Question

1. The following table depicts the yield curve for various bond maturities. Use the yield curve to calculate the one year expected yields (i) using the unbiased expectations theory. Time to maturity Multi-year return 2% 3% 4% 4.5% 5.5%

Answer 1

Assuming return given are compounded annually,

One year forward expected yield = ((1+f(0,T))^T)/((1+f(0,T-1))^(T-1)) - 1

for 1 year forward expected yield one year from now = ((1+f(0,2))^2)/((1+f(0,1))^1) - 1 = (1.03^2)/(1.02) - 1 = 4.01%

Time to Maturity	Multi-year return	Formula	1 year forward expected rate
1	2%		2%
2	3%	(1.03^2)/(1.02) - 1	4.01%
3	4%	(1.04^3)/(1.03^2) - 1	6.03%
4	4.5%	(1.045^4)/(1.04^3) - 1	6.01%
5	5.5%	(1.055^5)/(1.045^4) - 1	9.60%