1. Risk Management: Forwards and Futures 3 2. Risk Management: Options Risk Management: Swaps Key Formulas 65

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1 1. Risk Management: Forwards and Futures 3 2. Risk Management: Options Risk Management: Swaps Key Formulas Allen Resources, Inc. All rights reserved. Warning: Copyright violations will be prosecuted. Any use of these materials without the express written consent of the publisher is a violation of federal and/or international copyright laws. 15-1

2 Risk Management: Swaps 3. Risk Management: Swaps Learning Objectives This summary includes a review and an analysis of the principles set forth by CFA Institute. Upon review of this summary, you should be able to: Illustrate how to convert floating (fixed) debt to fixed (floating) debt using an interest rate swap...pg. 52 Describe how to calculate the duration of a swap...pg. 53 Describe how a variable rate borrower using an interest rate swap to convert floating rate exposure to fixed exposure, also converts interest rate risk to market value risk...pg. 53 Calculate the notional principal required in an interest rate swap to change the current risk (duration) of a bond portfolio to a target risk (duration) level...pg. 53 Describe how a firm can reduce its overall financing costs by issuing debt in its home currency and then using a currency swap to make payments in another currency...pg. 56 Illustrate the use of a currency swap to convert foreign currency denominated cash flows into domestic denominated currency cash flows without an exchange of notional principal...pg. 57 Illustrate how to use equity swaps to diversify a concentrated portfolio, alter the asset allocation of a portfolio, and provide international diversification without the sale of existing securities within the portfolio...pg. 59 Illustrate the use of interest rate swaptions to alter the payments of future loans and close out swap positions...pg Allen Resources, Inc

3 Study Session 15 Converting Floating Debt to Fixed Debt Learning Objective: Illustrate how to convert floating (fixed) debt to fixed (floating) debt using an interest rate swap. In many circumstances, interest rate swaps provide a cost-effective means of hedging interest rate exposure. As an example, consider the following two financial institutions: 1. Firm A has fixed-rate investments that provide a return of 12%. Its liabilities are floating rate loans at the 6-month LIBOR rate. Therefore, it faces the risk that LIBOR may increase. 2. Firm B has investments that generate a return of 150 basis points over 6-month LIBOR, but its liabilities are fixed-rate loans at 9%. Firm B faces the risk that LIBOR may fall. The swap dealer earns 10 basis points. We can represent the cash flows pictorially as follows: LIBOR 9% Firm A 10.5% 10.4% Swap dealer Firm B LIBOR LIBOR 12% LIBOR bps Both firms can eliminate interest rate risk by entering into a swap agreement. For example, suppose that B arranges through a swap dealer to make LIBOR payments to A. In exchange, A makes fixed payments of 10.5%. The swap dealer retains 10 basis points and passes the remaining 10.4% on to B. With the swap, A will receive a return of = 1.5%, and B receives 10.4% basis points 9% = 2.9% Study Guide for the Level III 2015 CFA Exam - Reading Highlights

4 Risk Management: Swaps Calculating Swap Duration Learning Objective: Describe how to calculate the duration of a swap. A swap can be viewed as a portfolio that combines a position in a fixed-rate bond with a floating-rate bond. For the party receiving the fixed payments, the swap is equivalent to a long position in a fixed-rate bond combined with a short position in a floating-rate bond. Therefore, the dollar duration of the swap will be equal to the difference between the dollar duration of the fixed-rate bond and the floating-rate bond. That is, for the fixed-rate receiver: Dollar duration Swap = Dollar duration Fixed rate bond Dollar duration Floating rate bond Learning Objective: Describe how a variable rate borrower using an interest rate swap to convert floating rate exposure to fixed exposure, also converts interest rate risk to market value risk. The dollar duration of the floating-rate portion of the swap will be small. At points close to the reset date, the floating-rate bond will have a dollar duration very near zero. Consequently, the dollar duration of the swap is essentially equal to the dollar duration of the fixed-rate bond. Adding the receive-fixed swap to a portfolio will increase the dollar duration of the portfolio. For the fixed-rate payer, the dollar duration of the swap is equal to the dollar duration of a floating-rate bond, minus the dollar duration of a fixed-rate bond. If the dollar duration of the floating-rate bond is small, then the dollar duration of the swap from the fixed-rate payer s view is minus the dollar duration of the fixed-rate bond. Since the dollar duration of this position is less than zero, adding it to a portfolio will reduce the dollar duration of the portfolio. Calculating Notional Principal Learning Objective: Calculate the notional principal required in an interest rate swap to change the current risk (duration) of a bond portfolio to a target risk (duration) level. To change the duration of a fixed income portfolio, we will need to calculate the required notional principal (NP) to use in the swap using the following formula: NP = MV Portfolio Target Portfolio Swap Duration Duration Duration Example VJA Corporation manages a $1 billion pension fund. The entire fund is invested in fixed income securities, with a duration of 7.5. The pension fund manager needs to reduce the duration of the portfolio to The fund manager believes that an interest rate swap is the best way to achieve the duration reduction. A one-year semi-annual swap using LIBOR as the reference rate has a duration of Allen Resources, Inc

