Hi there,
in the question set for the readings on Allen we have the following question:
329.1. A 10-year $1,000 face value bond has a coupon rate of 4.0% that pays an annual coupon. The bond's price is $852.80 due to a yield (YTM) of 6.0% with annual compounding. The daily yield volatility is 60 basis points and, for convenience, is assumed to have a normal distribution. The bond's duration is 7.81 years. Which is nearest to the 99.0% value at risk (VaR) under a full valuation ("revaluation") approach?
a) $33.67
b) $59.90
c) $87.13
d) $93.11
and the following answer:
Under full valuation, we re-price the bond assuming a shock of 0.006 * 2.33 = 1.3980%, such that price = -PV(7.3980%,10, 40, 1000)= $765.67. With the calculator: N = 10, I/Y = 7.398, PMT = 40, FV = 1000, and CPT PV = -765.668 The implied 99% full valuation VaR = $852.80 - $765.67 = 87.13. Note the duration is not required for full valuation VaR and it would be higher due to the linear approximation: $852.80*1.398%*7.81 = $93.11 > 87.13, due to lack of convexity adjustment (which would still leave a small gap).
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whilst I understand the full revaluation and the actual answer, seeing that the question stated 7.81 years duration this to me looks like MaCaulay Duration rather than Modified Duration and therefore the answer where I've highlighted in bold should not use 7.81 as duration (or delta) but rather should use 7.81 / (1+0.06) = 7.368, which is the Modified Duration. Is my analysis correct here or have I misunderstood the 7.81 years of duration?
thanks
Kashif
in the question set for the readings on Allen we have the following question:
329.1. A 10-year $1,000 face value bond has a coupon rate of 4.0% that pays an annual coupon. The bond's price is $852.80 due to a yield (YTM) of 6.0% with annual compounding. The daily yield volatility is 60 basis points and, for convenience, is assumed to have a normal distribution. The bond's duration is 7.81 years. Which is nearest to the 99.0% value at risk (VaR) under a full valuation ("revaluation") approach?
a) $33.67
b) $59.90
c) $87.13
d) $93.11
and the following answer:
Under full valuation, we re-price the bond assuming a shock of 0.006 * 2.33 = 1.3980%, such that price = -PV(7.3980%,10, 40, 1000)= $765.67. With the calculator: N = 10, I/Y = 7.398, PMT = 40, FV = 1000, and CPT PV = -765.668 The implied 99% full valuation VaR = $852.80 - $765.67 = 87.13. Note the duration is not required for full valuation VaR and it would be higher due to the linear approximation: $852.80*1.398%*7.81 = $93.11 > 87.13, due to lack of convexity adjustment (which would still leave a small gap).
===
whilst I understand the full revaluation and the actual answer, seeing that the question stated 7.81 years duration this to me looks like MaCaulay Duration rather than Modified Duration and therefore the answer where I've highlighted in bold should not use 7.81 as duration (or delta) but rather should use 7.81 / (1+0.06) = 7.368, which is the Modified Duration. Is my analysis correct here or have I misunderstood the 7.81 years of duration?
thanks
Kashif
