An investor is betting on a steepening of the yield curve by going long $25M par of 3-year zeros, and going short $25M par of 10-year zeros. Spot rates are currently 1% and 2%, respectively, compounded semi-annually.

a. (10 points) Calculate the market value of this portfolio, and its partial durations using calculus or +/-0.001 (10 basis points) shifts.

b. (10 points) Factor loadings for the 3 and 10 year rates are (in basis points):

PC1: (0.372, 0.376) PC2: (-0.267, 0.371)

Calculate this portfolio's market value exposures to these principal component factors, being sure to identify the units of your final answers.

c. (5 points) Determine the daily standard deviation of this investor's portfolio. The above principal components are from daily data, and the associated standard deviations of the factor scores are 17.55 (PC1) and 4.77 (PC2).