5 Study Session 15 Target Duration Portfolio NP = MVPortfolio SwapDuration NP =$1,000,000, NP =$1,000,000, NP = $500,000,000 Duration Since the pension fund manager wants to reduce the duration of the portfolio, she will need to enter into the one-year semi-annual swap as the pay-fixed party. Interest rates are inversely related to the value of the bond portfolio. Thus, in order to lower the duration of the portfolio, we need to enter into a position that will move directly with interest rates, or in other words, receive floating-rate payments. Thus, to increase the duration of a portfolio: pay floating; and to decrease the duration of a portfolio, pay fixed. Managing Structured Risk To manage the risk of structured notes such as a leveraged floater (leveraged floating rate note), a firm (below, WMG) will issue a structured note that pays a multiple, L, (hence the term leverage) of a specified floating rate. The proceeds from the sale of the note are used to finance a fixed-rate bond (below, from ABC Corp). WMG will then swap the fixed coupon payment it receive on the ABC bond to cover the floating payment owed (to PensionCo) on the structured note by entering into a separate swap agreement with Swapco, a swap dealer (the firm will payfixed and receive floating). When all of the transactions are complete, WMG will earn a small profit on the difference between the coupon received from the ABC bond and the fixed rate paid to SwapCo, the swap dealer. L Floating Principal L Fixed Principal PensionCo WMG SwapCo L Floating Payment Principal L Coupon Payment Principal ABC Corp Study Guide for the Level III 2015 CFA Exam - Reading Highlights

6 Risk Management: Swaps Thus, WMG: Pays: L Fixed Principal L Floating Principal Receives: L Floating Principal L Coupon Principal Therefore: Net profit = L (Coupon Fixed ) Principal Example The World Markets Group (WMG) designs structured notes. It has identified an opportunity to create a leveraged floater, using a 5% per year fixed rate bond from ABC Corporation. WMG issues a floating rate note set at 1.75 times LIBOR and raises $100 million with which it purchases $175 million of ABC Corporation s bond with a coupon of 5.05% per year. WMG then enters into a $175 million swap with a swap dealer (Swap Co) to pay-fixed at 5% per year and receive floating LIBOR. The net cash flow to WMG is: Net cash flow = L Principal (Coupon Fixed ) Net cash flow = 1.75 $100,000,000 ( ) Net cash flow = $87, net positive cash flow to WMG While this may seem a risk-free gain since WMG does not outlay any capital, in fact, this gain represents both credit risk of the ABC Corporation bond and counterparty risk of the swap dealer defaulting. Another type of structured note is the inverse floater. An inverse floater is structured to profit from a fall in a specified floating rate, such as LIBOR, below a pre-specified reference rate. Example WMG structures and issues an inverse floater, set at RR (Reference ) - LIBOR on a notional principal (Principal ) of $100 million. WMG uses the proceeds of the sale of the structured note to Pension Co. to purchase $100 million (Principal ) of ABC Corporation bonds with a coupon (Coupon ). WMG then swaps $100 million (Principal ) as the floating rate payer (Floating ) to receive fixed (Fixed ) Allen Resources, Inc

