on-year zero rate???

[dandy]

Hello
please can you help me
because there is quite a difficult task for me

zero-coupon government bonds with maturities ranging 1-5 years now have the following yields: 6%, 7%, 8%, 8,5%, 10,5%. using the expectations theory of the term structure what will you say the market expects the on-year zero rate to be one year from now???

Thanks in advance

 

[structurer]

around 8%

 

[afterworkguinness]

The solution is interest rate parity; the relationship between current spot rates and forward rates.
Firstly, let's clarify that the rate your trying to solve for is a forward rate - the 1 year forward rate maturing in 2 years (forward rate that starts in 1 year and goes for 1 year).
To prevent arbitrage, the 1 year forward rate, maturing in 2 years must equal :

(assuming annual compounding)

(1 + 2 year spot rate)^2 = (1 + 1 year spot rate)^1 * (1 +1 year forward rate maturing in 2 years)^1

Note the pattern of (1 + r)^t to calculate future values.

The logic behind this is that we should be indifferent if we invest now for 2 years at the 2 year spot, or invest for 1 year at the 1 year spot and roll over after 1 year for another 1 year (total time in the investment is still 2 years) at the 1 year forward rate agreed upon at time 0;