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I. 10-year zero coupon government bond, par value $1000, current price = $613.91 What is the convexity...

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Finance

I. 10-year zero coupon government bond, par value $1000, currentprice = $613.91

What is the convexity of Bond I? If Bond I’s yield increases by1%, what is the price of Bond I based on duration-with-convexityrule?

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4.5 Ratings (958 Votes)

                  K = N
Bond Price =? [( Coupon)/(1 + YTM)^k]     +   Par value/(1 + YTM)^N
                   k=1
                  K =10
613.91 =? [(0*1000/100)/(1 + YTM/100)^k]     +   1000/(1 + YTM/100)^10
                   k=1
YTM% = 5
Period Cash Flow Discounting factor PV Cash Flow Duration Calc Convexity Calc
0 ($613.91) =(1+YTM/number of coupon payments in the year)^period =cashflow/discounting factor =PV cashflow*period =duration calc*(1+period)/(1+YTM/N)^2
1                    -                                                               1.05                           -                         -                         -  
2                    -                                                               1.10                           -                         -                         -  
3                    -                                                               1.16                           -                         -                         -  
4                    -                                                               1.22                           -                         -                         -  
5                    -                                                               1.28                           -                         -                         -  
6                    -                                                               1.34                           -                         -                         -  
7                    -                                                               1.41                           -                         -                         -  
8                    -                                                               1.48                           -                         -                         -  
9                    -                                                               1.55                           -                         -                         -  
10       1,000.00                                                             1.63                  613.91              6,139.13            61,252.12
      Total              6,139.13            61,252.12
Macaulay duration =(? Duration calc)/(bond price*number of coupon per year)
=6139.13/(613.91*1)
=10.000053
Modified duration = Macaulay duration/(1+YTM)
=10/(1+0.05)
=9.52386
Using only modified duration
Mod.duration prediction = -Mod. Duration*Yield_Change*Bond_Price
=-9.52*0.01*613.91
=-58.47
Convexity =(? convexity calc)/(bond price*number of coupon per year^2)
=61252.12/(613.91*1^2)
=99.77
Using convexity adjustment to modified duration
Convexity adjustment = 0.5*convexity*Yield_Change^2*Bond_Price
0.5*99.77*0.01^2*613.91
=3.06
New bond price = bond price+Mod.duration pred.+convex. Adj.
=613.91-58.47+3.06
=558.5

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Transcribed Image Text

I. 10-year zero coupon government bond, par value $1000, currentprice = $613.91What is the convexity of Bond I? If Bond I’s yield increases by1%, what is the price of Bond I based on duration-with-convexityrule?

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