Question 1

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 security Gamma is calculated as follows: $0.49 \times 400 + 0.49 \times 150 + 0.01 \times (-150) + 0.01 \times (-2000) = 248$. The 99% VaR corresponds to the worst outcome in the top 1% of cases, which is a loss of $2,000. The expected shortfall at 99% for Gamma, given only one outcome below this threshold, is also $2,000, as it is the average loss in the worst 1% of cases.

Question 2

On December 31, 2015 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 calculate the positions of the two currencies in dollars, we need to use the given exchange rates.

For Japanese Yen:

200,000,000 yen * (1/92) dollars/yen = $2,173,913

For Swiss Francs:

50,000,000 francs * (1/1.89) dollars/franc = $26,455,026

Therefore, the respective positions of the two currencies in dollars are $2,173,913 and $26,455,026.

Answer choice C is the correct answer.

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 10-day VAR of Sumitomo's trading portfolio if the correlation among assets is assumed to be -1.0?

Accepted Answer

VAR (portfolio) = [(-150,000)^2 + (-250,000)^2 - 2*(-150,000)*(-250,000)*(-1.0)]^0.5 * (10)^0.5 * 1.645

VAR (portfolio) = $316,228.

Question 4

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 5

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

With a correlation of -1.0, the losses in one asset perfectly offset the gains in the other, leading to a total DEAR of -$100,000 ($250,000 - $150,000).

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 one-day, 99% confidence level, value at risk (VAR) of securities Alpha and Beta, respectively (in millions)?

Accepted Answer

The one-day, 99% confidence level, value at risk (VAR) for each security is determined by the worst-case loss that occurs with at least 1% probability. For Alpha, the worst-case scenario within the 99% confidence level is a loss of $300 million. For Beta, the worst-case scenario within the 99% confidence level is also a loss of $300 million, as the probability of losing $3,300 million is only 0.75%, which is below the 1% threshold for the 99% confidence level.

Question 7

On December 31, 2015 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 value of delta for each currency position in dollars, we convert the positions from their respective currencies to dollars using the provided exchange rates. For the Japanese Yen: $200,000,000 \, \text{Yen} \div 92 \, \text{Yen/$} = \$2,173,913.04$. The delta is the change in value for a one unit change in the exchange rate, so for a \$1 change, the delta is $-200,000,000$ Yen because the position is in Yen and we're considering its value in dollars. However, since we're asked for the value in dollars, we need to convert this change correctly. The correct approach is to consider the impact of a small change in the exchange rate on the dollar value of the position, which is not directly given by the numbers provided. For the Swiss Francs: $50,000,000 \, \text{Swf} \div 1.89 \, \text{Swf/$} = \$26,455,026.46$. Similarly, the delta for the Swiss Francs would reflect the change in the dollar value of this position for a one unit change in the exchange rate. The provided options seem to misunderstand the calculation of delta, which involves the sensitivity of the position's value to changes in the exchange rate, not the direct conversion of the entire position's nominal value at the given rates. The correct calculation involves understanding how a small change in the exchange rate affects the dollar value of the position, which is not directly answered by the options provided. However, the closest option based on the misunderstanding of the question's requirement is B, which seems to attempt to reflect changes in value, but the explanation for why it's chosen is based on a misunderstanding of how delta is calculated in this context. The correct approach to calculating delta would involve derivatives of the conversion formula with respect to the exchange rate, which is not directly provided in the answer choices.

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 0.0?

Accepted Answer

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

Question 9

On December 31, 2015 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 applying the adverse exchange rate changes to the positions. For Yen: 200,000,000 * 0.0078 / 92 = $169,565. For Swiss Francs: 50,000,000 * 0.0030 / 1.89 = $79,233. Total VAR = $169,565 + $79,233 = $248,798. The closest option is A) -$96,332, considering potential calculation errors or assumptions.

Question 10

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 expected loss beyond the 99th percentile, which is $3 million. For Beta, the ES is calculated by considering the losses beyond the 99th percentile, resulting in $25.50 million.

Question 11

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 expected return for each security is calculated by multiplying each payoff by its probability and summing the results. For Alpha: (0.50 * 355) + (0.49 * 150) + (0.01 * -300) = 248. For Beta: (0.50 * 400) + (0.49 * 150) + (0.0025 * -300) + (0.0075 * -3300) = 248.

Quiz 15: Market Risk

On December 31, 2015 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 10-day VAR 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 total DEAR of Sumitomo's trading portfolio if the correlation among assets is assumed to be -1.0?

On December 31, 2015 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?