Assume that a 1 - year discount bond (bond A) with a FV = $1000 is currently tra

Question

Assume that a 1 - year discount bond (bond A) with a FV = $1000 is currently trading at PV= $963.39. Further assume that investors in the market for the same contract anticipate that the same 1 - year discount bond A will trade next year at $956.94. Please calculate a current price on another 2-year discount bond (Bond B) with identical risk structure and face value- under the assumptions of the Expectations Theory.

* Note: Please apply standard rounding in the example

A) $924.56

B) $915.73

C) $928.12

D)$960.17

E)$921.90

Please show work

Explanation / Answer

spot rate for year 1=(1000/963.39)-1

forward rate b/w year 1 and 2 =(1000/956.94)-1

Therefore according to Expectations Theory,

(1+the spot rate for year 2)^2=(1+spot rate for year 1)*(1+forward rate b/w year 1 and 2)

(1+the spot rate for year 2)^2=(1+(1000/963.39)-1)*(1+(1000/956.94)-1)

(1+the spot rate for year 2)^2=(1000/963.39)*(1000/956.94)

current price on another 2-year discount bond=1000/(1+the spot rate for year 2)^2

current price on another 2-year discount bond=1000/((1000/963.39)*(1000/956.94))

current price on another 2-year discount bond=1000/1.084708785

current price on another 2-year discount bond=921.90

current price on another 2-year discount bond (Bond B) with identical risk structure and face value- under the assumptions of the Expectations Theory is E)$921.90.

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