Chapter 12, Swaps Video Solutions, An Introduction to Derivatives and Risk Management: With Stock-Trak Coupon

Problem 1

Consider a $$\$ 100$$ million equity swap with semiannual payments. When the swap is established, the underlying stock is at $1,215.52$. One party pays a fixed rate of 5.5 percent based on the assumption of 30 days per month and 360 days in a year. If the stock index is at $1,275.89$ on the first payment date, calculate the net swap payment, indicating which party pays it.

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02:14

Problem 2

Consider a currency swap for $$\$ 10$$ million and SF15 million. One party pays dollars at a fixed rate of 9 percent, and the other pays Swiss francs at a fixed rate of 8 percent. The payments are made semiannually based on the exact day count and 360 days in a year. The current period has 181 days. Calculate the next payment each party makes.

Suzana Milea

Numerade Educator

Problem 3

The CEO of a large corporation holds a position of 25 million shares in her company's stock, which is currently priced at $$\$ 20$$ and pays no dividends. She is concerned that, because of her large shareholdings and the fact that her compensation is tied to the performance of the stock, she is very poorly diversified, She does not think it is wise to sell a significant amount of stock, because she knows that she needs to be heavily invested in the stock to satisfy the shareholders, and she values the voting rights she has from owning so many shares. Nonetheless, she would be interested in synthetically selling about five million shares using an equity swap. Assume the role of a swap dealer and present three possible equity swap proposals, which are based on the three different types of cash flows that could be paid against payment of the return on the stock.

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Problem 4

A corporation enters into a $$\$ 35$$ million notional principal interest rate swap. The swap calls for the corporation to pay a fixed rate and receive a fioating rate of LIBOR. The payments will be made every 90 days for one year and will be based on the adjustment factor $90 / 360$. The term structure of LIBOR when the swap is initiated is as follows:
$$
\begin{array}{rl}
\hline \text { Days } & \text { Rate } \\
\hline 90 & 7.00 \% \\
180 & 7.25 \\
270 & 7.45 \\
360 & 7.55 \\
\hline
\end{array}
$$
a. Determine the fixed rate on the swap.
b. Calculate the first net payment on the swap.
c. Assume that it is now 30 days into the life of the swap. The new term structure of LIBOR is as follows:
$$
\begin{array}{rl}
\hline \text { Days } & \text { Rate } \\
\hline 60 & 6.80 \% \\
150 & 7.05 \\
240 & 7.15 \\
\$ 30 & 7.20 \\
\hline
\end{array}
$$
Calculate the value of the swap.

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04:01

Problem 5

Show how to combine a currency swap paying Swiss francs at a floating rate and receiving Japanese yen at a floating rate with another currency swap to obtain a plain vanilla swap paying Swiss francs at a floating rate and receiving Swiss francs at a fixed rate.

Md.Daniyal Arshad

Numerade Educator

02:34

Problem 6

A bank currently holds a loan with a principal of $$\$ 12$$ million. The loan generates quarterly interest payments at a rate of LIBOR plus 300 basis points, with the payments made on the 15th of February, May, August, and November on the basis of the actual day count divided by 360 . The bank has begun to believe that interest rates will fall. It would like to use a swap to synthetically alter the payments on the loan it holds. The rate it could obtain on a plain vanilla swap is 7.25 percent. Explain how the bank would use a swap to achieve this objective.

Breanna Ollech

Numerade Educator

Problem 7

Explain why interest rate swaps are more widely used than currency and equity swaps.

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Problem 8

A U.S. corporation is considering entering into a currency swap that will call for the firm to pay dollars and receive British pounds. The dollar notional principal will be $$\$ 35$$ million. The swap will call for semiannual payments using the adjustment $180 / 360$. The exchange rate is $$\$ 1.60$$. The term structures of dollar LIBOR and pound LIBOR are as follows:
$$
\begin{array}{lcc}
\hline \text { Days } & \text { Dollar LIBOR } & \text { Pound LIBOR } \\
\hline 180 & 7.00 \% & 6.50 \% \\
360 & 7.95 & 7.10 \\
540 & 7.45 & 7.50 \\
720 & 7.55 & 8.00 \\
\hline
\end{array}
$$
Answer the following questions.
a. Determine the appropriate pound notional principal. Use this result in each of the remaining questions.
b. Determine the fixed rates in dollars and in pounds.
c. For each of the following cases, determine the first payment on the swap:
i. Dollars fixed, pounds fixed
ii. Dollars fixed, pounds floating
ii. Dollars floating, pounds floating
iv. Dollars floating, pounds fixed
d. Now assume it is 120 days into the life of the swap. The new exchange rate is $$\$ 1.42$$. The new term structures are as follows:
$$
\begin{array}{rcc}
\hline \text { Days } & \text { Dollar LCBOR } & \text { Pound I.IBOR } \\
\hline 60 & 6.80 \% & 6.40 \% \\
240 & 7.05 & 6.90 \\
420 & 7.15 & 7.30 \\
600 & 7.20 & 7.45 \\
\hline
\end{array}
$$
Determine the value of the swap for each of the following cases:
i. Dollars fixed, pounds fixed
ii. Dollars fixed, pounds floating
iii. Dollars floating, pounds floating
iv. Dollars floating, pounds fixed

