Question 1

The DEAR of a bank's trading portfolio has been estimated at $5,000.It is assumed that the daily earnings are independently and normally distributed. What is the 10-day VAR?

Accepted Answer

The 10-day VAR can be calculated using the formula:

VAR = DEAR * z * sqrt(time)

where z is the z-score for the desired confidence level and time is the number of trading days in the period.

Assuming a 95% confidence level, the z-score is 1.645.

time = 10 days

VAR = $5,000 * 1.645 * sqrt(10) = $15,811.

Therefore, the answer is (C) $15,811.

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 is the value of delta for the respective positions of the two currencies in dollars?

Accepted Answer

The value of the Japanese Yen position in dollars is 200,000,000/92 = $2,173,913.04, and the delta is the change in value per unit change in the exchange rate, which is approximately -$21,524. The value of the Swiss Franc position in dollars is 50,000,000/1.89 = $26,455,026.46, and the delta is approximately -$261,930.

Question 3

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

DEAR = (dollar value of position) * (price volatility)
DEAR = ($20,000,000)F1F1F1S1F1F1F10 (5.4545 F1F1F1S1F1F1F10 -0.0020)= -$218,180.

Question 4

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 5

Cornbelt Bank's trading portfolio has the following equity positions: long 1,250 shares of Rio Tinto,a London mining and basic materials company,at a price of $40.00;long 2,500 shares of Intel at a price of $32.50;long 3,500 shares of Exxon/Mobile at a price of $65.00;short 1,000 shares of Credit Suisse at a price of $35.75;and short of 500 shares of Intel.What is the amount of capital that Cornbelt is required to keep against this portfolio according to the Basel Standardized approach?

Accepted Answer

The answer of Cornbelt Bank's trading portfolio has the following...

Question 6

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 is -1.0, the DEARs offset each other completely, so the total DEAR is the absolute difference between the two DEARs: |-150,000 - (-250,000)| = $100,000.

Question 7

The mean change in the value of a portfolio of trading assets has been estimated to be 0 with a standard deviation of 20 percent.Yield changes are assumed to be normally distributed. What is the maximum yield change expected if a 98 percent confidence (one-tailed)limit is used?

Accepted Answer

The answer of The mean change in the value of...

Question 8

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 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 total DEAR of Sumitomo's trading portfolio if the correlations among assets are ignored?

Accepted Answer

DEAR = (-$150,000 - $250,000)= -$400,000.

Question 10

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 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):

$\begin{array} { | l r r | } 
\text { SECURITY } & \text { PROBABILITY } & \text { PAYOFF } \
\text { Alpha } & 0.50 & 355 \
& 0.49 & 150 \
& 0.01 & - 300
\end{array}$ $\begin{array} { lcc } 
\text { SECURITY } & \text { PROBABILITY } & \text { PAYOFF } \
\text {Beta } & 0.50 & 1500 \
& 0.49 & - 300 \
& 0.0025 & - 3,300
\end{array}$ 
$\begin{array} { lcc } 
\text { SECURITY } & \text { PROBABILITY } & \text { PAYOFF } \
\text {Gamma } & 0.49 &400 \
&0.49&150 \
&0.01 &-150 \
&0.01&-2,000
\end{array}$ 
What are the expected returns for securities Alpha and Beta,respectively (in millions)?

Accepted Answer

11efbab3_799a_1d51_8e22_b5980cb932a6_TB1314_00

Question 12

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

The answer of On December 31,2015 Historic Bank had long...

Question 13

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

The total DEAR is calculated using the formula: √(DEAR1² + DEAR2² + 2 * correlation * DEAR1 * DEAR2). Plugging in the values: √((-150,000)² + (-250,000)² + 2 * 0.80 * (-150,000) * (-250,000)) = -$380,789.

Question 14

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 = $16,956.52. For Swiss Francs: 50,000,000 * 0.0030 / 1.89 = $79,375.40. Total VAR = $16,956.52 + $79,375.40 = $96,331.92, rounded to $96,332.

Question 15

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

Price volatility = (MD) * (potential adverse move in yield)
PV = (5.4545 F1F1F1S1F1F1F10 -0.0020)= -0.0109.

Question 16

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 modified duration of these bonds?

Accepted Answer

Zero coupon bonds have a duration that is equal to its maturity.
MD = D/(1 + R)= 6/(1.10)= 5.4545.

Question 17

The DEAR of a bank's trading portfolio has been estimated at $5,000.It is assumed that the daily earnings are independently and normally distributed. What is the 20-day VAR?

Accepted Answer

The 20-day VAR can be calculated by multiplying the daily earnings at risk (DEAR) by the square root of the number of days: $5,000 * √20 = $22,361.

Question 18

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

Using the formula for 10-day VAR with two assets and a correlation of -1.0:

VAR = [(DEAR1)^2 + (DEAR2)^2 - 2 x Corr x DEAR1 x DEAR2]^0.5 x [(1/10)^0.5]

VAR = [(150,000)^2 + (250,000)^2 - 2 x (-1.0) x 150,000 x 250,000]^0.5 x [(1/10)^0.5]

VAR = [$56,738,635]^0.5 x [(1/10)^0.5]

VAR = $316,227.77

Therefore, the 10-day VAR of Sumitomo's trading portfolio is -$316,228, which is closest to option B.

Question 19

The mean change in the value of a portfolio of trading assets has been estimated to be 0 with a standard deviation of 20 percent.Yield changes are assumed to be normally distributed. What is the maximum yield change expected if a 95 percent confidence (one-tailed)limit is used?

Accepted Answer

The answer of The mean change in the value of...

Question 20

The mean change in the value of a portfolio of trading assets has been estimated to be 0 with a standard deviation of 20 percent.Yield changes are assumed to be normally distributed. What is the maximum yield change expected if a 90 percent confidence (one-tailed)limit is used?

Accepted Answer

Maximum yield change expected (potential adverse move)= (0 F1F1F1S1F1F1F10 1.65 F1F1F1S1F1F1F10 0.20)= 0 F1F1F1S1F1F1F10 0.33.

Quiz 15: Market Risk

The DEAR of a bank's trading portfolio has been estimated at $5,000.It is assumed that the daily earnings are independently and normally distributed. What is the 10-day VAR?

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?

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?

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 total DEAR of Sumitomo's trading portfolio if the correlation among assets is assumed to be -1.0?

The mean change in the value of a portfolio of trading assets has been estimated to be 0 with a standard deviation of 20 percent.Yield changes are assumed to be normally distributed. What is the maximum yield change expected if a 98 percent confidence (one-tailed) limit is used?

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?

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?

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?

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 total DEAR of Sumitomo's trading portfolio if the correlation among assets is assumed to be 0.80?

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?

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 modified duration of these bonds?

The DEAR of a bank's trading portfolio has been estimated at $5,000.It is assumed that the daily earnings are independently and normally distributed. What is the 20-day VAR?

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?

The mean change in the value of a portfolio of trading assets has been estimated to be 0 with a standard deviation of 20 percent.Yield changes are assumed to be normally distributed. What is the maximum yield change expected if a 95 percent confidence (one-tailed) limit is used?

The mean change in the value of a portfolio of trading assets has been estimated to be 0 with a standard deviation of 20 percent.Yield changes are assumed to be normally distributed. What is the maximum yield change expected if a 90 percent confidence (one-tailed) limit is used?