You are currently holding a portfolio that consists of (a) $2000 cash and (b) one 10-year...

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You are currently holding a portfolio that consists of (a) $2000cash and (b) one 10-year zero coupon bond with a face value of$1000 and 12% yield to maturity. The Macaulay duration of theportfolio is
A. 1.3866
B. 2.4356
C. 2.7826
D. 3.9171
E. none of the above
please show all working and include equations thanks

Answer & Explanation Solved by verified expert

3.8 Ratings (663 Votes)

K = N

Bond Price =? [(Annual Coupon)/(1 + YTM)^k] + Par value/(1 + YTM)^N

k=1

K =10

Bond Price =? [(0*1000/100)/(1 + 12/100)^k] + 1000/(1 + 12/100)^10

k=1

Bond Price = 321.97

Total Portfolio value = Value of Cash + Value of 0 bond

=2000+321.97

=2321.97

Weight of Cash = Value of Cash/Total Portfolio Value

= 2000/2321.97

=0.8613

Weight of 0 bond = Value of 0 bond/Total Portfolio Value

= 321.97/2321.97

=0.1387

Duration of Portfolio = Weight of Cash*Duration of Cash+Weight of 0 bond*Duration of 0 bond

Duration of Portfolio = 0*0.8613+10*0.1387

Duration of Portfolio = 1.3866

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Transcribed Image Text

You are currently holding a portfolio that consists of (a) $2000cash and (b) one 10-year zero coupon bond with a face value of$1000 and 12% yield to maturity. The Macaulay duration of theportfolio isA. 1.3866B. 2.4356C. 2.7826D. 3.9171E. none of the aboveplease show all working and include equations thanks