7 Study Session 15 Here is how the swap appears: Floating Principal RR-Floating Principal Pension Co. WMG Swap Co. Fixed Principal Coupon Principal ABC Corp. Thus, WMG: Pays: Receives: Net profit: (RR - Floating Floating Principal ) Principal Coupon Principal Fixed Principal (Fixed + Coupon RR) Principal Since it is possible that the floating rate may rise above the reference rate, Pension Co. may want WMG to guarantee that it will not have to pay interest to WMG in the event that this occurs. Thus, WMG will purchase an interest rate cap on the swap. The cap will be set with an exercise (strike) rate equal to the reference rate and have a value equal to the principal note. The underlying rate would be the same as that used to determine the floating rate (e.g., LIBOR) and the caplets will have expiration dates that match the dates of the payments. Managing Currency Risk Learning Objective: Describe how a firm can reduce its overall financing costs by issuing debt in its home currency and then using a currency swap to make payments in another currency. A firm that would like to borrow funds in a foreign currency could choose to do so directly by issuing debt in the foreign country or indirectly by issuing the debt domestically and using a currency swap to swap the proceeds of the loan from domestic currency to foreign currency Study Guide for the Level III 2015 CFA Exam - Reading Highlights

8 Risk Management: Swaps If the firm is not well known in the foreign country, it will more than likely receive a less favorable rate than it would domestically. Thus, a firm will choose to borrow domestically and swap currencies, since it can achieve its goal of obtaining the required foreign capital less expensively. For example, ABC Corp. needs to raise 100 million in foreign currency to finance its expansion plans. ABC can issue 100 million in foreign currency denominated debt at 7.5% per year fixed, or it can issue 75 million of domestic currency denominated debt (the current spot exchange rate is Domestic/Foreign) at 6.75% per year fixed and swap the domestic currency for foreign currency. ABC decides to issue the debt domestically at 6.75% per year and enters into a currency swap with Swap Co. swapping the 75 million in domestic currency that it issued for 100 million of foreign. ABC Corp. will then pay-fixed foreign currency at 7.25% per year and receive-fixed domestic currency at 6.70% per year (: ABC could have also chosen to payfixed and receive floating as well.) Therefore ABC Corp. will: Pay-fixed foreign of: Receive-fixed domestic of: And pay-fixed domestic on the bond issue of: $100,000, % $75,000, % $75,000, % The net result is that ABC Corp will make foreign currency interest rate payments, as well as a small domestic interest payment of 6.75% 6.70% = 0.05%, thus effectively converting the loan from one currency to another. After entering into this swap, ABC Corp. may decide that foreign interest rates are going to fall and wish to capitalize (speculate) on this expectation by entering into another offsetting interest rate swap to convert its current foreign fixed payments into foreign floating payments. Of course, had ABC Corp. issued the original debt at a floating rate, it could have entered into an interest rate swap to pay-fixed, and received floating if it felt that interest rates were going to rise. Learning Objective: Illustrate the use of a currency swap to convert foreign currency denominated cash flows into domestic denominated currency cash flows without an exchange of notional principal. A firm may have a need to convert future cash inflows (such as foreign accounts receivable) from a foreign currency to domestic, or future cash outflows (such as foreign accounts payables) to a foreign currency from the domestic Allen Resources, Inc

