7.1. You are given a bond portfolio consisting of three individual bonds (R2023, R186 & R213) with different maturities and relevant information for each of the bonds.

BondAnnual couponYieldClean Price per R100 nominalDirty price per R100 nominalModified DurationConvexityExpected price change with one basis point yield changeExpected clean price after one basis point yield DECLINERunning (current) yieldPortfolio weightsR20237.75%5.45%R 105.770R 107.7022.437.480.026105.7967.20%20%R18610.50%7.35%R 116.148R 120.7504.6828.840.057116.2058.70%50%R2137.00%9.44%R 83.694R 85.4406.9464.900.05983.7538.19%30%Portfolio statistics7.60%R 104.336R 107.547100%

Answer the following question regarding the bond portfolio:

a) What is the modified duration and convexity of the portfolio? (2 Marks)

b) What is the new clean price and dirty price of the portfolio, if a parallel shift in the yield curve resulted in yields strengthening (declining) by 1 basis point (i.e. 0,01%)? (2 Marks)

c) Using clean price changes with respect to changes in yield as a risk statistic, which of the individual bonds has a risk that is closest to that of the bond portfolio? (1 Mark)

d) Suppose that the bond prices are not expected to change for the next 12 months, expected inflation is 5% and the real one-year interest rate is 2%. Is the current portfolio expected to outperform the one-year money market rate? Why or why not? (2 Marks)

7.2. Answer the following questions.

a) What are the different shapes of the term structure of interest rates and what do each of the shapes indicate about investor expectations? (3 Marks)

b) Identify the three central theories that attempt to explain why yield curves are shaped the way they are and briefly comment on how they differ in their explanations. (3 Marks)