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

You are currently holding a portfolio that consists of (a) $2000 cash and (b) one 10-year zero coupon bond with a face value of $1000 and 12% yield to maturity. The Macaulay duration of the portfolio 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

Solutions

Expert Solution

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

jeff jeffy answered 8 months ago

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