Mary Thomas works for Kershaw-Ross, a large investment bank located in London. Kershaw-Ross provides advice to portfolio managers, securities dealers, and hedge funds. Jack Bentley is Thomas assistant. Washington Capital Management, one of Thomas' clients, has a $5 million position in fixed-rate U.S. Treasury bonds. The firm would like to hedge this position using calls on Treasury bonds. The calls each cover $100,000 par value of bonds, have a delta of 0.4, and are out-of-the-money. To hedge this position, Thomas recommends that Washington Capital Management calculate the delta for the call options written on these Treasury bonds.
Later that week, Thomas discusses the particulars of option hedges with Francis Steele, Vice President at Washington Capital Management. Thomas describes how using gamma, the change in delta relative to the change in the underlying asset price, can increase the precision of the hedge. She states that this would be particularly true if the bond portfolio used calls that were at-the-money. Bentley adds that given the uncertainty surrounding U.S. Federal Reserve monetary policy, Kershaw-Ross has been advising clients to carefully monitor their bond positions for price changes. Bentley states that in Washington Capital Management's case, if the price of the underlying bond increases by 1% due to a yield curve shift, the calf hedge should be decreased because delta would have increased.
Thomas is analyzing the portfolio for one of his investors, Canopy Managers. Last year the portfolio had a market value of $4,881,000 and a dollar duration of $157,200. The current figures for the portfolio are provided below:
Canopy would like to alter the current dollar duration of the portfolio to last year's duration, and they would like to do so with the least amount of cash possible and a controlling position in one of the bonds.
Canopy Managers has also contracted to take out a 9-month loan for $5 million in three months at LIBOR. Canopy's chief financial officer has become concerned that interest rates might increase and has asked Thomas to investigate the possibility of hedging the position with a forward rate agreement. Thomas finds a forward rate agreement is available with the same maturity as Canopy's loan at a rate of 4.40%. The risk free rate is 3.8% and LIBOR is projected to be 4.60% at the inception of the loan.
The next week, Thomas and Bentley visit the headquarters of Capital Pension Management, one of Kershaw- Ross's largest clients. Capital is using contingent immunization to immunize a liability, but management is concerned about a possible rise in interest rates. Thomas states that if she were to recommend the most effective strategy to Capital, she would recommend that they use bonds with high yields because immunization will be cheaper. Bentley interjects that the risk from nonparallel shifts in the yield curve can be minimized by concentrating the cash flows around the horizon date.
Due to their tremendous success, Kershaw-Ross has outgrown their current headquarters and is going to expand their current building. Thomas's team has been charged with securing financing tor the renovations. They currently are considering a remodeling and addition that would cost approximately £5,000,000.
Thomas has secured the financing necessary for the renovations at a floating interest rate of LIBOR plus 150 basis points, with payments made quarterly over three years. Thomas believes that Kershaw-Ross should be able to complete the renovation of the building and close on the loan in one year. She is concerned, however, that interest rates will increase in the interim and has obtained a swaption to hedge the loan. She states that Kershaw-Ross should use a payer swaption to hedge the loan. Bentley evaluates the forecasts for future swap fixed rates as well as the current terms of various swaptions, which are provided below:
Fixed rate for a 1 -year payer swaption = 8.50%
Fixed rate for a 1-year receiver swaption = 8.60%
Projected swap fixed rate in one year = 9.30%
Fixed rate for a 4-year payer swaption - 9.40%
Fixed rate for a 4-year receiver swaption = 9.70%
Projected swap fixed rate in four years = 9.80%
To adjust the dollar duration of the Canopy portfolio to last year's level, the smallest amount Canopy will need to purchase of the bond that acts as a controlling position is closest to:
To rerurn the porrfolio to its original dollar duration, the manager could purchase additional amounts of each bond. Alternatively, the manager could select one of the bonds to use as a control-ling position. Since the dollar duration has fallen and Bond I has the longest duration, the manager could use the least amount of additional cash by increasing only the holding in Bond 1 (i.e., using Bond 1 as the controlling position):
Thus, the manager could purchase another $335,667 (= $1,115,667 - $780,000) of Bond 1. The new portfolio total value will he $4,217,000 + $335,667 = $4,552,667, and the portfolio dollar duration will he back to its original level:
(Study Session 9, LOS 29.g)