The following table shows the current prices for a set of government bonds with different maturities as of January $1,2022.$ The bonds are identical in every respect except for their time to maturity and coupon rate. All of the bonds will be redeemed at their par value of $100$ upon redemption. Assume that coupon payments are paid annually for simplicity.

Maturity $($year$)1$

$2$

$3$

$4$

Coupon Price Rate $()$

$0\mathrm{.}0095\mathrm{.}000\mathrm{.}0087\mathrm{.}500\mathrm{.}0898\mathrm{.}100\mathrm{.}1099\mathrm{.}20$

Yield to Maturity $?$

$?$

$?$

$?$

Theoretical Spot Rate

$?$

$?$

$?$

$?$

Compute the yield to maturity $($YTM$)$ for these bonds.

Estimate the theoretical spot rates and draw the theoretical spot rate curve. Critically evaluate how the curve describes the implications in terms of the expectations as well as the liquidity preference hypotheses.

Compute the implied forward two$-$year rate of interest at January $1,2023.$ Describe the conditions under which the calculated forward rate would be an unbiased estimate of the two$-$year spot rate of interest at January $1,2023.$