9 Study Session 15 For example, NUGRO Inc., a U.S. company, receives 10 million CAD, quarterly, for sales of specialty chemicals generated by their Canadian subsidiary Chem Co. NUGRO would like to enter into a swap to pay-fixed 6% per year Canadian and receive-fixed 6.25% per year U.S. currency at each of these four dates. The current spot rate is 0.75 USD/CAD. First, we will need to calculate the notional principal of the swap for both currencies: NP NP NP NP CAD CAD CAD CAD = Quarterly payment/(interest rate/number of payments per year) = $10,000,000/(0.06/4) = $10,000,000/0.015 = $666,666,666 CAD NP NP NP USD CAD Spot USD USD = NP Exchange rate = $666,666,666 CAD 0.75 USD/CAD = $500,000,000 USD The notional principal is calculated to determine the interest payments that are to be made on the swap. No actual exchange of principal occurs in this type of swap. Next, we shall calculate the quarterly payments that NUGRO will pay and receive: NUGRO will pay 10 million CAD and receive: Receive fixed = NP /4 USD Receive fixed = 7,812,500 USD Thus, NUGRO Inc. will convert each quarterly payment into U.S. dollars at a locked-in exchange rate without exchanging notional principal with the swap dealer. In addition to credit risk that the counter party (swap dealer) will default, NUGRO also faces the risk that the sales it expects to generate from its Canadian subsidiary, Chem Co., may not meet the required $7,812,500 payment obligation each quarter. Synthetic and Direct Creation of a Dual Currency Bond Firms can issue bonds that pay interest in one currency and principal in another. This is referred to as the direct creation of a dual currency bond. Swaps can be used to manage the exchange rate risk of such bonds by swapping the foreign payment owed by the firm. Thus, a firm will enter into a swap to pay foreign, either fixed or floating, (depending on whether the dual currency bond was issued as such) and receive domestic, either fixed or floating. A synthetic dual currency bond can be created by issuing a normal bond and then entering into a currency swap. The bond issuer receives the currency from its swap counterparty in which it is making the interest payments on the bond and pays the desired foreign currency to its swap counterparty Study Guide for the Level III 2015 CFA Exam - Reading Highlights

10 Risk Management: Swaps The notional principal of the swap will be based on the payment owed in the foreign currency. As before, the notional principal is only used to determine the periodic cash flows swapped; no exchange of principal actually occurs. Equity Swaps Learning Objective: Illustrate how to use equity swaps to diversify a concentrated portfolio, alter the asset allocation of a portfolio, and provide international diversification without the sale of existing securities within the portfolio. Swaps can also be used to diversify a concentrated portfolio, diversify a domestic portfolio, internationally, or change the asset allocation of a portfolio. Example John Klaus is the executive director for the Arts for Kids endowment fund. A recent patron of the arts donated $10 million of XYZ Inc. stock to the endowment fund. John would like to reduce the risk of the fund s exposure to such a large holding in the stock, but does not want to upset the donor by liquidating the stock all at once. John enters into a swap to pay the total return on the XYZ Inc. stock to receive the total return on the S&P 500 minus 10bps. Three months later, XYZ stock has risen by 1% and the S&P 500 has risen by 1.5%. John would therefore: Pay: $10,000,000 1% = $100,000 And receive: $10,000, % 0.10% = $140,000 Thus, the fund would receive a net cash inflow of $40,000. Equity Swaps Versus Other Swaps As we can see, one of the most significant differences between the cash flow payments of interest rate and currency swaps with that of equity swaps is the possibility of large cash flow payments that may be required of either party. For example, if the S&P 500 had fallen 3% and XYZ stock had risen 10%, John s endowment fund would have been required to make a $10,000, % = $1,310,000 net payment to the swap dealer. Conversely, had the S&P 500 risen by 5% and XYZ stock fallen by 15%, then the swap dealer would have been required to make a $10,000, % = $1,990,000 payment to the endowment fund. In addition to the possibility of a significant negative cash flow payment, equity swaps can also lead to large tracking errors when there is not a perfect correlation between the underlying index and the investment portfolio Allen Resources, Inc

