exam 1 sample questions #129

[Anonymous]

Hi all

A quick one on one of the sample questions! The question is as follows:

A bond pays semi-annual coupons at an annual rate of 10%, and will mature in a year. What is its modified duration? Assume the yield curve is flat for the next 12 months at 5%.
(a) 0.700
(b) 1.000
(c) 1.500
(d) 0.953

We can calculate the duration of the bond as follows:
PV of 1st coupon payment: $5/(1 + 5%/2) = $4.878
PV of final payment: $105/(1 + 5%) = $100

Weighted average of the two = (0.5*$4.878 + 1*$100)/($4.878 + $100) = 0.9767, ie this is the Macaulay duration.

…..

I’m struggling to understand why the PV of the second payment is using r of 5% rather than 5%/2? Have I missed something really obvious here?

[NILANJOY DAS]

Hi ,

I think you got macaulay duration of 0.976730988

Now you need to divide with Yield which will be : 1.025 .

So Result will be = 0.976730988/1.025 = 0.952908281 ~= .0953

[Anonymous]

I think not dividing 5% by 2 was an error…

[Anonymous]

Maybe this will help someone else confused by this.

This is because you are calculating the present value of a future cash flow.

The first cashflow ($5) is due in 6 months, you are discounting from 6 months in the future back to the present, i.e., discount using 1/( 1+ 5%*0.5)

The second cashflow ($105) is due in 12 months, you are discounting from 12 months in the future back to the present, i.e., 1/(1+5%*1)

[Author]

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