Independent solution

How to solve this Cash-Flow and Risk Matching question

Setup

Setup

Treat each row as a net surplus cash-flow stream and form its present value as a function of yield.

hX(0.25)=102400−1920001.25+1000001.253=0h_X(0.25)=102400-\frac{192000}{1.25}+\frac{100000}{1.25^3}=0

Model

Model

For X, both surplus value and first derivative vanish at 25%, satisfying value and duration balance.

hX′(0.25)=1920001.252−3(100000)1.254=0h_X'(0.25)=\frac{192000}{1.25^2}-\frac{3(100000)}{1.25^4}=0

Compute

Compute

Its second derivative is positive; by contrast, Y has a nonzero first derivative and Z has a nonzero value.

hX′′(0.25)=196608>0h_X''(0.25)=196608>0

Answer

Answer

Only cash-flow set X meets all Redington conditions, so choice A is correct.

X only is Redington immunized(A)\boxed{\text{X only is Redington immunized}\quad\text{(A)}}