关于Mock题2022年A卷上午题的32题，衍生

关于Mock题2022年A卷上午题的32题，衍生部分，我用画图法算出来是3.6%，选不出来。老师在视频中没有用这个方法，难道是不能用这个方法？为什么呢？如果可以，那我哪里算出了，麻烦老师指导一下。谢谢

Fabricantes Conchos Case Study

Gabriela Torres is the CFO of Fabricantes Conchos (FabC), an automobile parts manufacturer located in Chihuahua, Mexico. She is currently evaluating the firm’s debt structure and anticipated financing needs.

FabC sells most of its product to US auto companies and their suppliers through long-term contracts priced in US dollars. FabC’s debt is denominated in US dollars. Torres actively manages the firm’s interest rate risk profile using interest rate and fixed-income derivatives, specifically OTC forwards, futures, and swap contracts.

Torres explains to her deputy, Alejandro Gutiérrez, “The derivatives contracts we enter into are typically priced using a carry arbitrage model to have zero cost to us at origination. In addition to requiring current interest rates and coupon payments of the underlying bonds, the model makes three assumptions: (1) There are no transaction costs for buying and selling securities; (2) short-selling proceeds become available when the short is covered; and (3) we can borrow and lend at the same risk-free rate of interest.”

Gutiérrez mentions a major new contract requiring FabC to increase its working capital by borrowing USD35 million in six months. Torres states she is concerned interest rates will rise substantially in the near future and is considering entering a long position (pay fixed) in a 6 × 24 forward rate agreement to lock in the price of the new loan. She asks Gutiérrez what the fixed rate would be using a 30/360 convention and the spot interest rates found in Exhibit 1.

Exhibit 1. 

USD Interest Rates

MonthsSpot

Interest RatePV Factor62.10%0.9896122.64%0.9743183.07%0.9560243.35%0.9372303.56%0.9183363.81%0.8974423.92%0.8794483.98%0.8627544.02%0.8468604.03%0.8323

Torres tells Gutiérrez, “If we issue a long-term bond, it makes more sense to enter a bond futures contract in order to hedge interest rate changes. Typically, bond futures are quoted with pricing that reflects interest accrued since the last coupon payment. Therefore, in markets where spot prices are quoted “clean” rather than “dirty,” there can be some disconnect between spot and futures prices. In addition, a conversion factor must be applied to quoted bond prices because more than one bond can be delivered to fulfill the terms of the contract. The short (selling) counterparty to the contract will always want to deliver the cheapest bond when the forward contract matures. The conversion factor attempts to adjust for differences in pricing between the bonds that can be delivered to fulfill a particular contract.”

Torres continues, “We are about to enter into a five-year loan with semi-annual interest payments based on prevailing six-month LIBOR. I think it might make sense to simultaneously enter into a pay-fixed five-year interest rate swap with semi-annual payments to effectively convert that to a fixed-rate loan. Based on the interest rates shown in Exhibit 1, what would the fixed rate be?”

Question

Gutiérrez’s fixed-rate calculation for the forward rate agreement should be closest to:

1. 3.73%.
2. 3.88%.
3. 5.59%.