Long-Term Capital Management was a prominent hedge fund of Greenwich, Conn, whose partners included two Nobel Prize winners. In September 1998, a cash infusion of $3.5 billion from a consortium of commercial banks and investment firms rescued this hedge fund with the support from the Federal Reserve Bank of New York.
Among the many strategies employed by the firm was one in which Treasury Bonds were shorted and the proceeds of these sales were used to purchase higher yielding (and higher risk) mortgage-backed or corporate debt securities. The strategy - known as playing a credit spread - generates huge profits as long as bond yields remain stable. But since the stock market began plunging in July of 1998, investors fled for cover in the quality of liquid U.S. government securities and required higher risk premia on all risky assets. This question analyzes the risk of this investment strategy in a highly stylized example.
Suppose in September 1997, the fund was invested in the following two positions:
- A long position of 1,000,000 less liquid fixed-income securities (LLS) (such as off-the-run Treasury securities, mortgage-backed securities, corporate bonds, etc.) maturing in 5 years with an annual interest payment of 7.5% (each bond has a face value of $100,000).
- A short position of 950,000 Treasury securities (TS) maturing in 5 years with an annual interest payment of 6.5% (each bond has a face value of $100,000). The table summarizes the yield curve of zero-coupon bonds in September 1997 and September 1998:
|
September 1997
|
September 1998
|
|
Maturity
|
TS
|
LLS
|
TS
|
LLS
|
|
1 Year
|
5.50%
|
6.50%
|
4.50%
|
7.50%
|
|
2 Years
|
5.75%
|
6.75%
|
4.75%
|
7.75%
|
|
3 Years
|
6.00%
|
7.00%
|
5.00%
|
8.00%
|
|
4 Years
|
6.25%
|
7.25%
|
5.25%
|
8.25%
|
|
5 Years
|
6.50%
|
7.50%
|
5.50%
|
8.50%
|
a. What are the market values of the two bonds in September 1997? What is the equity value of the hedge fund?
Questions b and c look at the situation in September 1998 under two possible scenarios. In the first scenario the yield curve does not change and in the second scenario the yield spread increases. Assume that the hedge fund does not adjust its positions between September 1997 and September 1998. Thus, the fund still holds in 1998 the bonds it purchased or short-sold in 1997. Assume that the bonds just paid a coupon payment in early September 1998 and that they have now a remaining maturity of 4 years.
1. Suppose that the yield curve does not change and is the same in September 1998 as it was in September 1997. For example, in September 1998, a Treasury bond with a maturity of one year has a yield of 5.5%. What are the current market values of the two bonds? How high are the net interest receipts of the fund? What is the value of the fund?
2. Actually, the yield curve changed considerably between September 1997 and 1998, as shown in the Table above. For example, in September 1998, a Treasury bond with a maturity of one year had a yield of 4.5%, while less-liquid securities yielded 7.5%. What are the current market values of the two bonds? How high are the net interest receipts of the fund? What is the value of the fund?