A fictitious fixed income fund currently holds 10 US Treasury notes, 500 high yield corporate bonds, and$100,000cash in its portfolio. The Treasury note has 3 years to maturity, a coupon rate of2.00%paid semi-annually, and a face value of$100,000for each bond. The high yield corporate bond has 1 year to maturity, a coupon rate of8.00%paid semi-annually, and a face value of$1,000for each bond. Assume that the Treasury note is risk-free, but the high yield corporate bond has default risk. Specifically, the issuing company will honor coupon payments of the bond. Yet, at maturity, with probability30%, the company will default and repay only70%of the face value of the bond; otherwise, the principal will be repaid in full. The cash earns monthly interest of1.00%per annum.

1) Table 4 shows the continuously compounded risk-free rate for different maturi- ties. Calculate the prices of the Treasury note and the corporate bond (rounded to 3 decimal places). Note that prices of bonds are typically quoted for a face value of $100. Then, calculate the portfolio weight (percentage in market value) of each component in the portfolio.

Table 4: Yield curve of the continuously compounded risk-free rate. Term (year) Rate 0.5 1.74% 1.0 1.53% 1.5 1.39% 2.0 1.31% 2.5 1.28% 3.0 1.24%