A dealer in government securities currently holds $875 million in 10-year Treasury
bonds and $1,410 million in 6-month Treasury bills. Current yields on the T-bonds
average 7.15 percent while 6-month T-bill yields average 3.38 percent. The dealer is
currently borrowing $2,300 million through one-week repurchase agreements at an
interest rate of 3.20 percent. What is the dealer's expected (annualized) carry income?
Suppose that 10-year T-bond rates suddenly rise to 7.30 percent, T-bill rates climb to
5.40 percent and interest rates on comparable maturity RPs increase to 5.55 percent.
What will happen to the dealer's expected (annualized) carry income and why?
Should this dealer have moved to a long position or a short position before the interest
rate change just described? Should the dealer alter his or her borrowing plans in any way? Please explain your answer.
To calculate the dealer's expected carry income, we need to consider the yields on the securities and the borrowing costs.
First, let's calculate the carry income under the current conditions:
- The dealer holds $875 million in 10-year Treasury bonds with an average yield of 7.15%, resulting in an annual carry income of (0.0715 * $875 million).
- The dealer also holds $1,410 million in 6-month Treasury bills with an average yield of 3.38%, resulting in an annual carry income of (0.0338 * $1,410 million).
Next, let's calculate the borrowing cost:
- The dealer is borrowing $2,300 million through one-week repurchase agreements at an interest rate of 3.20%. The borrowing cost is (0.0320 * $2,300 million).
To calculate the dealer's expected carry income, we subtract the borrowing cost from the sum of the carry income from the bond and bills:
Expected Carry Income = (0.0715 * $875 million) + (0.0338 * $1,410 million) - (0.0320 * $2,300 million).
Now, let's calculate the expected carry income after the interest rate changes:
The new yield on the 10-year T-bonds is 7.30% and the new yield on the 6-month T-bills is 5.40%. The new borrowing rate on the repurchase agreements is 5.55%.
We calculate the new carry income using the same formula as before, but substituting the new yields and borrowing rate:
New Carry Income = (0.0730 * $875 million) + (0.0540 * $1,410 million) - (0.0555 * $2,300 million).
To analyze the impact on the dealer's expected carry income, we compare the new carry income with the previous carry income. If the new carry income is greater, the expected carry income has increased. If the new carry income is smaller, the expected carry income has decreased.