Question

# Consider the following step up security (\$1,000 par) with semi-annual coupons (all CFs are at the...

Consider the following step up security (\$1,000 par) with semi-annual coupons (all CFs are at the end of the semi-annual):

 Year 1 2 3 Coupon rate 3% 4% 5%

16. Manager B plans to buy the security at middle of year 1 (after the 1st coupon payment) and hold it to maturity with YTM of 4.2%. What is the security’s Mod Duration (in years) at the middle of year 1? Round the final answer to nearest 3 decimals i.e. 1.234.

Mod Duration or Modified Duration refers to the Price Volatality and is given by :

Macaulays duration/Periodic Ytm factor

Now Macaulays duration is the average waiting time for the cash flows of the bond and is given by :

Sigma of PV of cash flows discounted by Ytm×time periods of receiving CF

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Sigma of PV of cash flows discounted at Ytm

 Year(x) cash flows P.V.at Ytm(w) Wx 1 15(3/2=1.5%of1000) 15/1.021=14.691 14.691 2 20 19.186 38.371 3 20 18.791 56.373 4 25 23.006 92.023 5 1025 923.837 4919.183 Total 1000 5120.641 Macaulays Duration 5120.641/1000 5.121 half years 5.121/2=2.561years

Mod duration=2.561/1.021=2.508%

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