Question

Butterfly Trade It is April 1, 2020. Consider the following Treasury yield curve:

Maturity Coupon Price

2-year 3/31/2022 2.00% 100-00

5-year 9/30/2025 3.50% 100-00

10-year 9/15/2030 4.75% 100-00

There are 2 portfolios, each with $100 Million market value.

Portfolio I: 5-year bullet.

Portfolio II: 2-year/10-year barbell.

1.) Today, you invest the $100 Million in each portfolio, so that the portfolios have the same duration. The trades settle tomorrow. How much is invested in the 2-year and in the 10-year?

2.) Suppose you believe that 9 months from today the 2-year yield will be 50 basis points higher and the 10-year yield will be 25 basis points lower.

a.) Which strategy outperforms on a total rate of return basis?

3.) Discuss the issues/complexities involved with solving question #2.

This is all the information that's given.

Answer 1

Since both the portfolio have same duration, i.e. 5 Years to maturity, therefore,

2x + 10(1-x) = 5

8x = 5

x=.625

Therefore, 62.5% of total investment (100 Mn) are made in 2 year bond and 37.5% investment is made in 10 year bond;

Investment in 2 year bond= 62.5 Mn

Investment in 10 year bond= 37.5 Mn

Part 2: Now after 9 months, 2 year bonds ROR increases by 50 basis points while that of 10 year bond decreases by 25 basis points.

for 2 years ROR on barbell portfolio will be (2*.625+ 4.75*.375)= 3.03

After 2 years replace the 2 year bond with new 2 year bond,

Therefore new ROR = (2.5*.625+ 4.75*.375) = 3.343

This proves that the first portfolio with Bullet investment strategy will outform the second portfolio.