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Problem 9

A pension fund wants to enter into a six-month equity swap with a notional principal of $$\$ 60$$ million. Payments will occur in 90 and 180 days. The swap will allow the fund to receive the return on a stock index, currently at 5,514.67. The fund is considering three different types of swaps, one of which would require it to pay a fixed rate, another that would require it to pay floating rate, and another that would require it to pay the return on another stock index, which is currently at 1,212.98. Refer to these as swaps 1,2 , and 3. The term structure is as follows:
$$
\begin{array}{ccc}
\hline \text { Term } & \text { Rate } & \text { Discount Bond Price } \\
\hline 90 \text { days } & 9 \% & \mathrm{~B}_4(90)=1 /(1+0.09(90 / 360))=0.9780 \\
180 \text { days } & 10 & \mathrm{~B}_0(180)=1 /(1+0.10(180 / 360))=0.9594 \\
\hline
\end{array}
$$
a. Find the fixed rate for swap 1 .
b. Find the payments on day 90 for swaps 1, 2, and 3. For swap 3, assume that on day 90 stock index 1 is at $5,609,81$ and stock index 2 is at $1,231.94$. Be sure to indicate the net payment.
c. Assume it is 30 days into the life of the swap. Stock index 1 is at $5,499.62$, and stock index 2 is at $1,201.45$. The new term structure is as follows:
$$
\begin{array}{rlr}
\hline \text { Term } & \text { Rate } & \text { Discount Bond Price } \\
\hline 60 & 6.80 \% & \mathrm{~B}_{y_0}(90)=1 /(1+0.068(60 / 360))=0.9858 \\
150 & 7.05 & \mathrm{~B}_{91}(180)=1 /(1+0.0705(150 / 360))=0.9715 \\
\hline
\end{array}
$$
Find the values of swaps 1,2 , and 3 .

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Problem 10

You are a pension fund manager who anticipates having to pay out 8 percent (paid semi-annually) on $$\$ 100$$ million for the next seven years. You currently hold $$\$ 100$$ million of a floating-rate note that pays $\mathrm{LIBOR}+2 \mathrm{I} / 2$ percent. You view this as an attractive investment but realize that if LIBOR falls below $5 \mathrm{I} / 2$ percent, you will not have enough cash to make your fixed payments. You arrange a swap with a dealer who agrees to pay you 6 percent fixed, while you pay it LIBOR. Determine your cash flow as a percent of the nocional principal at each payment date under this arrangement. Assume for simplicity that each period is 180 days and that there are 360 days in the year.

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Problem 11

A hedge fund is currently engaged in a plain vanilla euro swap in which it pays euros at the euro floating rate of Euribor and receives euros fixed. It would like to convert this position into one in which it pays the return on the S\&P 500 and receives euros at a fixed rate. Show how it can use currency and equity swaps to maintain its position in the plain vanilla euro swap and convert its overall position to the one desired.

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Problem 12

(Concept Problem) An asset management firm has a $$\$ 300$$ million portolio consisting of all stock. It would like to divest 10 percent of its stock and invest in bonds. It considers the possibility of synthetically selling some stock using equity swaps. It does not, however, want to receive a fixed or floating rate. If it actually sold the stock, it would invest in a broadly diversified portfolio of bonds. In fact, there are bond indices that are quite representative of the universe of bonds in which it would invest. Design a strategy using swaps that would enable it to achieve its objective.

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Problem 13

Why is notional principal often exchanged in a currency swap but not in an interest rate or equity swap? Why would the parties to a currency swap choose not to exchange the notional principal?

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01:02

Problem 14

Consider a $$\$ 30$$ million notional principal interest rate swap with a fixed rate of 7 percent, paid quarterly on the basis of 90 days in the quarter and 360 days in the year. The first floating payment is set at 7.2 percent. Calculate the first net payment. and identify which party, the party paying fixed or the party paying floating, pays.

Amy Jiang

Numerade Educator

01:42

Problem 15

Explain how the following types of swaps are analogous to transactions in bonds.
a. Interest rate swaps
b. Currency swaps

Kaylee Mcclellan

Numerade Educator

Problem 16

A swap dealer quotes that the rate on a plain vanilla swap, for it to pay fixed, is the five-year Treasury rate plus 10. To receive fixed, the dealer quotes the rate as the five-year Treasury rate plus 15. Assuming the five-year Treasury rate is 7.60 percent, explain what these quotes mean.

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Problem 17

The U.K. manager of an international bond portfolio would like to synthetically sell a large position in a French government bond, denominated in euros. The bond is selling at its par value of $€ 46.15$ million, which is equivalent to $£ 30$ million at the current exchange rate of $\{0.65$. The bond pays interest at a fixed rate of 5.2 percent annually for 10 years. The manager would like to sell the bond and invest the proceeds in a pound-denominated floating-rate bond. Design a currency swap strategy that would achieve the desired objective and identify the payments that would occur on the overall position, which includes both the French bond and the swap. The fixed rates on the currency swap are 4.9 percent in pounds and 5.7 percent in euros.

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Problem 18

Explain how swaps are similar to but different from forward contracts.

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02:47

Problem 19

Suppose that a party engages in a swap, but before the expiration date of the swap, the party decides that it would like to terminate the position. Explain how it can do so.

Jennifer Stoner

Numerade Educator

Problem 20

Explain how an interest rate swap is a special case of a currency swap.

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Problem 21

(Concept Problem) Consider a currency swap with but two payment dates, which are one year apart, and no exchange of notional principals. On the first date, the party pays U.S. dollars at a rate of 4 percent and receives British pounds at a rate of 3.5 percent. Since the payments are annual, no adjustment, such as days $/ 360$, is necessary. The notional principals are $$\$ 10$$ million and $$\$ 6.25$$ million. Explain from an American's perspective how this transaction is like a series of forward contracts on the pound. Also, explain how the transaction can be fairly priced, which you can assume it is, even though the implied forward rate is the same for both maturities.

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