11 Study Session 15 Example We will continue with our previous example of the Arts for Kids endowment fund, and assume that John has the authority to invest in foreign securities. Realizing the diversification benefits of adding international investments to the portfolio, John decides to exchange 10% of the endowment s domestic holdings for exposure to international securities. The endowment fund s domestic portfolio has a high correlation to the return of the S&P 500. Rather than selling out the position in the cash market, John can swap the total return of the S&P 500 for the total return of an international index, such as the MSCI EAFE. Three months later, the S&P 500 has risen 1%, the MSCI EAFE has risen 1%, but the endowment fund s underlying portfolio has only risen 0.5%. As we can see, the endowment fund is not perfectly correlated to the S&P 500, and thus the portfolio did not generate enough of a return to match the cash flow payment required. Equity swaps can also be used to alter the asset allocation of an investment portfolio. As we have already shown, the process is quite simple. All that we need to do is swap the return of one index for the return of another, such that we achieve the desired percentage allocation. In addition to changing the equity allocation, we can also change the allocation between stocks and bonds, as follows: The $100 million Omega Balanced Fund has a current allocation of 40% bonds and 60% stocks. Of the 60% stocks, 25% are small cap and 75% are large cap. Of the bonds, 10% are Treasuries and 90% are corporates. The fund manager is expecting an overall market decline over the next year and would like to reposition the portfolio to a 50% bond to 50% equity allocation. Furthermore, she would like to change the allocation of small to large cap stocks to 20% and 80%, respectively, and she would like to reduce the corporate bond exposure to 70% and boost the Treasuries to 30%. The manager of the fund will use 1-year swaps to facilitate the transactions, as follows: Stocks: Current exposure of small cap is $100,000,000 60% 25% = $15,000,000 Desired exposure of small cap is $100,000,000 50% 20% = $10,000,000 Thus, enter swap to pay return on $5,000,000 small cap index and receive LIBOR on $5,000,000. Current exposure of large cap is $100,000,000 60% 75% = $45,000,000 Desired exposure of large cap is $100,000,000 50% 80% = $40,000,000 Thus, enter swap to pay return on $5,000,000 large cap index and receive LIBOR on $5,000,000. Bonds: Current exposure of Treasuries is $100,000,000 40% 10% = $4,000,000 Desired exposure of Treasuries is $100,000,000 50% 30% = $15,000, Study Guide for the Level III 2015 CFA Exam - Reading Highlights

12 Risk Management: Swaps Thus, enter swap to receive return on $11,000,000 Treasury bond index and pay LIBOR on $11,000,000. Current exposure of Corporate is $100,000,000 40% 90% = $36,000,000 Desired exposure of Corporate is $100,000,000 50% 70% = $35,000,000 Thus, enter swap to pay return on $1,000,000 corporate bond index and receive LIBOR on $1,000,000. Notice that the sum of all of the LIBOR cash flows nets to zero (pay $11,000,000 and receive $5,000,000 + $5,000,000 + $1,000,000 = $0); thus, all that we are left with is the shift in the various asset and sector allocations. Once again, our swap positions have the same problems as before since we are exposed to the possibility of large negative cash flows (for which we may need to liquidate a portion of the portfolio to meet), and tracking error between the indexes used in the swaps and the actual underlying portfolios. The Use of Swaps by Corporate Insiders In addition to adding diversification to a portfolio, swaps can also be used to diversify the risk of a corporate insider s overexposure to his own company s stock. Example Janet Blake, the CFO of Euro Tour Inc., owns 10% of the company s outstanding stock. Currently, this single holding represents 90% of her wealth, and she is concerned about having such a large portion of her assets in a single investment. She decides to enter into a swap to exchange the return on 75% of her outstanding shares for the return of the S&P 500. Thus, similar to the equity swap we illustrated earlier, Janet will receive the total return of the S&P 500, in exchange for paying the total return on Euro Tour Inc. stock to the swap dealer. However, since Janet is a corporate insider, there are several implications that she needs to consider when entering into this type of swap transaction. She must consider the following: Cash Flow Crunch Janet is responsible for paying the total return of the stock to the counter party. Should the total return of the stock be greater than the total return from the S&P 500, Janet will be required to pay this additional amount. Increased Agency Costs One of the main concerns for shareholders is the fact that Janet still retains the voting power of the shares, but no longer has a strong incentive to act in the best interests of the other shareholders of the firm, since she has substantially reduced her exposure to the stock. Her interests are not as dependent on the firm s fortunes, and therefore she may act to benefit herself, rather than the firm Allen Resources, Inc

