Question

We want the duration of our bond portfolio to equal D=10 years (the duration of our liability). So, we need to choose weights such that: D=10= w0Ds0+ WoDro Since D30-13.636 years and Dio-7.935 years, and w30+w10-1, we get: 10=w(13.636)+(1-wo)(7.935) so w 0.3622 and wo 1- W 0.6378

please show step-by-step on how to solve this

not on Excel

Answer 1

Mathematical equations has been used to solve the weight of each asset          
Assume weight of one asset=       x  
duration=       13.636  
weight of second asset will be 1-x as total weight is 1           
duration=       7.935  
          
Total duration required=       10  
          
          
so 10 = D1*weight 1 + D2*weight 2          
10 = x*13.636 + (1-x)*7.935          
10 = 13.636x + 7.935 - 7.935x          
10-7.935 = 13.636x-7.935x          
2.065= 5.701 x  
x = 2.065/5.701          
x =   0.3622171549      
          
So weight of first asset=   0.3622      
weight of second asset = 1-0.3622=   0.6378