Please answer these true or false questions:

$1.$ A smaller yield change of a $$10,000$ price change implies a lower interest rate risk in a bond portfolio compared to a bigger yield change of a $$10,000$ price change in a benchmark bond portfolio.

$2.$ When a $$hot$($sought after$)$ bond is used as collateral, bond dealers are willing to offer to lend funds at a lower repo rate than the average repo rate in the market.

$3.$ An option$-$free bond has a duration of $7\mathrm{.}3,$ which means that the bond has a weighted average life of $7\mathrm{.}3$ years.