13 Study Session 15 Negative Signals In addition, investors may see her actions as a negative indication about the future potential of the stock. Regulatory and Tax Consequences Along with the concerns of shareholders and investors, Janet must also keep in mind that the swap transaction falls under insider trading regulations, and therefore she must provide adequate disclosure. Finally, the swap constitutes an effective sale of the security and, as such, will not provide a tax advantage to her. Swaptions Learning Objective: Illustrate the use of interest rate swaptions to alter the payments of future loans and close out swap positions. Companies that are looking to borrow funds at a future date can use swaps to lock-in the rates today against any possible future rise in rates. However, the swap will also exclude them from taking advantage of lower interest rates, should rates fall. A swaption gives the holder the right, but not the obligation, to enter into a swap at a later date. By using a swaption, a company can choose to exercise its right to enter into a swap, depending upon the interest rates at that time. If rates are not favorable, the swaption is exercised, and the company enters into the swap. If rates are favorable, the swaption is allowed to expire, and the advantageous current rates are used. Example Ajax Inc. is anticipating the need for $15 million to finance a prospective plant that it will build in six months time. Ajax would like to borrow the funds for three years at a fixed rate, but will finance the project at LIBOR, which is currently at 6% per year. Ajax decides to use a swaption that will protect it against a rise in interest rates but still enable it to take advantage of falling rates, should they occur. The cost of the swaption is $100,000 and it allows Ajax to enter into a fixed rate swap at 6.1% per year in six months time to receive floating at LIBOR. We will assume that LIBOR at the time of the swap is 5% per year. Thus, Ajax pays $100,000 today for the swaption. Six months later the swaption is out-of-themoney and Ajax allows it to expire and borrows at LIBOR of 5% per year. Ajax then enters into a swap to pay-fixed 5.1% per year and receive-floating of 5% per year. Thus, Ajax pays less than the 6.1% per year fixed specified in the swaption Study Guide for the Level III 2015 CFA Exam - Reading Highlights

14 Risk Management: Swaps What if instead of 5% per year, LIBOR was at 6.5%? Then Ajax would enter into a loan at 6.5% per year floating and exercise the swaption, effectively paying 6.1% fixed on the swap and receiving 6.5% floating. It would have to pay 6.5% per year on the loan however. Thus, it will have a net obligation of 6.1%, effectively locking in the rate of the exercise price of the swaption. In addition to using a swaption to initiate a swap, should rates not be favorable when funds are required, a swaption can also be used to terminate an existing swap. For example, in our second scenario, the swaption was exercised and the swap initiated. One year later, Ajax feels that interest rates may start to fall in the future and decides to purchase a swaption that is exercisable at anytime (American style) that can be used to terminate the existing swap. The terms of the swaption will therefore specify an underlying swap with the exact opposite terms to the current swap it holds. In other words, Ajax will be the floating payer (at LIBOR) and will receive a fixed rate of 6.1%. Converting Callable Debt to Non-Callable Debt The callable feature of a bond is simply an option that an issuer has to call away (cancel or payout) the bond if interest rates should fall. If the issuer of the callable bond no longer desires the callable feature, it can sell the call option on the bond by selling a receiver swaption. Thus, the issuer of the bond can recapture a portion of the higher coupon rate it pays on the bond by synthetically removing the call feature through the sale of a receiver swaption. For example, Ajax has a $10 million callable bond currently outstanding for which it pays a 7% per year coupon. Ajax feels that interest rates are not likely to fall over the remaining two years of the bond s life and decides to recapture the value of the call option. Thus, Ajax sells the call option on the bond by issuing a receiver swaption for $250,000. The payment Ajax receives from the sale of the swaption effectively reduces the 7% per year coupon. Alternatively, an issuer that has a non-callable bond outstanding, for which it would like to have the right to call the bond and reissue the bond (should rates fall), can purchase a receiver swaption to synthetically add the desired call feature to the bond. Thus, if interest rates were to fall, the issuer could exercise the swaption and enter into a swap to pay floating and receive-fixed. Similar to our previous example, if we assume that the bond in question is now non-callable, the purchase of a swaption for $250,000 would effectively increase the 7% per year coupon rate of the non-callable bond Allen Resources, Inc. All rights reserved. Warning: Copyright violations will be prosecuted. Any use of these materials without the express written consent of the publisher is a violation of federal and/or international copyright laws Allen Resources, Inc