求助~~~~做了半天也做不出来

show that the duration of a portfolio of bonds is equal to the weighted average of the durations of the induvidual bonds in the portfolio(assume that the yield curve is horizontal)
拜托高手写的详细点   我是菜鸟

Consider a portfolio of 2 bonds. Z = Z1 + Z2

Z = Z1 + Z2

=> dZ/dy = dZ1/dy + dZ2/dy
=> -D*Z = -D1*Z1 + -D2*Z2
=> D = (Z1/Z)*D1 + (Z2/Z)*D2