Questions on Market Risk
Dr. Sudhakar Raju
FN 6700
ASSIGNMENT 4 - QUESTIONS ON MARKET RISK (VALUE AT RISK)
1. What is meant by market risk?
2. Why is the measurement of market risk important to the manager of a financial institution?
3. What is meant by daily earnings at risk (DEAR)? What are the three measurable components? What is the price volatility component?
4. Follow bank has a $1 million position in a five-year, zero-coupon bond with a face value of $1,402,552. The bond is trading at a yield to maturity of 7.00 percent. The historical mean change in daily yields is 0.0 percent, and the standard deviation is 12 basis points.
a. What is the modified duration of the bond?
b. What is the maximum adverse daily yield move given that we desire no more than a 5 percent chance that yield changes will be greater than this maximum?
c. What is the price volatility of this bond?
d. What is the daily earnings at risk for this bond?
5. What is meant by value at risk (VAR)? How is VAR related to DEAR in J.P. Morgan’s RiskMetrics model? What would be the VAR for the bond in problem (4) for a 10-day period? With what statistical assumption is our analysis taking liberties? Could this treatment be critical?
6. The DEAR for a bank is $8,500. What is the VAR for a 10-day period? A 20-day period? Why is the VAR for a 20-day period not twice as much as that for a 10-day period?
7. The mean change in the daily yields of a 15-year, zero-coupon bond has been five basis points (bp) over the past year with a standard deviation of 15 bp. Use these data and assume the yield changes are normally distributed.
a. What is the highest yield change expected if a 90 percent confidence limit is required; that is, adverse moves will not occur more than one day in 20?
b. What is the highest yield change expected if a 95 percent confidence limit is required?
8. In what sense is duration a measure of
FN 6700
ASSIGNMENT 4 - QUESTIONS ON MARKET RISK (VALUE AT RISK)
1. What is meant by market risk?
2. Why is the measurement of market risk important to the manager of a financial institution?
3. What is meant by daily earnings at risk (DEAR)? What are the three measurable components? What is the price volatility component?
4. Follow bank has a $1 million position in a five-year, zero-coupon bond with a face value of $1,402,552. The bond is trading at a yield to maturity of 7.00 percent. The historical mean change in daily yields is 0.0 percent, and the standard deviation is 12 basis points.
a. What is the modified duration of the bond?
b. What is the maximum adverse daily yield move given that we desire no more than a 5 percent chance that yield changes will be greater than this maximum?
c. What is the price volatility of this bond?
d. What is the daily earnings at risk for this bond?
5. What is meant by value at risk (VAR)? How is VAR related to DEAR in J.P. Morgan’s RiskMetrics model? What would be the VAR for the bond in problem (4) for a 10-day period? With what statistical assumption is our analysis taking liberties? Could this treatment be critical?
6. The DEAR for a bank is $8,500. What is the VAR for a 10-day period? A 20-day period? Why is the VAR for a 20-day period not twice as much as that for a 10-day period?
7. The mean change in the daily yields of a 15-year, zero-coupon bond has been five basis points (bp) over the past year with a standard deviation of 15 bp. Use these data and assume the yield changes are normally distributed.
a. What is the highest yield change expected if a 90 percent confidence limit is required; that is, adverse moves will not occur more than one day in 20?
b. What is the highest yield change expected if a 95 percent confidence limit is required?
8. In what sense is duration a measure of