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eturns of two strategies are equal: Therefore 2(i2t) = it + iet+1 Solving for i2t it + iet+1 i2t = 2 13 169。 2023 Pearson Education Canada Inc. Expected Return from Strategy 1 More generally for nperiod bond: it + iet+1 + iet+2 + ... + iet+(n–1) int = n In words: Interest rate on long bond = average short rates expected to occur over life of long bond Numerical example: Oneyear interest rate over the next five years 5%, 6%, 7%, 8% and 9%: Interest rate on twoyear bond: (5% + 6%)/2 = % Interest rate for fiveyear bond: (5% + 6% + 7% + 8% + 9%)/5 = 7% Interest rate for one to five year bonds: 5%, %, 6%, % and 7%. 169。 2023 Pearson Education Canada Inc. 14 Expectations Hypothesis and Term Structure Facts Explains why yield curve has different slopes: 1. When short rates expected to rise in future, average of future short rates = int is above today’s short rate: therefore yield curve is upward sloping 2. When short rates expected to stay same in future, average of future short rates are same as today’s, and yield curve is flat 3. Only when short rates expected to fall will yield curve be downward sloping Expectations Hypothesis explains Fact 1 that short and long rates move together 1. Short rate rises are persistent 2. If it ? today, iet+1, iet+2 etc. ? ? average of future rates ? ? int ? 3. Therefore: it ? ? int ?, ., short and long rates move together 15 169。 2023 Pearson Education Canada Inc. 1. When short rates are low, they are expected to rise to normal level, and long rate = average of future short rates will be well above today