$(24$ points total$)$ Consider the attached article $($WSJ $10/31/23$ p$.$ B$1)$ "What's Next for Bond Yield After Hitting $5\%"$ which discusses the state of the bond market shortly after the $10$ year rate peaked at $5\%.$

a$.(10$ points$)$ The article asserts that inverted yield curves are "infamous" because they presage a recession.

i$.$ If the yield curve is determined according to the Pure Expectations Model, is it correct to assert that an inverted yield curve signals that interest rates are expected to decline? Explain why or why not.

ii$.$ If the yield curve is determined according to the Liquidity Preference Model, is it correct to assert that an inverted yield curve signals that interest rates are expected to decline? Explain why or why not.

b$.(7$ points$)$ The article asserts that, if the yield curve is inverted, investors holding long$-$term bonds "lose money just from the passage of time". Assume that the yield curve is determined by pure expectations, and that it is currently inverted. If interest rates evolve as expected, is it true that an investor who holds a long$-$term bond will fare worse than an investor who buys shortterm bonds and rolls them over at maturity? Explain.