1, 5 and 10 year semi-annual compounded spot rates are currently 1.0%, 2.0% and 2.5%. A hedge fund has the following portfolio:

o Long $200M par, 1-year zeros

o Short $500M par, 5 year zeros

o Long $450M par, 10 year zeros

You calculated the market value, duration and convexity of this portfolio (using calculus, or, the numerical approach with i=0.001) for PS4.

Calculate the 3 partial durations of this portfolio (again use calculus, or, the numerical approach with i=0.001). Check that the sum of partials equals duration (it will be exact with calculus, very close with numerical methods).

Calculate the gain or loss of this portfolio given each of the first three principal components on Hulls Table 9.6.

Evaluate the standard deviation of the portfolio gain/loss from part b and the three-factor scores in Table 9.7 of Hull.