UCL Capital Management owns Treasury bonds with a face value of $100 million, an annual coupon of 5%, a maturity of 3 years, and a yield-to-maturity of 5%. The fund also has liabilities with a face value of $95 million, an annual coupon of 4%, a maturity of 2 years, and a yield-to-maturity of 2.9%.

a) (5 points) Calculate the market values of UCL Capital Managements assets and liabilities.

b) (10 points) UCL Capital Management is concerned that interest rates in the economy will increase in the future, leading to a long-term loss to the funds equity value. The fund considers duration hedging of assets and liabilities. Specifically, UCL Capital Management wants to:

• sell a fraction of its assets at a current high market price;

• use the proceeds to buy zero-coupon Treasury bonds with a maturity of 1 year. The 1-

  year spot rate is 1%. What fraction of its assets should UCL Capital Management sell?

  c) (8 points, difficult) Still concerned, UCL Capital Management considers convexity hedging of assets and liabilities. It wants to:

sell a fraction of its assets;

use the proceeds to buy zero-coupon Treasury bonds with maturities of 1 and 2 years. The 1-year spot rate is still 1%, while the 2-year spot rate is 2.94%.

What fraction of its assets should UCL Capital Management sell now?

d) (7 points) UCL Capital Management is concerned about a high liquidity cost of duration and convexity hedging, due to the need to terminate a large fraction of assets. At the same time, new internal research shows that interest rates will increase for sure. Therefore, the fund considers, as a duration hedge, put options on 10-year Treasury bonds. The underlying bonds have a duration of 8.82. Put options have a of -0.5 (, or Delta, is the option price sensitivity to a bond price change). As before, if the fund wants to buy options, it must sell a fraction of its assets to finance the hedge, so that the total market value of assets remains the same. Conversely, if the fund wants to short-sell options, it must buy more of the current asset, which is financed by the short sale. Should UCL Capital Management buy or short sell put options? What is the value of the option hedge? Discuss.