Explain the traditional term structure theories and set out what each one implies for forward rates and for the yield curve's shape

Pure expectations theory says forward rates are unbiased forecasts of future short rates, so an upward slope means rates are expected to rise and every maturity earns the same expected return over a given horizon. Local expectations theory applies that only over short horizons. Liquidity preference adds a positive term premium that rises with maturity, so forwards overstate expected rates and a mildly rising curve can accompany flat expectations. Segmented markets theory treats each maturity as a separate market set by supply and demand. Preferred habitat agrees that each segment has its own natural buyers, but allows them to move to other maturities if paid enough. Look for which theory explains the shape without changing expected rates.