On January $11,2024,$ the U$.$S$.$ Department of the Treasury reported the following rates for Treasury bonds:

$10-$year bond rate $=3\mathrm{.}98\%$; $20-$year bond rate $=4\mathrm{.}32\%$

a$.$ Under the expectations theory, what is the expected $10-$year bond rate $($forward rate$)10$ years from now? Based on your answer, what are rates expected to do $($rise$/$fall$/$stay the same$)?$ Explain why

Expected $10-$year Treasury bond rate $10$ years from now $=\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

Rate are expected to $\_\_\_\_\_\_\_\_\_\_\_$ because $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

b$.$ For the same above suppose there is a liquidity premium of $0\mathrm{.}10\%$ for a $10-$year bond and $0\mathrm{.}20\%$ for a $20-$year bond, under the liquidity premium theory $($adjusting for liquidity premiums incorporated in bond rates$)$ what is the new expected $10-$year bond rate $10$ years from now? Based on your answer, what are rates expected to do $($rise$/$fall$/$stay the same$)?$ Explain why and why the expected rate under the liquidity premium theory differs from that of the expectations theory.

Expected Rate with LP $\_\_\_\_\_\_\_\_\_\_$ Rates Expected to $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

b$.$ Briefly explain the market segmentation theory $($Chapter $2).$ What is a primary weaknesses for this theory?