Question

a) In the first trading day of 1998, Hang Seng Index closed at 10680.60, while in the last trading day of 2017, it closed at 29919.15. What is the average annual growth rate of Hang Seng Index in this 20-year?

b) The following yield curve is observed of the U.S. Treasury securities on 28th October 2019:

Maturity (Year)	Yield Rate (%)
1	1.60
2	1.64
3	1.65

Suppose the pure expectation theory is correct. Forecast the expected one-year yield rate of one year later and of two years later respectively.   

Answer 1

(a) Average annual growth rate is the arithmetic average growth during the period of 20 years.

Given, Index on closing of year 2017 (I₁₎= 29,919.15

Index on first day of 1998 (I₀) = 10,680.60

No. of years (n) =20

Average Annual Growth rate during 20 years=( I₁-I₀)/I₀*n = (29,919.15-10,680.60)/(10,680.60*20 )= 0.090063 Or, 9.0063%

(b) Expected one-year yield rates (forward rates) are as follows:

One year later: 1.68%

Two years later: 1.67%

Computation below: