Swaps Fundamentals PDF

Swaps Fundamentals Corporate Finance Institute® Course Objectives Overview of Swaps Interest Rate Swaps Currency Swaps Equity Swaps Commodity Swaps Basis Swaps Swaptions Variance Swaps Credit Default Swaps Corporate Finance Institute® What is a Swap A swap contract is a derivative in which two count...

Swaps Fundamentals Corporate Finance Institute® Course Objectives Overview of Swaps Interest Rate Swaps Currency Swaps Equity Swaps Commodity Swaps Basis Swaps Swaptions Variance Swaps Credit Default Swaps Corporate Finance Institute® What is a Swap A swap contract is a derivative in which two counterparties exchange cash flows (known as “legs”) of equal expected values at periodic intervals. Often one leg is a fixed payment, while the other is a floating payment. The sums exchanged can be different in: Amounts (e.g. one fixed & the other variable) Currencies (e.g. USD vs. EUR) Corporate Finance Institute® Fixed Financial Receiver The two payments are the legs or sides of the swap. Fixed Floating (a market price based on the type of the swap) Instrument Payer Floating The swap terms specify the duration and frequency of payments. Swap Basics Most swaps are tailor-made contracts. 1. Swap trade in an OTC-type environment between financial institutions or market makers. 2. One of the parties is a swap dealer (swap bank) and is usually a large bank. 3. The bank offsets a swap through an inter-dealer broker after it executes the swap. 4. NPV of both payment streams must be the same. 5. Maturity is generally 1 – 5 years. 6. Swaps are usually used for hedging, speculating, or managing risk. Corporate Finance Institute® Types of Swaps Interest Rate Swaps Currency Swaps Equity Swaps Fixed Amount Fixed Currency A LIBOR + Spread Floating Amount Fixed Currency B Return on Equity (LIBOR) Basis Swaps Commodity Swaps Index Rate 1 Fixed Amount Index Rate 2 Return of a Commodity E.g. Cross Currency Basis Swaps Corporate Finance Institute® Interest Rate Swaps Corporate Finance Institute® Interest Rate Swaps – Structure An interest rate swap is the exchange of fixed interest payments for floating rate payments between two parties. Usually, one of the parties is a swap dealer (swap bank). Interest Rate ↓ Fixed Rate Interest Rate ↑ Net Payment Received +$ Swap Rate Net Payment Received +$ Fixed Receiver Fixed Payer Pay Floating Floating Rate Pay Fixed Receive Fixed LIBOR + Spread Receive Floating Interest payments are netted, and the party that owes more in interest at a settlement date makes a payment equal to the difference to the other party. Net Fixed Rate Payment Made (Received) by Fixed Payer = [Swap Fixed Rate – (Floating Rate)] x (# Days / 360) x Notional Principal Corporate Finance Institute® Interest Rate Swaps – Key Features Term Notional Amount Payment Frequency Floating Rate Fixed Rate Payer / Receiver Corporate Finance Institute® Normally between 2 and 30 years The notional amount is not paid or received. It is used to calculate the cash flows. Payments are typically made either quarterly, semi-annually or annually. This is normally based on LIBOR. It is reset throughout the swap term thus each floating payment will be different. The fixed rate is set at the beginning of the swap. It is also known as the swap rate. In a payer swap you pay the fixed leg and receive the floating leg, and vice versa for a receiver swap. Long Swap vs. Short Swap Bond Equivalence of Swap: Receive Float (LIBOR) Long Float Bond Long Swap (Buyer) Pay Fixed Short Fixed Bond Value of Swap (Long) = V(Float) – V(Fixed) Receive Fixed Long Fixed Bond Short Swap (Seller) Short Float Bond Pay Float (LIBOR) Value of Swap (Short) = V(Fixed) – V(Float) Corporate Finance Institute® The Underlying Motive of Interest Rate Swaps It is important to understand the relationship between interest rates and the pricing of bonds. In an interest rate swap, one party wants greater certainty for their cash flow, while the other looks for potentially larger returns. Interest rate swaps can be used to increase or reduce the interest rate exposure. A portfolio manager that is making investment decisions for a bond fund will often have a view on the future direction of interest rates. Interest Rate Swaps: Corporate Finance Institute® Pay fixed Receive floating When rate increases, the profit made on the swap offsets the losses on the fund. The Underlying Motive of Interest Rate Swaps It is important to understand the relationship between interest rates and the pricing of bonds. In an interest rate swap, one party wants greater certainty for their cash flow, while the other looks for potentially larger returns. Interest rate swaps can be used to increase or reduce the interest rate exposure. A portfolio manager that is making investment decisions for a bond fund will often have a view on the future direction of interest rates. Interest Rate Swaps: Corporate Finance Institute® Receive fixed Pay floating When rate decreases, the profit made on the swap adds to the performance of the fund. Why Use Interest Rate Swaps 1. Speculative Trading Requires little capital upfront Speculates on movements of interest rates while avoiding the cost of long and short positions Corporate Finance Institute® 2. Entering New Markets Arbitrage opportunities 3. Managing Risk Firms with floating rate liabilities can use IRS Hedge against interest rates Change the profile of cash flows Lower debt costs Interest Rate Swaps – Risks Counterparty risk is usually relatively low when both parties are large companies or financial institutions. Corporate Finance Institute® The unpredictable nature of floating interest rates also increases the inherent risk. Example – Swap in Action Notional Amount = $100,000 Fixed Rate = X% Company A Motivation: Company B Floating Rate = LIBOR + Y% Motivation: Interest rates will go up Interest rates will go down Potential profit from floating rate return Risk protection against possible declining rates Interest payment term = annual Corporate Finance Institute® Example – Swap in Action – Initiation Value of Swap = $0 Fixed Rate = 4% Company A Receives 4% Company B Floating Rate = 3% + 1% = 4% LIBOR = 3% Corporate Finance Institute® Receives 4% Example – Swap in Action – After 1 Year Scenario 1: Interest rate goes up LIBOR = 4% ↑ Fixed Rate = 4% x $100,000 = $4,000 Company A Company B Floating Rate = 4% + 1% = 5% x $100,000 = $5,000 Profit = $1,000 Net Payment = $1,000 Corporate Finance Institute® Example – Swap in Action – After 1 Year Scenario 2: Interest rate goes down LIBOR = 2.5% ↓ Fixed Rate = 4% x $100,000 = $4,000 Company A Company B Floating Rate = 2.5% + 1% = 3.5% x $100,000 = $3,500 Profit = $500 Net Payment = $500 Corporate Finance Institute® Considerations of Pricing and Valuing Interest Rate Swaps Corporate Finance Institute® Quotation: Swap Rate and Swap Spread Swap rate is the fixed interest rate that the receiver demands in exchange for the uncertainty of having to pay the short-term LIBOR (floating) rate over time. Value (Float) = Value (Fixed) Swap spread is the difference between a swap rate and the rate of an on-the-run treasury with the same maturity as the swap. It is the additional amount an investor would earn on a swap as compared to a riskfree fixed rate investment. Swap Spread = Swap Rate – Yield on Government Bond Corporate Finance Institute® Quotation: Swap Rate and Swap Spread Large positive swap spreads generally indicate that a great number of market participants are willing to swap their risk exposures. Corporate Finance Institute® Swap spreads are used to measure credit risk and liquidity, and as an indicator of a country’s credit conditions. During the 2008 Financial Crisis, swap rates declined to the level of on-the-run treasuries (the swap spread was negative for the 30-yr maturity). Swap Curve A swap curve describes the implied yield curve based on the floating rates associated with an interest rate swap. Fixed income traders use the swap curve as a benchmark to determine the swap spread. In the valuation of IRS, one could derive a zero rates curve and forward rates using techniques such as the Bootstrapping process or spline model. U.S. Treasury Curve U.S. Interest Rate Swap Curve 1.60% Real Expected Returns It shows investors the possible return that can be gained for a swap on different maturity dates. U.S. Swap and Treasury Curves 1.40% 1.20% 1.00% 0.80% 0.60% 0.40% 0.20% 0.00% 1Y 2Y 3Y 5Y 7Y 10Y Maturity Source: https://www.barchart.com/economy/interest-rates, as of 18 June 2020 Corporate Finance Institute® 30Y Cash Flow Schedule / Calculating Payments Corporate Finance Institute® Calculating Swap Payments With The Same Frequency Fixed Leg Swap Maturity 2 years Fixed Leg 4%, Semi-annual Floating Leg Notional Day Count 2 100 $100MM 1.8 3.6% 6 Months 3.8% 12 Months 4.2% 18 Months 4.6% The payments are netted so only a single payment is made. 2 2 100 1.9 2.1 2.3 100 Floating Leg 30/360 Now 2 Time 6-month LIBOR 6-month LIBOR Corporate Finance Institute® 100 Time Fixed Leg ($MM) Floating Leg ($MM) Net ($MM) Now 100 100 - 6 Months 2.0 1.8 0.2 12 Months 2.0 1.9 0.1 18 Months 2.0 2.1 (0.1) 24 Months 2.0 2.3 (0.3) 24 Months 100 100 - Calculating Swap Payments With Two Different Frequencies Fixed Coupon Bond Floating Rate Note Corporate Finance Institute® Calculating Swap Payments With Two Different Frequencies Calculating the fixed cash flows: Fixed Cash Flow = Rate% x 30 / 360 Days x Notional Amount 360 Example 180 x $10,000,000 Fixed Cash Flow = 1.9903% x 360 = $99,515 Notional Rate Days in Period Corporate Finance Institute® $10MM 1.9903% 180 Calculating Swap Payments With Two Different Frequencies Calculating the floating cash flows: Floating Cash Flow = Rate% x Actual Days in Period x Notional Amount 360 Example 92 x $10,000,000 Floating Cash Flow = 1.18094% x 360 = $30,180 Notional Rate 1.18094% Start Date 05/15/2017 End of First Quarter 08/15/2017 Days in Period Corporate Finance Institute® $10MM 92 Pricing vs. Valuation of Swaps Timeline of a Swap Contract Time = 0 Time = T+1 At Initiation Price: Swap Fixed Rate Level at which PV(Floating) = PV(Fixed) Value of Swap: 0 The value of swap will fluctuate as the structure of interest rates changes. Interest rates ↑ : PV(Floating) > PV(Fixed) Interest rates ↓ : PV(Floating) < PV(Fixed) Corporate Finance Institute® Pricing an Interest Rate Swap Corporate Finance Institute® Example – Calculating Swap Rate ABC Ltd. has entered into a fixed-floating swap: Type Calculate present value factors – B0(360), B0(720), B0(1080), B0(1440): Fixed For Floating Tenor 4 years Settlement Annual Notional Principal $10MM 01 B0 Days = 1 1 + (L0 Days x Days ) 360 LIBOR Rates L0(360) 02 1 Year 3% 2 Year 4% 3 Year 5% Calculate fixed rate on swap: 4 Year 6% 1 − BLast Σ Present Value Factors Corporate Finance Institute® Example – Calculating Swap Rate Present Value Factors Tenor LIBOR Rate 1 Year 3% 1 / [1 + 3% x (360 / 360)] B0(360) = 0.971 2 Year 4% 1 / [1 + 4% x (720 / 360)] B0(720) = 0.926 3 Year 5% 1 / [1 + 5% x (1080 / 360)] B0(1080) = 0.869 4 Year 6% 1 / [1 + 6% x (1440 / 360)] B0(1440) = 0.806 Σ Present Value Factors = 3.572 Swap Rate = Corporate Finance Institute® 1 − BLast 1 − 0.806 = = 5.43% 3.572 Σ Present Value Factors Valuing an Interest Rate Swap Corporate Finance Institute® Valuing a Swap – Method 1 Method 2: Method 1: Offsetting Approach Discount Remaining Fixed Cash Flows Determine the present value of the remaining fixed interest rate payments Compare this to the present value of the floating rate side of the original swap Corporate Finance Institute® Offset the floating cash flows by creating an offsetting swap with a new swap rate calculated based on current time Calculate the present value of remaining net cash flows Valuing a Swap – Method 1 Example Example: Time: Three years left Fixed Rate: 5% annual Floating: 12-month LIBOR Notional Amount: $100 Current Swap Rate: 4% Corporate Finance Institute® Fixed Rate Bond Floating Rate Bond 100 100 Payments ($) 5 5 5 Periods 1 2 3 LIBOR Periods 1 2 3 Valuing a Swap – Method 1 Example Time Cash Flow Discount Factor at 4.00% Present Value 1 5 0.9615 $4.8075 2 5 0.9246 $4.6228 3 105 0.8890 $93.3450 Price $102.7753 Fixed Leg Valuation: Floating Leg Valuation: The fixed leg is valued as a normal fixed rate bond. The yield (discount rate) is the current swap rate of 4%. At each rate setting date, the value of the floating rate bond is $100. The floating rate note is worth $100 when the swap is originated. Value = $102.7753 Value = $100.00 Swap Value = $102.7753 – $100 = $2.7753 Corporate Finance Institute® Valuing a Swap – Method 2 Method 1: Method 2: Discount Remaining Fixed Cash Flows Offsetting Approach Determine the present value of the remaining fixed interest rate payments Compare this to the present value of the floating rate side of the original swap Corporate Finance Institute® Offset the floating cash flows by creating an offsetting swap with a new swap rate calculated based on current time Calculate the present value of remaining net cash flows Valuing a Swap at T+1 – Method 2 Example Floating CFs to be received For remaining payments: Net CFs: + Inflow / - Outflow Original Swap Fixed CFs to be paid Fixed CFs to be received Offsetting Swap Using New Swap Rate Value = Sum PV of remaining Net CFs Floating CFs to be paid Corporate Finance Institute® Valuing a Swap at T+1 – Method 2 Example Example: Type Using the previous example of ABC Ltd. entering into a 4-year swap, assume that one year has passed and the company needs to calculate the new value of the swap as it considers closing out the swap. Trade Date First Settlement 1 Year Second Settlement Fixed For Floating Tenor 4 years Settlement Annual Notional Principal $10MM Third Settlement Last Settlement 1 Year 2 Year 3 Year Corporate Finance Institute® Valuing a Swap at T+1 – Method 2 Example Step 1: Recall that the fixed rate on the original swap is 5.43%. We’ll need the current market LIBOR rates for the relevant payments left. Tenor LIBOR Rate Discount Factors 1 Year 3.20% 0.9690 2 Year 4.02% 0.9242 3 Year 4.68% 0.8718 Σ Discount Factors = 2.765 Current Fixed Rate = Corporate Finance Institute® 1 − BLast 1 − 0.8718 = = 4.63% 2.765 Σ Discount Factors Valuing a Swap at T+1 – Method 2 Example Step 2: Taking the present value of these net cash flows as of time = 1 year at the current fixed rate of 4.63%. Remaining payments left Trade Date First Settlement Second Settlement Third Settlement 1 Year 2 Year Last Settlement 3 Year Original Swap (CFs to Be Paid) at 5.43% $543K $543K $543K Offsetting Swap (CFs to Be Received) at 4.63% $463K $463K $463K Net CFs ($80K) ($80K) ($80K) Discount Factor 0.9690 0.9242 0.8718 PV of Net CFs @ Current Fixed Rate of 4.63% $77,520 $73,937 $69,747 Sum of PV of Net CFs $221,200 Value of swap after one year Corporate Finance Institute® Valuing a Swap at T+1 – Method 2 Example Think of it intuitively: Periodic Swap Periodic Swap Fixed Rate at Fixed Rate at Time 0 t=1 Year Swap Value = Notional Amount x (PSFR0 – PSFR1) x Σ PV Factors of Remaining Coupon Payments = $10MM x (5.43% – 4.63%) x 2.765 = $221,200 Corporate Finance Institute® Discounting Methods: LIBOR vs. OIS An Overnight Indexed Swap (OIS) is a derivative contract in which the periodic floating rate is equal to the geometric average of an overnight rate over every day of the payment period. The index rate is typically the rate for overnight unsecured lending between banks (e.g. the federal fund rate for US dollars). LIBOR-OIS Spread = LIBOR – Overnight Indexed Swap Rate The LIBOR-OIS spread is an indicator of the risk and liquidity of money-market securities. The LIBOR-OIS spread has historically been around 10 basis points but during the financial crisis, the spread spiked to 364 bps indicating a severe credit crunch. The major reason for using OIS rather than LIBOR as a term structure for pricing interest rate swaps is that OIS discounting better reflects the counterparty credit risk in a collateralized interest rate swap. Corporate Finance Institute® Interest Rate Swaps Summary Key points: 1 An interest rate swap is a bilateral agreement to swap a fixed rate of interest for a floating rate of interest. 2 Interest rate swaps have a term, notional, payment frequency, and currency. 3 The fixed rate is set at the start of the swap. 4 Interest rate swaps are valued by decomposing them into positions in fixed and floating rate bonds. 5 At the inception of a swap, the swap has no value. 6 Swaps can be used by fund managers to increase or reduce the sensitivity of a fixed income portfolio to changes in rates. Corporate Finance Institute® Currency Swaps Corporate Finance Institute® Currency Swaps – Structure (3-Stage Process) Currency 2 $ Notional Initiation: Party A Cash Flows: Receives Currency 2 Float Pays Currency 1 Float Currency 1 $ Notional Party B Currency 2 Interest Party A Currency 1 Interest Party B Currency 2 $ Notional Expiration: Party A Corporate Finance Institute® Currency 1 $ Notional Party B Pays Currency 2 Float Receives Currency 1 Float Currency Swaps – Key Features Currency Swap Also called cross currency swaps (XCCY) Legs Denominated in different currencies Profile of Cash Flows Currency swaps change the profile of cash flows. Can be fixed-fixed, fixed-floating (circus swap), or floating-floating (cross currency basis swap) Exchanged at initiation and expiration in the predetermined currency Cash Flow Exchanges Notional Corporate Finance Institute® Why Use Currency Swaps 1. Hedging Risk Hedge risk in other currencies 2. Raising Capital in Other Currencies at a Cheaper Cost Lock in fixed exchange rates 3. Increasing Credit Exposures More than using interest rate swaps Corporate Finance Institute® Companies that are doing business in another country can access capital at a lower cost. 4. Overall Tool to Manage Risk for Portfolio Used by portfolio managers to hedge risk Example – Currency Swap in Action (Fixed-Fixed) Wants to build a manufacturing facility in India Wants to build a plant in the US $10MM USD 35MM INR at 11% Patel Enterprises Patel gets loan from Indian Bank 35MM INR Smith Ltd $10MM at 3% 8% Smith gets loan from US Bank 20% $10MM at 3% 35MM INR at 11% Indian Bank Corporate Finance Institute® US Bank Example – Currency Swap in Action (Fixed-Fixed) 35MM INR At initiation: Patel Enterprises On every settlement date: $10MM Smith Ltd (Assume annual payment) 3% x $10MM = $300K Patel Enterprises 11% x 35MM = 3.85MM INR Smith Ltd $0.3MM 3.85MM INR Indian Bank Corporate Finance Institute® US Bank Example – Currency Swap in Action (Fixed-Fixed) At expiration: Patel returns $10MM Patel Enterprises Smith returns 35MM INR Smith Ltd $10MM 35MM INR Indian Bank Corporate Finance Institute® US Bank Pricing a Currency Swap Corporate Finance Institute® Example – Calculating Currency Swap Rate and Payments Suppose a pension portfolio manager enters into a one-year currency swap with semi-annual settlements based on a $1MM notional principal and the equivalent amount of Euros (€). Currency Swap Tenor 1 year Settlements Semi-annual Notional Principal $1MM Current Exchange Rate (€/$) Term 1.25 LIBOR EURIBOR 180 3.2% 4.5% 360 4.6% 6.6% Corporate Finance Institute® Part 1: Calculate the swap fixed rate in both currencies Part 2: Calculate cash flows on a fixed-fixed currency swap Part 3: Calculate cash flows on a fixed-floating currency swap Part 4: Calculate the value of the currency swap after time has passed Part 1: Calculate Fixed Rate in USD and EURO Step 1: Calculate Present Value Factors Step 2: Calculate Semi-Annual Fixed Rate Step 3: Annualized Swap Fixed Rate Corporate Finance Institute® Fixed Rate in USD Fixed Rate in EUR B0(180) = 1/ [1 + 3.2% x (180/360)] = 0.9843 B0(180) = 1/ [1 + 4.5% x (180/360)] = 0.9780 B0(360) = 1/[1 + 4.6% x (360/360)] = 0.9560 B0(360) = 1/[1 + 6.6% x (360/360)] = 0.9381 1 − BLast Σ Present Value Factors = 1 − 0.9560 = 2.27% 0.9843 + 0.9560 2.27% x (360/180) = 4.54% 1 − BLast Σ Present Value Factors = 1 − 0.9381 = 3.23% 0.9780 + 0.9381 3.23% x (360/180) = 6.46% Part 2: Calculate Cash Flows on Fixed-Fixed Currency Swap Notional principal in EUR (€) = $1MM x At Initiation: €1 = €800,000 $1.25 $1MM A B €800K At the end of 6 months: 3.23% x €800K = €25,840 A B 2.27% x $1MM = $22,700 At expiration: €800K A B $1MM Corporate Finance Institute® Part 3: Calculate Cash Flows on Fixed-Floating Currency Swap Notional principal in EUR (€) = $1MM x At Initiation: €1 = €800,000 $1.25 $1MM A B €800K At the end of 6 months: 4.5% x (180/360) x €800K = €18,000 A B 2.27% x $1MM = $22,700 At expiration: €800K A B $1MM Corporate Finance Institute® Part 4: Calculate Value for Fixed-Fixed Currency Swap Annual Fixed Rate in USD (FS$): 4.54% Annual Fixed Rate in EUR (FS€): 6.46% Exchange Rate ($/€): 1.21 First Settlement Initiation Last Settlement 180 – 60 = 120 days 2 Months 360 – 60 = 300 days 2 Months later: Corporate Finance Institute® Term LIBOR EURIBOR 120 3.0% 4.0% 300 4.2% 5.9% Part 4: Calculate Value for Fixed-Fixed Currency Swap Term LIBOR USD Discount Factors B60 EURIBOR EUR Discount Factors B60 120 3.0% 1/[1 + 3.2% x (120/360)] = 0.99 4.0% 1/[1 + 4% x (120/360)] = 0.987 300 4.2% 1/[1 + 4.2% x (300/360)] = 0.966 = B60(300)$ 5.9% 1/[1 + 5.9% x (300/360)] = 0.953 = B60(300)€ Σ Discount Factors = 1.956 1.940 Tip: Select the currency you want to value the swap in (USD$). Value of Currency Swap = Value of Fixed Leg ($) – Value of Fixed Leg (€) V$ = Notional$ x [FS$ x ΣB$ + B60(300)$] – ($/€) x Notional€ x [FS€ x ΣB€ + B60(300)€] = $1MM x (4.54%/2 x 1.956 + 0.966) – ($1.21/€) x €800K x (6.46%/2 x 1.94 + 0.953) = $1,010,401 – $983,161 = $27,240 Corporate Finance Institute® Part 4: Calculate Value for Fixed-Fixed Currency Swap Check your answer intuitively… USD EUR Term Cash Flow PV Cash Flow PV 180 $22,700 $22,473 €25,840 €25,504 360 $1,022,700 $987,928 €825,840 €787,025 $1,010,401 V$ = $1,010,401 – $983,161 = $27,240 Corporate Finance Institute® €815,529 x 1.21 = $983,161 Currency Swaps Summary Key points: 1 Notional get exchanged at the beginning and expiration of the swap. 2 Valuations have to take into account fluctuations in the exchange rate. 3 Coupon payments are not netted. 4 Currency swaps can be used to increase capital in another currency and reduce borrowing costs. 5 You can have variations of currency swaps: Fixed-fixed: Patel-Smith example Fixed-floating (circus swap): e.g. TESLA pays LIBOR in USD and receives 6% in INR Floating-floating (cross currency basis swap): e.g. TESLA pays LIBOR in USD and receives LIBOR in EUR) Corporate Finance Institute® Total Return Swaps (Equity Swaps) Corporate Finance Institute® Total Return Swaps A total return swap (TRS) is a bilateral financial transaction where the counterparties swap the total return of a single asset (or basket of assets) in exchange for periodic cashflows. The cash flows are typically a floating rate such as LIBOR +/- a basis point spread and a guarantee against any capital losses. Payer of Total Return Receiver of Total Return Total Return on Underlying Asset LIBOR + Spread When the underlying asset is an equity or an equity index, it is known as an equity swap. Corporate Finance Institute® Equity Swaps – Structure An equity swap contract is a derivative contract between two parties that involves the exchange of one stream (leg) of equity-based cash flows linked to the performance of a stock or an equity index, with another stream (leg) of fixed-income cash flows. Swap Fixed Rate 1 Equity Amount Payer Return on Equity (Index / Stock) Floating/Fixed Payer Floating Rate 2 Equity Amount Payer Floating/Fixed Payer Return on Equity 3 Corporate Finance Institute® Return on Equity Equity Amount Payer Return on Equity Floating/Fixed Payer Long Equity Swap vs. Short Equity Swap Bond Equivalence of Swap: Long Swap Receives returns on equity Pays fixed on swap Receive Returns on Stock Long Stock Pay Fixed / Floating Short Fixed Bond (or FRN) Value of Swap (Long) = V(Return on Stock) – V(Fixed) Short Swap Receives fixed Pays returns on equity Receive Fixed / Floating Short Stock Pay Returns on Stock Value of Swap (Short) = V(Fix) – V(Return on Stock) Corporate Finance Institute® Long Fixed Bond (or FRN) Equity Swaps – Key Features Equity swaps are different from other swaps such that: Payer One side of the equity swap can make payments for both sides. Payment is not known until the end of the settlement period. E.g. if the return on equity/index is negative, the pay fixed side has a payment equivalent to the negative return on the equity/index. Notional Equity swaps do not imply the exchange of principal amounts. Cash Flow Exchanges Occurs on fixed dates Payment Corporate Finance Institute® Who and Why Use Equity Swaps 1. Exposure to Stocks or Equity Index Exposure to equity without owning it 5. Synthetic Prime Brokerage Substitute for borrowing stock or equity finance Corporate Finance Institute® 2. Avoiding Transaction Costs Valuable for strategy that involves a high volume of transactions 6. Reporting Do not need to report on balance sheet 3. Hedging Instrument Forego short-term negative returns on equity without foregoing stock ownership 7. Financial Benefit Tax benefits 4. Accessing More Securities May allow investing in securities that are otherwise unavailable Equity Swaps – Risks Equity swaps are subject to three key risks: Counterparty Risk Expiration Dates Risk of default on payment obligation Do not create open-ended exposures to equities since swap contracts have termination and expiration dates Corporate Finance Institute® Market/Macro Economic Risk Inherent macro economic risk and interest rate risk Delta One Desks Delta One desks exist in many banks to provide the return of an index without all the hassle of buying the underlying securities. Equity Swap (Underlying: Oil-based Stocks) X % * Notional Client Synthetically Long Equities Dividends and Capital Gains Delta One Bank X Synthetically Short Equities The Delta One desks will buy the underlying securities and/or various derivatives to gain the exposure required. Corporate Finance Institute® Pricing and Valuation of Equity Swaps Corporate Finance Institute® Equity Swaps – Bloomberg Example Based on GBP LIBOR FTSE100 Payment = LIBOR% x Notional $ Payment = % Movement on Index x Notional $ Corporate Finance Institute® 68 Equity Swap Example – Pay Floating, Receive Return on Equity Equity Total Return Swap: Suppose a buyer of a pay floating, receive return on equity swap is interested in the stock of SLC Incorporated. Swap Equity Leg Interest Leg Notional SLC Total Return 12-Month LIBOR + 400 bps $10MM SLC Inc. Stock Price at Initiation $10.00 Price at the End of First Period $9.90 Dividend $0.40 LIBOR 12-Month Rate at Initiation Corporate Finance Institute® 5% Equity Swap Example – Pay Floating, Receive Return on Equity Equity total return swap – At the end of first period cash flow: Equity Leg: Position = $10MM Notional / $10 = Dividend = 1MM x $0.40 = Capital Gain/(Loss) = 1MM x ($9.90 – $10) = 1MM Shares $400,000 ($100,000) $300,000 Interest Leg: [12-Month LIBOR (5%) + 400 Bps] x $10MM Notional = $900,000 Net Payment: The buyer (equity receiver) pays the seller (float receiver) = Corporate Finance Institute® $600,000 Pricing of Equity Swaps Pay a fixed rate and receive return on equity swap Calculate the fixed swap rate that will give the swap a zero value at inception Swap Fixed Rate = Corporate Finance Institute® 03 02 01 Pay a floating rate and receive return on equity swap 1 − BLast Σ Present Value Factors There is no fixed rate. The market value of swap at initiation equals zero. Pay a return on one equity and receive return on another equity swap There is no fixed rate. The market value of swap at initiation equals zero. Valuation of Equity Swaps 01 Pay Fixed & Receive Return on Equity Swap 02 Pay Floating & Receive Return on Equity Swap 03 Pay Return on Equity & Receive Return on Another Equity Swap Corporate Finance Institute® (1 + Return on Equity) x Notional – PV(Remaining Fixed Rate Payments) (1 + Return on Equity) x Notional – PV(Next Coupon Payment + Par Value) = Notional x Equity Pricet – Notional x [FS0 x Σ PV Factors + Bt (Days Left Till Last)] Equity Pricet 0 (1 + Return on Index 2) x Notional – (1 + Return on Index 1) x Notional Valuation of Equity Swaps Important to note that: Cash payments on the equity legs are based on the percentage return on the underlying equity instrument over each settlement period, not on the changes in price over each settlement period. Corporate Finance Institute® The past performance of underlying equity over previous settlement periods has no impact on the current value of equity swaps. The only thing that matters is how the underlying has performed since the last settlement date. Example: 1st settlement: $100 2nd settlement: $90 3rd settlement: $110 Valuing Pay Fixed for Return on Equity Swap – Example Notional: $5MM Tenor: 1-year swap with quarterly payments Receives: Return on S&P 500 Index Pays: Fixed rate At Initiation: S&P Index = 2700 Days 1 − B0(N) Swap Fixed Rate = Σ Present Value Factors LIBOR % B0 90 3.25% 0.9920 180 3.75% 0.9816 270 4.00% 0.9710 360 4.66% 0.9555 Total 3.9001 Corporate Finance Institute® = 1 − 0.9555 3.9001 = 1.141% (Quarterly Swap Rate) Annualized Swap Rate = 1.141% x (360/90) = 4.564% Valuing Pay Fixed for Return on Equity Swap – Example If two months (60 days) have passed, what is the value of the equity swap to the fixed rate payer? Trade Date First Settlement 60 Days Second Settlement 30 Days 120 Days Third Settlement Last Settlement 210 Days 300 Days Days LIBOR % B0 30 3.10% 0.9974 120 3.25% 0.9893 = Notional x [FS0 x ΣB + B60(300)] 210 3.60% 0.9794 = $5MM x (4.564%/4 x 3.9313 + 0.9652) 300 4.33% 0.9652 = $5,050,281 Total 3.9313 S&P Index = 3000 Corporate Finance Institute® Swap Value = PV of remaining fixed rate payments 60 days into term V60 (S&P 500) = $5MM x (3000/2700) = $5,555,555 V60 (Fixed Rate Payer) = $5,555,555 – $5,050,281 = $505,274 Valuing Return on One Equity, Pay on Another Equity Swap – Example Tenor: 1-year swap with quarterly payments Notional: $5MM Receives: Return on S&P 500 Index Pays: Return on NASDAQ If 100 days have passed, what is the value of the swap? At Initiation: At the End of 1st Settlement: 100 Days Passed: S&P Index 2700 S&P Index 2900 S&P Index 3000 NASDAQ 9732 NASDAQ 9600 NASDAQ 9700 S&P NASDAQ Swap Value at 100 Days = $5MM x (3000/2900) – $5MM x (9700/9600) = $5,172,413 – $5,052,083 = $120,330 Corporate Finance Institute® Equity Swaps Summary Key points: 1 Cash flows are based on a predetermined notional amounts. 2 Equity swaps are flexible and provide synthetic exposures to equities. 3 The payment on an equity swap is not known until the end of the settlement period. 4 One side of the equity swap can end up making payments for both sides. Corporate Finance Institute® Commodity Swaps Corporate Finance Institute® Commodity Swaps A commodity swap is a type of derivative contract that allows two parties to exchange cash flows which are dependent on the price of an underlying commodity. Commodity swaps are very important in many commodity-based industries, such as oil and livestock. Corporate Finance Institute® Commodity Swaps – Key Features Exchanges Notional Floating Leg Corporate Finance Institute® No commodities are exchanged during the ‘swap trade’. Cash is exchanged instead. The notional principal is never exchanged. Commodity swaps are similar to fixed-floating interest rate swaps, but the floating leg is based on the price of the underlying commodity instead of LIBOR or EURIBOR. Commodity Swaps – Key Features Two types of commodity swaps: Commodity for Interest Swaps Fixed-Floating Commodity Swaps Corporate Finance Institute® Similar to the interest rate fixedfloating swaps, except that both legs are commodity-based Used by commodity producers and consumers to lock in commodity prices Similar to equity swaps Total return on the commodity is exchanged for some money market rate (+ / - a spread) Commodity Swaps – Structure Fixed-Floating Commodity Swaps: Net cashflows are made Fixed Payment (Based on Commodity Price Today) Seller Pays floating Receives fixed Buyer Floating Payment (Based on Commodity Index) Pays fixed Receives floating Commodity for Interest Swaps: Fixed Payment (Based on Interest Rates) Seller Corporate Finance Institute® Pays floating Receives LIBOR (floating) Buyer Floating Payment (Return on Commodity) Pays LIBOR (floating) Receives $ floating Why Use Commodity Swaps 1. Hedging E.g. Airlines hedging fuel prices Hedge against fluctuations in the market price of the commodity or price spreads 4. Eliminating Basis Risk Eliminate basis risk arising from futures contracts A swap contract completes the market in the absence of futures. Corporate Finance Institute® 2. Locking in Prices for Commodities Secure a fixed commodity price for a later purchase 5. Speculation Generate profits by the difference between spot prices and the prices of derivative products 3. Expanded Market Cash settlement allows investors to expand their portfolio into commodities without having the infrastructure for delivery. Commodity Swaps – Risks Counterparty Risk Built-In Risk Tradeoff Unregulated market E.g. Banks that set up swap contracts have fees that are built into the price. Give up risk while giving up any upside Corporate Finance Institute® E.g. Hedging locks a low price in when prices are high, but it also locks in a high price when prices are low. Pricing and Valuation of Commodity Swaps Corporate Finance Institute® Considerations in Pricing Commodity Swaps Factors to consider in pricing a commodity swap: Cost of hedging Liquidity of the underlying commodity Seasonality and its effect on underlying commodity market The variability of the futures market In pricing a commodity swap, it is helpful to think of the swap as a strip of forward contracts, each priced at inception with zero market value (in a present value sense). Corporate Finance Institute® Valuation of Commodity Swaps Valuation of commodity swaps can be thought of as valuing a series of commodity forwards, each priced at inception with zero value. The fixed coupon payment is generally the weighted average of commodity forward prices. To calculate the value of a commodity swap: 01 02 03 04 Calculate each payment for the fixed leg Project prices for future payment dates and calculate payments for the floating leg For each payment date, calculate the discount factor using the appropriate interest rates Calculate each payment as quantity x price 05 06 07 Calculate the net payment (fixed payment – floating payment) Multiply net payment and discount factor to calculate PV for each payment Sum of the present value of all payments to get the mark to market of the trade Corporate Finance Institute® Example – Valuing a Commodity Swap (Fixed-Floating) Commodity Swap: Terms: 4 years Payment: Annual Volume: 3,000 barrels 01 Calculate Net Payments = Investment Bank side (Fixed Payment) – Oil Producer (Floating Payment) Corporate Finance Institute® $43/BBL Swap Price Oil Producer (Pays Floating) Investment Bank (Pays Fixed) NYMEX Crude Oil 02 Calculate PV of each net payment 03 Sum all PVs to calculate the swap value (MTM) Example – Valuing a Commodity Swap (Fixed-Floating) Fixed Payments = $43/BBL x 3,000 Barrels = $129,000 Fixed Payments by Bank $129K $129K $129K $129K Projected Future Prices of Crude Oil $42/BBL $43.90 $43.50 $44/BBL Float Payments by Oil Producer $126K $131.7K $130.5K $132K Net Payment ($2.7K) ($1.5K) ($3K) Discount Factors at 4% 0.962 0.925 0.889 0.855 PV of Each Payment $2,886 ($2,497) ($1,333) ($2,565) Σ Value (POV: Oil producer paying floating) = Corporate Finance Institute® $3K ($3,509) Commodity Swaps Summary Key points: 1 No notional gets exchanged. 2 Valuations are determined by forward prices of the commodity. 3 Coupon payments are netted. 4 It involves periodic delivery of the commodity, or its cash equivalent, for a fixed periodic payment. 5 There are two types of commodity swaps: Fixed-floating commodity swaps Commodity for interest swaps Corporate Finance Institute® Basis Swaps Corporate Finance Institute® What Are Basis Swaps Basis swaps involve floating-floating exchange of two different interest rates or indexes. Some popular basis swaps: One Index vs. Another Index Tenor Basis Swaps Cross Currency Basis Swaps (CCBS) Two Different Indexes Different Points on a Yield Curve Exposure to Currency Fluctuations 3-M USD T-Bill vs. 3-M USD LIBOR 1-M USD LIBOR vs. 3-M USD LIBOR 3-M USD LIBOR vs. 3-M EURIBOR Corporate Finance Institute® Basis Swaps – Key Features Floating Rate Floating rates should be different (e.g. 1-month EURIBOR vs. 3-month EURIBOR). Quotation Basis swap is quoted as a spread (basis points). Basis swap structured across currencies Used primarily for swapping liquidity as a firm may borrow in liquid currency and swap the loan into its less liquid domestic currency Floating payments could involve different reference rates, such as 3-month LIBOR, 1-month LIBOR, 6-month LIBOR, prime rate, etc. Indexes may have different payment frequencies. E.g. 1-M LIBOR for 3-M LIBOR swap where the 1-M LIBOR side makes monthly payments and the 3-M LIBOE side makes quarterly payments Cross Currency Basis Swap Reference Rate Payment Frequency Corporate Finance Institute® Why Use Basis Swaps 1. Eliminating Basis Risk E.g. A bank that lends at prime rate but finances using LIBOR. 4. Locking in Exchange Rates For cross currency basis swaps, one can lock in exchange rates for a set period of time. Corporate Finance Institute® 2. Limiting Interest Rate Risk A company could have different lending and borrowing rates. 5. Speculation 3. Hedging Divergence of Different Rates USD Tenor Basis Swap – 1-month vs. 3-month Corporate Finance Institute® Cross Currency Basis Swaps (CCBS) A cross currency basis swap exchanges the difference between the two floating rates in a currency swap called the basis swap spread, usually quoted against USD LIBOR flat rate. Basis Swap Spreads Reflect the dynamics of supply and demand Indicate demand for a certain currency over another Indicate the relative creditworthiness of banks in one currency dominion vs. the other Corporate Finance Institute® Fixing Date The fixing date for the two legs may differ depending on the convention for the relevant reference rates. In a typical EUR/USD basis swap, both EUR and USD legs are tied to the 3-month deposit rates. Notional Principal Differ slightly from other basis swaps Notional principals are exchanged in a standard CCBS using prevailing spot exchange rates. Cross Currency Basis Swaps Application Cross currency basis is a measure of dollar shortage in the market. The more negative the basis becomes, the more severe the shortage. In hedging foreign currency exposures: Yield of Foreign Investments + Cross Currency Basis Spread Dollar-funded Investors Negative basis can work in their favor Corporate Finance Institute® Opposite Party Foreign Investment Cross Currency Basis Swaps (CCBS): Interpretations EUR/USD Basis Swap (3-M EURIBOR vs. 3-M LIBOR) Term: 5 years Current Spread: -22 bps spread Quarterly Payments: 3-M LIBOR Flat x Actual Days / 360 (3-M EURIBOR – 22 bps) x Actual Days / 360 The CCBS spread is an indicator of funding conditions. Negative spread means that institutions are willing to receive fewer interest payments on funds lent in non-USD currencies. Corporate Finance Institute® Negative EUR/USD swap on surging USD demand due to uncertainty Mark-to-Market and Non-Mark-to-Market Cross currency basis swaps can be either: Non-Mark-to-Market CCBS Mark-to-Market CCBS Adjustments to the notional principal at the quarterly payment dates based on prevailing spot exchange rates Since exchange rate fluctuates, small amounts of money are transferred between the parties to compensate. Standard CCBS trade on a mark-tomarket basis. Corporate Finance Institute® No adjustments to the notional Cross Currency Basis Swap (Floating-Floating) – Structure EUR $ Notional Initiation: European Company Cash Flows: USD $ Notional Counterparty The basis spread partly reflects the difference in credit risks implied by the two reference rates. (EURIBOR + Cross Currency Basis Spread) on EUR Notional Receives EUR Float Pays USD Float European Company US LIBOR on USD Notional Pays EUR Float Receives USD Float Counterparty EUR $ Notional Expiration: European Company Corporate Finance Institute® USD $ Notional Counterparty Cross Currency Basis Swap Example Notional: 10,000,000 EUR EUR/USD Basis Spread: -22 bps (-0.22%) Tenor: 1 year Payments: Quarterly Initiation Q1 Q2 Q3 1.45 1.46 1.39 1.36 3-M EURIBOR 0.73% 0.71% 0.69% 0.75% 3-M LIBOR 0.44% 0.40% 0.39% 0.36% EUR/USD Spot Assume 90 days in each period Note: Use prevailing rates of EURIBOR and LIBOR to calculate cash flow payments Corporate Finance Institute® Q4/Maturity Cashflow Calculations For Non-Mark-to-Market EUR: Notional (€) Initiation: Basis Desk Investor USD: Notional (€) / S(0) Spot Exchange Rate at Initiation USD Leg: Notional (€) / S(0) x LIBOR (t – 1) x 90/360 Payments: Investor EUR Leg: Notional (€) x [EURIBOR (t – 1) +/– Basis Spread] x 90/360 Expiration: USD: Notional (€) / S(0) Investor EUR: Notional (€) Corporate Finance Institute® Basis Desk Basis Desk Cashflow Calculations For Non-Mark-to-Market Investor → Basis Desk Basis Desk → Investor 10,000,000 x 1.45 = $14,500,000 €10,000,000 Payment 1: 10MM x (0.73% – 0.22%) x 90/360 = €12,750 (10MM x 1.45) x 0.44% x 90/360 = $15,950 Payment 2: 10MM x (0.71% – 0.22%) x 90/360 = €12,522 (10MM x 1.45) x 0.40% x 90/360 = $14,500 Payment 3: 10MM x (0.69% – 0.22%) x 90/360 = €12,011 (10MM x 1.45) x 0.39% x 90/360 = $14,138 Payment 4: 10MM x (0.75% – 0.22%) x 90/360 = €13,250 (10MM x 1.45) x 0.36% x 90/360 = $13,050 Expiration: €10,000,000 10,000,000 x 1.45 = $14,500,000 Initiation: Corporate Finance Institute® Cashflow Calculations For Mark-to-Market EUR: Notional (€) Initiation: Investor USD: Notional (€) / S(0) USD Leg: Notional (€) / S(t – 1) x LIBOR (t – 1) x 90/360 + Adjustment: Notional (€) x [S(t) – S(t – 1)] Payments: Investor EUR Leg: Notional (€) x [EURIBOR (t – 1) +/– Basis Spread] x 90/360 Expiration: Spot Exchange Rate for Last Period Basis Desk USD: Notional (€) / S(t – 1) Investor EUR: Notional (€) Corporate Finance Institute® Basis Desk Basis Desk Cashflow Calculations For Mark-to-Market Investor → Basis Desk Basis Desk → Investor 10,000,000 x 1.45 = $14,500,000 €10,000,000 Payment 1: 10MM x (0.73% – 0.22%) x 90/360 = €12,750 (10MM x 1.45) x 0.44% x 90/360 = $15,950 Adjustment: (1.46 – 1.45) x 10MM = $100K Payment 2: 10MM x (0.71% – 0.22%) x 90/360 = €12,522 (10MM x 1.46) x 0.40% x 90/360 = $14,600 Adjustment: (1.39 – 1.46) x 10MM = ($700K) Payment 3: 10MM x (0.69% – 0.22%) x 90/360 = €12,011 (10MM x 1.39) x 0.39% x 90/360 = $13,553 Adjustment: (1.36 – 1.39) x 10MM = ($300K) Payment 4: 10MM x (0.75% – 0.22%) x 90/360 = €13,250 (10MM x 1.36) x 0.36% x 90/360 = $12,240 Expiration: €10,000,000 10,000,000 x 1.36 = $13,600,000 Initiation: Corporate Finance Institute® Pricing of Cross Currency Basis Swaps 1. FX Forward Rates and Projections of Floating Rates Calculate from the nominal swap curve in each currency Corporate Finance Institute® 2. Principals Exchanged Think of it as the exchange of two bonds One denominated in the home currency and paying the home currency’s floating rate The other denominated in the foreign currency, paying the foreign currency’s floating rate + the variable spread 3. Yield to Maturity Calculate yield to maturity on each bond by adjusting the internal rate of return (IRR) on the foreign bond by the foreign currency’s appreciation implied by the forward FX rate Basis Swaps Summary Key points: 1 Basis swaps are floating-floating swaps where these indexes are based on interest rates with different maturities, in different currencies, or prime rates. 2 Cross currency basis swaps can be either mark-to-market or non-mark-to-market. 3 Basis swaps limit interest rate risk since a company could have different lending and borrowing rates. Corporate Finance Institute® Swaptions Corporate Finance Institute® Swaptions Options Swaps Swaptions Combination of a regular swap and an option Corporate Finance Institute® Gives the holder the right (not the obligation) to enter a swap at the predetermined swap rate (exercise rate) Gives the buyer the right (not the obligation) to buy or sell an underlying asset or instrument at a specified exercise price on a specified date Only executed if the exercise price is more favorable than the spot price Swaptions – Key Features Notional Amount Exchanged if the swaption is exercised Fixed Rate Strike of the swaption Payment Frequency Can have different payment frequencies for the fixed rate Floating Leg E.g. Payment frequency of a 3-month LIBOR would be quarterly Settlement Physically or cash settled The difference between swaps and swaptions is that a swap contract is an actual agreement to trade the derivatives, while a swaption is a contract to purchase the right to enter into a swap contract during the indicated period. Corporate Finance Institute® Types of Swaptions Fixed Payment Payer Swaptions Owner Pays fixed Receives floating Receiver Swaptions Counterparty Floating Payment Pays floating Receives fixed Floating Payment Owner Straddle Swaptions Corporate Finance Institute® Counterparty Pays floating Receives fixed Combination of the payer and receiver swaptions The owner bets on a large move in the value of the underlying in either direction (purchases both a put and call option). If there is little movement, the owner of the swaption makes no profit. Fixed Payment Pays fixed Receives floating Why Use Swaptions 1. Hedging Macroeconomic Risks E.g. Interest rate risk 2. Hedging Fixed Income Portfolio Hedging the risks associated with financial securities such as bonds 3. Changing Payoff Profile Used by financial institutions Swaptions are primarily employed by large corporations and financial institutions, including investment banks, commercial banks, and hedge funds. Corporate Finance Institute® Example of Using Swaptions Motivation: Market Swap Fixed Rate ↑ Exercise the Swaption: Enter Into an Offsetting At-Market Swap: Take the pay-fixed, receive-floating side of a swap at the predetermined exercise rate Receive-fixed, pay-floating side Exercise Rate < Market Rate Exercise Rate < Swap Fixed Rate = Market Rate Exercise Rate < Swap Fixed Rate Annuity = Offsetting Swap Rate – Swaption Exercise Rate Corporate Finance Institute® Variance Swaps Corporate Finance Institute® Session Objectives Define what variance swaps are Understand the structure and terms of variance swaps Understand who and why use variance swaps Calculate the profit and loss of a variance swap Corporate Finance Institute® Understand the mechanics of how variance swaps work Variance Swaps – Where Do They Come From When an asset’s price is volatile, we are uncertain about the future returns we will earn. This volatility can be measured statistically. Standard Deviation % Return % Return Range Time Measures the movements in the asset price from the lowest low to the highest high Measures the extremes of an asset’s price movement Corporate Finance Institute® Time Based on the average or standard movement in the asset price Often called the volatility and is expressed as a percentage on an annual basis What Is Volatility Volatility of a financial asset is commonly measured by the standard deviation of its returns. It is the dispersion of returns for a given security or the market; it represents uncertainty. S&P 500 Index (Market Index) 3,500 SPX Price 3,000 2,500 Dot Com Bubble Global Financial Crisis 2,000 1990’s 2008 1,500 Black Monday 1,000 The Crash of ‘87 COVID-19 Market Crash 2020 500 0 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 2018 2020 Corporate Finance Institute® Generic Properties of Equity Market Volatility Anticorrelated with the underlying over short periods of time Corporate Finance Institute® Can increase suddenly in spikes Observed to experience different regimes Mean reverting Historical Volatility vs. Implied Volatility Historical (Realized) Volatility Price fluctuations of the underlying asset Standard deviation Movement of a stock / index over a 60day period Lognormal Daily Returns = In ( Implied Volatility Volatility of the contract implied by the market Supply / demand and time value are major factors Price Today – Price Yesterday ) Price Yesterday Historical Volatility = Standard Deviation of Lognormal Daily Returns Corporate Finance Institute® Building Blocks of Variance Products Realized Variance Variance Strike Implied volatility Historical volatility The fixed side of a variance swap The actual variance of the underlying asset over the life of the swap The payments on the swap will be based on whether the realized variance over the term of the swap is greater or less than the variance strike. Both volatility and variance describe the risk of a particular asset. The mathematical difference is that: Variance = Volatility2 Corporate Finance Institute® Realized Volatility and Implied Volatility – Uses of Variance Swaps S&P 500 60-Day Historical Volatility COVID-19 Volatility 3-Month Implied Volatility 60-Day Historical Volatility 80 3-Month Implied Volatility 80 70 70 COVID-19 Market Crash 2020 60 50 60 50 40 40 30 30 20 20 10 10 Corporate Finance Institute® 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 0 0 Jan-2020 Strike Level Feb-2020 Mar-2020 Apr-2020 Variance Swaps – Structure Variance swaps allow market participants to speculate on or hedge against the volatility of a security or an index of securities. Volatility swap is the same as a variance swap since volatility is the square root of variance. Fixed Payment Variance / Volatility Strike Buyer of Volatility Seller of Volatility Market view: expects cooler markets than forecasted Corporate Finance Institute® Floating Payment Realized Variance / Volatility Market view: expects more volatile market than forecasted Variance Swaps – Structure Settlement Payment = Vega Notional x (Realized Variance – Variance Strike) Volatility Premium = Profit Gained From the Difference Between Implied and Realized Volatility Volatility premium is the return an investor gets as the compensation for insuring the other investor for risk of losses during sudden increases in market volatility and extreme market events. Corporate Finance Institute® Why Use Variance Swaps 1. Direct Exposure to the Volatility of an Underlying Asset 2. Diversifying Asset 4. Speculative Trading 5. Variance Dispersion and Correlation Trading Generating alpha Hedging volatility exposure, market conditions, and equity positions Corporate Finance Institute® 3. Hedging Trading variance swaps on an index against variance swaps on its constituents provides exposure to equity correlation 6. Relative Value Single Stock Volatility Use volatility pairs or crosssectional regression volatility models to find rich/cheap singlestock volatility Variance Swaps – Key Features Investors trading variance swaps have knowledge of vanilla option pricing and hedging. Notional Different measures of notional in terms of Vega and variance notional Mark-to-Market Value Calculated using a simple valuation of forward-starting variance swaps Variance Swap Strikes Correlated with Black-Scholes implied volatility derived from option prices Realized Volatility Major driver of variance swap levels and prices Variance swaps on single-stocks and sector indices are usually sold with caps. Often set at 2.5x the strike of the swap and “cap” realized volatility above this level Protects short variance investors so they can quantify their maximum possible loss Investors Caps Corporate Finance Institute® Notionals – Variance or Vega Notional Vega is a measure based on volatility; it is the measure of change in the option price for a 1% move in the implied volatility of the underlying asset. Vega notional represents the average profit or loss for a 1% change in volatility and gives a more economically meaningful idea of the variance swap’s exposure to volatility. P&L Profit and loss (P&L) of a variance swap is expressed in terms of vega notional: Vega Notional Payoff for Variance Swaps = Variance Notional x (Realized Variance – Variance Strike2 ) Variance Notional = Vega Notional 2 x Variance Strike OR Vega Notional = Variance Notional x (2 x Variance Strike) Corporate Finance Institute® Variance Swaps Example – Contract Terms Variance Swap Trade Date Jan 6, 2020 Maturity Date July 6, 2020 Variance Buyer/Seller Underlying S&P 500 Index Denominated Currency USD Vega Notional $100,000 Strike Price 20 Cap Level (2.5 x Strike = 50) T+2 after the observation end date, the equity amount will be calculated and paid: Vega Notional x [Min Realized Volatility, Cap Level – Strike Price] 2 x Strike Price Corporate Finance Institute® If equity amount > 0: variance seller will pay variance buyer. If equity amount < 0: variance buyer will pay variance seller. Variance Swaps Example – Calculating Profit and Loss P&L = Vega Notional x Realized Variance – Variance Strike2 2 x Variance Strike Realized Volatility are squared since we are looking in terms of variance. Variance Strike = 20 Realized Variance = Min Cap2 , Realized Volatility2 Scenario 1: If in 6 months, index realized 30% volatility, the long position will receive: Realized Volatility2 – Variance Strike2 302 – 202 = $1.25MM = $100,000 x P&L = Vega Notional x 2 x 20 2 x Variance Strike Profit = $1,250,000 = 12.5 Vegas $100,000 Scenario 2: If in 6 months, index realized 14% volatility, the long position will pay: P&L = $100,000 x Loss = 14 2 – 202 = ($510,000) 2 x 20 ($510,000) = 5.1 Vegas $100,000 Corporate Finance Institute® Variance Swaps Example – Maximum Losses For a long variance swap, the maximum loss will occur when the realized volatility is zero: Max Loss = $100,000 x Long Variance Swap 02 – 202 = ($1MM) 2 x 20 Variance swaps, especially on single-stocks and sector indices, are usually sold with caps. Caps are often set at 2.5x the strike of the swap, capping realized volatility above this level. – E.g. Strike = 20  Cap = 20 x 2.5 = 50 Short Variance Swap Corporate Finance Institute® – Buyers would be capped to a maximum profit of: $100,000 x 502 – 202 = $5.25MM 2 x 20 This allows sellers of swaps to quantify their maximum possible loss. Therefore, sellers would have a maximum loss of $5.25MM when the realized volatility is at least 50. Variance Swaps – Bloomberg Example Underlying Strike Price Variance Notional Vega Notional Corporate Finance Institute® Credit Default Swaps Corporate Finance Institute® Session Objectives Define the terminologies associated with credit default swaps (CDS) Explain the structure of a credit default swap Identify who and why use CDS Understand the pricing and valuation of CDS Corporate Finance Institute® Understand the pricing and maturity of standardized CDS Credit Default Swaps – Basic Terminology Credit default swap (CDS) is an agreement between two parties where one side buys protection against specific risks associated with credit events (e.g. defaults, bankruptcy, restructuring, or credit rating downgrades). It acts as an insurance policy which pays out if a particular entity defaults on its debts. Reference Entity The issuer or “name” of the debt that underlies a credit derivative Reference Asset / Obligation Normally senior, unsecured bond or loan Credit Event Notional Value Duration Recovery Rate Corporate Finance Institute® Default that would trigger payment Total par value insured Years of contract The percentage of par value that is recovered in the event of a credit event Credit Default Swaps – Standard Maturity Dates To help standardize single-name CDS contracts, the International Swaps and Derivatives Association (ISDA) introduced a number of documentation changes in 2009. One of the changes was the introduction of the four standard maturity dates on which CDS premiums are paid: Mar 20 Jun 20 Sep 20 Dec 20 This makes CDS an exchange-tradable instrument. The final premium payment is made on the maturity date, or the following business day. Other payment dates are calculated by working back quarterly from the maturity date. Corporate Finance Institute® Credit Default Swaps – Structure Reference Entity CDS buyer buys bonds from reference entity for which it shall receive interest and principal. CDS buyer pays premiums to seller to insure interest and principal payments from reference entity. Interest and Principal Credit Spread Payments Default occurs Protection Buyer May own underlying credit asset Purchases credit protection Corporate Finance Institute® Payment if Credit Event Occurs Cash / physical settlement Buyers and sellers can be: Reduces credit exposure Banks Pension funds “Short side” Hedge funds Protection Seller Doesn’t usually own underlying credit asset Sells credit protection “Long side” Credit Default Swaps – Key Features Quotation Mostly quoted in terms of spreads (bps) CDS Spreads Can be greater or less than the coupon Maturities Range from 1 to 10 years Represents the size of the contract Mostly in the range of $10MM – $20MM Single-name CDS: based on one specific borrower (reference entity) and offers a payoff if that specific borrower experiences a credit event Index CDS: involves several reference borrowers which allow market participants to take positions on the credit of a portfolio of companies Tranche CDS: covers a portfolio of borrowers but only to a pre-specified amount of losses Notional Principal Types of CDS Corporate Finance Institute® Credit Default Swaps – Key Features Value or Price of CDS Contract Terms Corporate Finance Institute® Can change over the contract term due to changes in the credit quality of the reference obligation Specified in the ISDA master agreement, which both parties sign Why Use Credit Default Swaps 1. Hedging Event Risk 2. Speculation and Leverage Protecting lenders against credit risk (e.g. default) Leverage with CDS (e.g. portfolio manager owns $1MM of assets, sells CDS on $100MM of bonds, receives 2% from buyer) E.g. Bond issuer goes bankrupt and is unable to repay principal Capitalizing on valuation disparities (taking the difference in pricing of credit risk in CDS market relative to another market) Hedging portfolio risk Curve trade (buys a CDS with one maturity and sells one with different maturity from the same reference entity) 3. Decrease Exposure to Currency Risk Corporate Finance Institute® 4. Managing Credit Risk Shifting credit exposures to institutional investors with investment horizons better suited to these risks Credit Default Swaps – Risks Counterparty Credit Risk Risk of default CDS Premium The buyer could be paying a premium for something that will never happen. If a credit event occurs, sellers have to pay up. Complicated CDS Modeling Difficult to trust observed market prices Prices are not easily determined Difficult to aggregate risks / hard to measure default correlations One of the main risks historically associated with credit default swaps was the lack of federal regulation. However, this issue was addressed in 2010 with the introduction of the Dodd-Frank Act after the 2008 Financial Crisis. Corporate Finance Institute® CDS Settlement on Default – Physical Physical Settlement: On default, the protection seller pays the protection buyer the nominal value of the swap in return for the defaulted obligation. Example: Assume two parties entered into a CDS contract on ABC company with a notional value of $10MM. Notional $10MM Protection Buyer Corporate Finance Institute® Delivery of ABC Bonds Protection Seller CDS Settlement on Default – Cash Cash Settlement: On a credit event, the protection seller pays the protection buyer an amount reflecting the obligation’s discount to par (Notional Value – Post-default Market Value of Reference Obligation). The post-default value of the bonds is determined through an auction process that is facilitated by ISDA. Example: Assume the post-default market value of ABC company = $3MM (recovery rate = 30%). Notional Value – Post-default Market Value = $10MM – $3MM = $7MM Cash Protection Buyer Corporate Finance Institute® Protection Seller Recovery Rate and Payout Ratio Payout Ratio Recovery Rate The percentage of the par value that is recovered Generally an assumption of 40% is common for unsecured debt. Determined by the auction taken part by large investment banks Corporate Finance Institute® Determines the amount that the protection seller must pay the protection buyer An estimate of the expected credit loss Payout Ratio = 1 – Recovery Rate Payout Amount Payout Amount = Payout Ratio x Notional Amount Pricing & Valuation of Credit Default Swaps Corporate Finance Institute® Pricing Concepts – CDS Spread and Upfront Premium CDS spread or credit spread are periodic payments paid by the protection buyer to the seller. It is the return over LIBOR that is required to protect against credit risk. Typical standard rates: Investment-Grade Company / Index 1% (100 bps per year) High-Yield Company / Index 5% (500 bps per year) If this standard rate is too high or low for a particular reference obligation, the discrepancy is accounted for via an upfront premium. Standard Rate Is Too Low Standard Rate Is Too High Protection buyer will pay an upfront premium (positive upfront premium) Protection seller will pay an upfront premium (negative upfront premium) Corporate Finance Institute® CDS Premium Payments Upfront Payment = PV (Protection Leg) – PV (Premium Leg) Contingent payment seller will pay if default occurs (credit spread) Payments made by the protection buyer (fixed coupon) Upfront Premium % = (CDS Spread – Coupon) x Duration CDS Price (Per $100 Notional) = $100 – Upfront Premium % Example Upfront Premium % = (5% – 4%) x 5 = 5% Underlying Bond Coupon 4% CDS Spread 5% Duration Corporate Finance Institute® 5 Years The buyer must make an upfront payment to the seller. CDS Price = $100 – 5% x $100 = $95 Example 1 – Understand a CDS Quote JLS Inc. Duration 5 Years Upfront Premium 2.00% Coupon 100 bps Until Default Long Position On Default (Post Default Price = 40) $10MM Physical Settlement: Upfront Premium $200,000 Delivers $10MM Par JLS Inc. Bond Annual Premium $100,000 Receives $10MM The premium will typically be paid quarterly (i.e. $25,000 per quarter). Corporate Finance Institute® Cash Settlement: Receives 60% x $10MM = $6MM Cash Example 2 – CDS via Bloomberg – Positive Upfront Premium Credit Spread Coupon Upfront Premium % Price of CDS Corporate Finance Institute® Example 2 – CDS via Bloomberg – Positive Upfront Premium Looking at it intuitively… Year Annual Payments Year Annual Payments 0 - 0 378.79 1 178.9529 1 100.00 2 178.9529 2 100.00 3 178.9529 3 100.00 4 178.9529 4 100.00 5 178.9529 5 100.00 Total Present Value OR Total Present Value In this example, the spread of 178.9529 bps is more than the coupon of 100 bps. Protection seller receives money upfront. Corporate Finance Institute® Example 2 – CDS via Bloomberg – Negative Upfront Premium Credit Spread Coupon Upfront Premium % Price of CDS Corporate Finance Institute® Example 2 – CDS via Bloomberg – Negative Upfront Premium Looking at it intuitively… Year Annual Payments Year Annual Payments 0 - 0 (217.407) 1 54.9365 1 100.00 2 54.9365 2 100.00 3 54.9365 3 100.00 4 54.9365 4 100.00 5 54.9365 5 100.00 Total Present Value OR Total Present Value In this example the spread of 54.9365 bps is less than the coupon of 100 bps. Protection seller pays money upfront. Corporate Finance Institute® Factors That Determine CDS Pricing 1. Probability of Default Default could occur if any coupon or principal payment is missed. “Probability of Survival” 2. Hazard Rate Reflects the probability that an event (default) will occur given that it has not already occurred Probability of Default = (1 – Probability of Survival) 3. Loss Given Default The amount lost if a default occurs Loss Given Default = Full Payment – Recovery Corporate Finance Institute® 4. Expected Loss The probability weighted amount lost if a default occurs Expected Loss = Loss Given Default x Probability of Default Example – Calculate Probability of Default and Expected Loss 1st Payment 2nd Payment Cash Flows $50 $50 + $1,000 = $1,050 Hazard Rate 1% 4% Bond Duration Coupon Par Value 2 Years 5% $1,000 Recovery Rate = 40% 01 Calculate the probability of default Corporate Finance Institute® 02 Calculate the expected loss Example – Part 1: Calculate Probability of Default Scenario 1: Default Occurs on the First Payment Scenario 2: Default Occurs on the Last Payment Default Does Not Occur at the End of Year 1/Year 2: Bondholder will receive: Bondholder will receive: Bondholder will receive: Year 1: $50 x 40% = $20 Year 1: $50 Year 1: $50 Year 2: $1,050 x 40% = $420 Year 2: $1,050 x 40% = $420 Year 2: $1,050 Probability of this scenario: Probability of this scenario: 1% (100% – 1%) x 4% = 3.96% Probability of Survival = (100% – 1%) x (100% – 3.96%) = 95.08% Probability of Default = 100% – 95.08% = 4.92% Corporate Finance Institute® Example – Part 2: Calculate Expected Loss Loss for Scenario 1 Loss for Scenario 2 Loss on 1st Payment: $50 – $20 = $30 Loss on 2nd Payment: $1,050 – $440 = $630 Loss on 2nd Payment: $1,050 – $440 = $630 Total Loss = $30 + $630 = $660 Total Loss = $630 Probability of this scenario: Probability of this scenario: 1% 3.96% Expected Loss = (1% x $660) + (3.96% x $630) = $31.55 Corporate Finance Institute® Credit Curve Credit curve shows the spreads on a company’s debt for a range of maturities. These are the spreads on top of LIBOR required by investors to hold the debt instrument. Credit Spread = Probability of Default % x Loss Given Default % Properties: 1. Constant hazard rate will result in a relatively flat credit curve. Corporate Finance Institute® 2. Upward sloping credit curve indicates a higher likelihood of default in later years. 3. Downward sloping credit curve indicates a higher probability of default in early years. Changes in Credit Curve Factors impacting the value of a CDS include changes in: Credit Quality of the Reference Entity Probability of Default Shape of the Credit Curve Corporate Finance Institute® Expected Loss Given Default Duration of the CDS Strategy Using the Credit Curve Curve trade is a strategy where a trader is long and short CDS that have different maturities and are based on the same reference entity. Expectation Credit curve will steepen Corporate Finance Institute® Curve Trade Strategy Short long-term CDS Long short-term CDS Profit and Loss From Change in Credit Spread Profit for Protection Buyer = Change in Spread x Duration x Notional % Change in CDS Price = Change in Spread (in bps) x Duration Corporate Finance Institute® Example – Profit and Loss From Change in Credit Spread A portfolio manager purchased $10MM of CDS protection for ABC Company with a duration of 3 years. ABC Company’s credit spread was originally 200 bps and it widened to 400 bps. What does this credit spread change imply? Is this CDS worth more or less now after the spread widened? Credit Spread Upfront Premium Corporate Finance Institute® 200 bps 400 bps This change of credit spread implies that the credit worthiness has worsened for company ABC. Increases ↑ The portfolio manager will gain since they can sell the protection for a higher premium. Example – Profit and Loss From Change in Credit Spread Calculate the P&L for the portfolio manager: Step 1: % Change in CDS Price = Change in Spread (in bps) x Duration = 200 x 3 Years = 6% Step 2: Profit for Portfolio Manager = Change in Spread x Duration x Notional = 200 x 3 x $10MM = $600,000 Corporate Finance Institute® Credit Default Swaps Summary Key points: 1 Credit default swaps are like insurance on bonds. 2 The buyer makes (or potentially receives) an upfront payment and then makes regular payments every quarter. 3 The annual coupon is 100 bps for investment-grade companies and 500 bps for high-yield companies (standard rate). 4 Claims can be either physically or cash settled on default. 5 Buyer or seller don’t have to necessarily own the underlying credit exposure. Corporate Finance Institute®