1) After reading the following excerpt from an article titled "Smith Plan to Shorten", what type of portfolio strategy is Smith Affiliated Capital pursuing?
"When the economy begins to rebound and interest rates start to move up, Smith Affiliated Capital will swap 30-year Treasuries for 10-year Treasuries and those with average remaining lives of nine years, according to Bob Smith, Executive V.P. The New York firm doesn't expect this to occur until the end of this year or early next, however, and sees the yield on the 30-year Treasury first falling below 7%. Any new cash that comes in now will be put into 30-year Treasuries, Smith added."
Part II. Numerical Problems: you are required to show steps/formulas/solutions to obtain credit. That is, I need to be able to follow how you get the answer; you cannot simply tell me that the answer is generated by computer.
1) The table below provides returns on a portfolio along with returns for the corresponding benchmark index for the past twelve months. Compute the tracking error and the annualized tracking error from the following information.
|
Month
|
Portfolio Return (%)
|
Benchmark Index Return (%)
|
|
Jan
|
-0.19
|
-0.37
|
|
Feb
|
0.15
|
-0.19
|
|
Mar
|
-0.13
|
0.17
|
|
Apr
|
-0.37
|
-0.06
|
|
May
|
-0.33
|
0.26
|
|
Jun
|
-0.04
|
0.07
|
|
Jul
|
-0.17
|
0.06
|
|
Aug
|
0.18
|
-0.08
|
|
Sep
|
-0.38
|
-0.22
|
|
Oct
|
-0.40
|
-0.13
|
|
Nov
|
-0.40
|
-0.50
|
|
Dec
|
-0.44
|
-0.33
|
2) Assume that bond XYZ is the underlying asset for a futures contract with settlement six months from now. In the cash market bond XYZ is selling for $70 (par value is $100); bond XYZ pays $9.5 in coupon interest per year in two semiannual payments of $4.75, and the next semiannual payment is due exactly six months from now; and the current six-month interest rate at which funds can be loaned or borrowed is 7.5%.(each is worth 5 points, 15 points total).
(a) What is the theoretical futures price?
(b) What action would you take if the futures price is $75?
(c) Suppose that the borrowing rate and lending rate are not equal. Instead, suppose that the current six-month borrowing rate is 9% and the six-month lending rate is 7.5%. What is the boundary for the theoretical futures price?
3) A portfolio manager wishes to hedge a bond with a par value of $33 million by selling Treasury bond futures. Assume the conversion factor for the cheapest-to-deliver issue is 0.71. The price value of a basis point of the bond to be hedged is 0.0696 and the price value of a basis point of the cheapest-to-deliver issue at the settlement date is 0.07965.(each is worth 5 points, 10 points total).
(a) What is the hedge ratio?
(b) How many Treasury bond futures contracts should be sold to hedge the bond?
4) Suppose that a life insurance company has issued a four-year Guaranteed Investment Contract (GIC) with a fixed-rate of 8%. Assume also that the life insurance company has the opportunity to invest $17 million in what it considers an attractive four-year floating-rate instrument in a private placement transaction. The interest rate on this instrument is six-month LIBOR plus 100 basis points. The coupon rate is set every six months.
Suppose the life insurance company can enter into a swap with a bank which has a portfolio consisting of four-year term commercial loans with a fixed interest rate. The principal value of bank's portfolio is $17 million, and the interest rate on all its loans in its portfolio is 9%. The loans are interest-only loans; interest is paid semiannually, and the principal is paid at the end of four years. To fund its loan portfolio, assume that the bank is relying on the issuance of six-month certificates of deposit(CDs). The interest rate that the bank plans to pay on its six-month CDs is six-month LIBOR plus 140 basis points. The life insurance company can seize this opportunity to cover its commitment to pay a 8% rate for the next four years on the $17 million GIC it has issued.
|
Fixed rate |
Floating rate |
| Bank |
9% |
six- month LIBOR +1.4% |
| Life Insurance |
8% |
six- month LIBOR +1% |
Under what circumstances might it be feasible for the life insurance company to invest the funds in a floating-rate security and enter into a four-year interest-rate swap in which it pays a floating rate and receives a fixed-rate?