Calculate the one-year forward rates of interest implied by the November 1992 yield curve over the period 1993-2002.
We need a starting point. Use 1993 as 3.8% 4.65 = 2 year rate = (3.8+x)/2.
According to the expectations theory, the 2 year rate = sum of the previous year's rate and the year before that, or the 2 previous 1 year rates.
x = 5.5 %
That is your answer for 1994.
Next, for 1995, you have a 3-year rate = 5.23 = (3.8+5.5+x)/3
x = 6.39 %
Maturity Aug-91 Aug-92 Nov-92
3 m 5.33% 3.13% 3.20%
6 m 5.39% 3.21% 3.43%
1 yr 5.78% 3.47% 3.80%
2 y 6.43% 4.19% 4.65%
3 y 6.80% 4.72% 5.23%
4 y 7.23% 4.86% 5.72%
5 y 7.43% 5.60% 6.12%
6 y 7.51% 5.87% 6.34%
7 y 7.74% 6.12% 6.56%
8 y 7.79% 6.32% 6.87%
9 y 7.86% 6.47% 6.95%
10 y 7.90% 6.59% 7.18%
30 y 8.14% 7.39% 7.53%