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n t het w o pe r i od b on d a nd h ol ding i t f or the t w o pe r i od s( 1 + ) ( 1 + ) 11 2 ( ) 12 ( )S i nc e ( ) is v e r y sm a l lt he e xp e c t e d r etttttttiiiiiii?? ? ? ???2t ur n f or h ol ding t he tw o pe r i od b on d f or tw o pe r i od s is2tiCopyright 169。 2022 Pearson AddisonWesley. All rights reserved. 620 Expectations Theory— In General (cont’d) 1111111I f t wo one pe r i od bonds a r e bought wit h t he $1 i nv e st m e nt( 1 ) ( 1 ) 11 ( ) 1()( ) i s e xt r e m e l y sm a l lS i m pl i f y i ng we ge tetteet t t teet t t tettettiii i i ii i i iiiii???????? ? ?? ? ? ? ?? ? ??Copyright 169。 2022 Pearson AddisonWesley. All rights reserved. 621 Expectations Theory— In General (cont’d) 2112B oth b on ds w i l l b e h e l d on l y if the e xp e c t e d r e t ur ns a r e e qu a l22T he tw o pe r i od r a t e m ust e qu a l the a v e r a ge o f the tw o on e pe r i od r a t e sF or b on ds w i t h l on ge r m a t ur i t i e set t tetttttnti i iiiiiii?????????1 2 ( 1 )...T he pe r i od int e r e st r a t e e qu a l s the a v e r a ge o f the o ne pe r i odi nte r e st r a t e s e xp e c t e d t o oc c ur o v e r th e pe r i od l i f e o f the b on de e et t niinnn? ? ?? ? ?Copyright 169。 2022 Pearson AddisonWesley. All rights reserved. 622 Expectations Theory— Exercise ? If one year interest rate over the next five years is expected to be 3%,4%,5% ,6% and7% ? Under Expectation Theory , the interest rate on a twoyear bond, a threeyear bond , a fouryear bond and fiveyear bond must be? ? Twoyear bond : (3%+4%)/2=% ? Threeyear bond : (3%+4%+5%)/3=4% ? Fouryear bond :(3%+4%+5%+6%)/4=% ? Fiveyear bond: (3%+ 4%+5%+6%+7%)/5=5% If interest rates are expected to rise in the future , then longterm interest rate is higher than short term one Copyright 169。 2022 Pearson AddisonWesley. All rights reserved. 623 Expectations Theory ? Explains why interest rates on bonds with different maturities move together over time (fact 1) A rise in shortterm rates will raise people’s expectations of future shortterm interest rates, thus raise longterm rates, causing shortterm and long term rates to move together ? Explains why yield curves tend to slope up when shortterm rates are low and slope down when shortterm rates are high (fact 2) ? When shortterm interest rates are low ,people generally expect them to rise to some normal level in the future? average of future expected shortterm rates is high relative to current shortterm