is assumed to be 0.0?

Sumitomo Bank's risk manager has estimated that the DEARs of two of its major assets in its trading portfolio, foreign exchange and bonds, are -$150,000 and -$250,000, respectively -What is the total DEAR of Sumitomo's trading portfolio if the correlation among assets is assumed to be -1.0?

Sumitomo Bank's risk manager has estimated that the DEARs of two of its major assets in its trading portfolio, foreign exchange and bonds, are -$150,000 and -$250,000, respectively -What is the 10-day VAR of Sumitomo's trading portfolio if the correlation among assets is assumed to be -1.0?

City bank has six-year zero coupon bonds with a total face value of $20 million. The current market yield on the bonds is 10 percent. -What is the 10-day VAR assuming the daily returns are independently distributed?

City bank has six-year zero coupon bonds with a total face value of $20 million. The current market yield on the bonds is 10 percent. -What is the daily earnings at risk (DEAR) of this bond portfolio?

City bank has six-year zero coupon bonds with a total face value of $20 million. The current market yield on the bonds is 10 percent. -What is the price volatility if the maximum potential adverse move in yields is estimated at 20 basis points?

Sumitomo Bank's risk manager has estimated that the DEARs of two of its major assets in its trading portfolio, foreign exchange and bonds, are -$150,000 and -$250,000, respectively -What is the total DEAR of Sumitomo's trading portfolio if the correlations among assets are ignored?