In: Finance
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
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 |