Suzanne Evans
Well-Known Member
AIM: Define the Value-at-Risk (VaR) measure of risk, discuss assumptions about return distributions and holding period ...
Questions:
28.1. A portfolio consists of two zero-coupon bonds, each with a current value of $50.0 million; the first maturing in 3.0 years the second maturing in 7.0 years. The yield curve is flat, with all yields at 6.0%. The daily volatility is 1.0% and assumed to be i.i.d. normally distributed. Using only duration's linear approximation (not convexity) and assuming annual compounding, which is nearest to the portfolio's 99.0% 10-day value at risk (VaR)?
a. $11.6 million
b. $27.5 million
c. $34.7 million
d. $36.8 million
28.2. Because the asset price is $20.00, a long position in 100 call option contracts (i.e., 10,000 options) has a current notional value of $200,000. The options are at-the-money (ATM) with percentage (per option) delta of 0.60. The asset has a volatility of 18.0% per annum. If we assume returns are i.i.d. normal and a year contains 250 trading days, which is nearest to the 99.0% 10-day value at risk (VaR) under a delta-normal assumption; i.e., if assume only delta's linear approximation (delta-Normal) and ignore gamma?
a. $7,605
b. $10,066
c. $15,252
d. $21,018
28.3. A two-asset 130/30 long/short portfolio has $130 million invested in an asset with 24.0% volatility per annum hedged with a $30 million short position in an asset with a 16.0% volatility per annum. The correlation between asset returns, which are i.i.d. normal, is 0.30. Which of the following is nearest the portfolio's 99.0% confident 10-day relative value at risk (VaR)?
a. $8.33 million
b. $10.52 million
c. $14.03 million
d. $30.11 million
Answers:
Questions:
28.1. A portfolio consists of two zero-coupon bonds, each with a current value of $50.0 million; the first maturing in 3.0 years the second maturing in 7.0 years. The yield curve is flat, with all yields at 6.0%. The daily volatility is 1.0% and assumed to be i.i.d. normally distributed. Using only duration's linear approximation (not convexity) and assuming annual compounding, which is nearest to the portfolio's 99.0% 10-day value at risk (VaR)?
a. $11.6 million
b. $27.5 million
c. $34.7 million
d. $36.8 million
28.2. Because the asset price is $20.00, a long position in 100 call option contracts (i.e., 10,000 options) has a current notional value of $200,000. The options are at-the-money (ATM) with percentage (per option) delta of 0.60. The asset has a volatility of 18.0% per annum. If we assume returns are i.i.d. normal and a year contains 250 trading days, which is nearest to the 99.0% 10-day value at risk (VaR) under a delta-normal assumption; i.e., if assume only delta's linear approximation (delta-Normal) and ignore gamma?
a. $7,605
b. $10,066
c. $15,252
d. $21,018
28.3. A two-asset 130/30 long/short portfolio has $130 million invested in an asset with 24.0% volatility per annum hedged with a $30 million short position in an asset with a 16.0% volatility per annum. The correlation between asset returns, which are i.i.d. normal, is 0.30. Which of the following is nearest the portfolio's 99.0% confident 10-day relative value at risk (VaR)?
a. $8.33 million
b. $10.52 million
c. $14.03 million
d. $30.11 million
Answers: