Barbelling:

Consider a Treasury coupon bond with maturity $18$ months, and maturity value $$100,000,$

trading at par.

Consider now two other Treasury coupon bonds, with maturity $12$ months and $30$ months,

respectively, also trading at par. Assume a flat yield curve, with y$2($Coupon$)=$ y$3($Coupon$)=$

y$5($Coupon$)=2\%.$

Construct a barbell portfolio of the second two bonds, with the same modified duration and

price of the first bond.

Specifically, compute:

$1.$ the portfolio weights of the two bonds in the barbell;

$2.$ the maturity values of the two bonds in the barbell.

Calculate the prices of the first bond and of the barbell portfolio, under the following two

scenarios $($use present values$)$:

$1.$ all interest rates immediately decrease by $50$ basis points;

$2.$ the yield curve immediately changes in a non$-$parallel fashion: y$2($Coupon$)0=$ y$2($Coupon$)$

$50$ basis points, y$3($Coupon$)0=$ y$3($Coupon$),$ and y$5($Coupon$)0=$ y$5($Coupon$)+50$ basis points.