 # Pure expectation theory

As per one of the sentence of the subjected theory “If short term rates are expected to rise in the future, interest rate yields on longer maturities will be higher than those on shorter maturities” Could anybody help me in understanding this better? If rate rises than the PV of the bond will be at discount, how come interest rate yields on longer maturities will be high? Thanks in advance!

Let’s say you look at purely discounted bonds and assume that expectation hypothesis holds. forward rates are equal to expected future rates. Expected short term rates are 1%, 3% and 5%. Then yields are going to be equal to 1% for 1 year bond, (1%+3%)/2=2% for 2 year bond and (1%+3%+5%)/3=3% for 3 year bond (I use log rates). You expect that all bonds will go up 1% the first year, 3% the second year and 5% the third year. Does that help?

"If rate rises than the PV of the bond will be at discount, how come interest rate yields on longer maturities will be high? " You answered your own question here. As you said, when interest rates rise, the PV (or price) of the bond will be at a deeper discount, so the yield will be higher. Buying a \$1000 par-value bond for \$600 will have a higher yield than buying it for \$800.

thanks to both of you for your replies. I guess I am confusing with the terminologies. just to clarify, yield is not the same as interest. yield is the return that you get. as in if the pv of a par value 1,000 is 950 than my yield is expected to be 50? thisisbrianly Wrote: ------------------------------------------------------- > "If rate rises than the PV of the bond will be at > discount, how come interest rate yields on longer > maturities will be high? " > > You answered your own question here. As you said, > when interest rates rise, the PV (or price) of the > bond will be at a deeper discount, so the yield > will be higher. Buying a \$1000 par-value bond for > \$600 will have a higher yield than buying it for > \$800.

No, yield factors in the price discount/premium of a bond and the expected interest rate payments over the remaining life of the bond. For example, a 5 year bond issued with a 4% coupon will trade at par as long as yields for comparable bonds stay at 4%. Say for example one day after that bond is issued at par, interest rates increase so that the same bond issued a day later would yield 4.5% (extreme but gets the point across), the price of the original bond will decrease so that the discount on the bond plus the 4% coupon payments will yield 4.5%. Think about it this way… why would anyone pay par for a bond yield 4% when they can get an almost identical bond yielding 4.5% at par.