Learning_Module_14_Swaps_Forwards_and_Futures

Learning Module 14: Swaps, Forwards, and Futures Strategies

LOS: Demonstrate how interest rate swaps, forwards, and futures can be used to modify a portfolio’s risk and return.

Managing Interest Rate Risk with Swaps, Forwards, and Futures

Interest Rate Swaps

Use: Employed to modify a portfolio’s duration or to convert fixed-rate cash flows to floating-rate cash flows, and vice versa.
Receive-Fixed Swap: Increases portfolio duration, functionally equivalent to buying a long-term bond.
Pay-Fixed Swap: Decreases portfolio duration, functionally equivalent to issuing or shorting a fixed-rate bond.

Interest Rate Futures & Forwards

Objective: To modify portfolio duration, and thus interest rate risk, by using a Hedge Ratio (HR).
Basis Point Value (BPV): Represents the change in value of an asset for a one basis point (0.01%) change in yield. \[BPV = \text{MDUR} \times 0.0001 \times \text{Market Value}\]
Hedge Ratio (BPVHR): Determines the number of futures contracts needed to achieve a target duration. \[N_f = \left( \frac{BPV_T - BPV_P}{BPV_F} \right)\] Where $BPV_F$ is the BPV of the futures contract.
Futures BPV Calculation: Derived from the Cheapest-to-Deliver (CTD) bond in the futures contract. \[BPV_F = \frac{BPV_{CTD}}{CF}\] Where $CF$ = Conversion Factor of the CTD bond. The combined formula for the number of contracts is: \[N_f = \left( \frac{BPV_T - BPV_P}{BPV_{CTD}} \right) \times CF\]
Interpretation:
- If $BPV_T < BPV_P$: Sell futures (take a short position) to reduce the portfolio’s duration.
- If $BPV_T > BPV_P$: Buy futures (take a long position) to increase the portfolio’s duration.

Example: Hedging Bond Holdings

Scenario: A manager wishes to fully hedge a €50 million German bund portfolio (with a duration of 9.50) using Euro-Bund futures.
Step 1: Calculate the portfolio’s BPV ($BPV_P$). For a portfolio value of €49.531M, $BPV_P = 9.50 \times 0.0001 \times \text{€49.531M} = \text{€47,054}$.
Step 2: Calculate the $BPV_{CTD}$ from the Cheapest-to-Deliver bond’s details.
Step 3: Determine the number of contracts to sell. For a full hedge, the target BPV ($BPV_T$) is 0, so $N_f = - \frac{BPV_P}{BPV_{CTD}} \times CF$.

LOS: Demonstrate how currency swaps, forwards, and futures can be used to modify a portfolio’s risk and return.

Managing Currency Exposure

Currency Swaps

Structure: Involves exchanging principal amounts at both the beginning and end of the agreement (a key difference from interest rate swaps). Parties also exchange interest payments in different currencies.
Cross-Currency Basis Swap:
- Primarily used to lend one currency and borrow another (e.g., to fund foreign operations).
- Basis: Refers to the spread added to or subtracted from the reference rate of one leg (typically a non-USD currency) to balance supply and demand.
- Negative Basis: Indicates strong demand for USD, leading non-USD lenders to accept a lower rate (Reference Rate - Basis).
Example (LBO Funding): A firm borrows inexpensive CAD locally and then swaps it for USD to finance a US acquisition. The firm pays USD floating and receives CAD floating plus a basis, effectively eliminating FX risk on the principal.

Currency Forwards and Futures

Use: Employed to hedge specific future cash flows, such as capital calls or the repatriation of funds.
Hedge Ratio: Typically 1.0. \[N = \frac{\text{Amount to Hedge}}{\text{Contract Size}}\]
Example: A Venture Capital (VC) firm anticipating a CAD inflow sells CAD futures to lock in its USD equivalent value.
Basis Risk: The risk that the futures price and the spot price do not converge perfectly or move in perfect lockstep before maturity.

LOS: Demonstrate how equity swaps, forwards, and futures can be used to modify a portfolio’s risk and return.

Managing Equity Risk

Equity Swaps

Structure: Involves exchanging the return on an equity (either an index or a single stock) for a fixed or floating interest rate, or for the return on another equity.
Total Return Swap (TRS): Includes both price appreciation/depreciation and dividend payments.
Uses:
- To gain synthetic exposure to a market without physically owning the shares, thereby avoiding custody fees and taxes.
- To temporarily hedge existing equity exposure (e.g., Pay Equity Return / Receive Floating Rate).
Example: A manager anticipates a decline in the S&P 500. They enter a swap to Pay the S&P 500 Return and Receive a Floating Rate.
- Scenario Down: If the portfolio loses value, the swap generates a profit (Receiving Floating Rate - Paying a Negative Equity Return).

Equity Forwards and Futures

Beta Management: Used to adjust a portfolio’s current Beta ($\beta_S$) to a Target Beta ($\beta_T$). \[N_f = \left( \frac{\beta_T - \beta_S}{\beta_f} \right) \left( \frac{S}{F} \right)\] Where $S$ = Value of the Portfolio; $F$ = Value of one Futures Contract ($Price \times Multiplier$).
Cash Equitization:
- Utilizing futures to gain market exposure on cash holdings, thereby reducing the “cash drag” on performance.
- In this context, the Cash Beta ($\beta_S$) is treated as 0, and the Target Beta ($\beta_T$) is typically the Index Beta (usually 1).
- Formula: \[N_f = \left( \frac{\beta_T}{\beta_f} \right) \left( \frac{\text{Cash}}{F} \right)\]

Example: Increasing Beta

Goal: To increase a portfolio’s Beta from 0.85 to 1.10 using FTSE 100 futures.
Calculation: $N_f = \frac{1.10 - 0.85}{1.0} \times \frac{\text{Portfolio Value}}{\text{Futures Value}}$. A positive result indicates that futures need to be bought.

LOS: Demonstrate the use of volatility derivatives and variance swaps.

Volatility Derivatives

Volatility Futures (VIX Futures)

Underlying: The VIX Index, which represents the implied 30-day volatility of S&P 500 options.
Characteristics:
- The VIX is known for its mean-reverting tendency.
- It exhibits a negative correlation with equities, making it a valuable tool for hedging tail risk.
Term Structure:
- Contango: An upward-sloping term structure where longer-term VIX futures are priced higher than shorter-term ones. Common in stable markets. This results in a negative roll yield for long positions (a cost of carry).
- Backwardation: A downward-sloping term structure where shorter-term VIX futures are priced higher. Occurs predominantly during periods of market stress.
ETPs: Exchange Traded Products (ETPs) that track the VIX often suffer from decay due to the constant rolling of futures positions in contango markets.

Variance Swaps

Definition: A forward contract on the realized variance (the square of volatility) of an underlying asset.
Payoff: Offers a pure play on variance, without the path dependency associated with options.
- The payoff is Convex in volatility terms, meaning a long variance swap position is effectively long volatility and long Gamma.
Key Terms:
- Vega Notional ($N_{\text{Vega}}$): Represents the average Profit & Loss (P&L) for a 1% change in volatility.
- Variance Notional ($N_{\text{Var}}$): Used in the valuation of the swap. \[N_{\text{Var}} = \frac{N_{\text{Vega}}}{2 \times \text{Strike}(X)}\]
Settlement Amount: \[\text{Settlement Amount} = N_{\text{Var}} \times (\text{Realized } \sigma^2 - \text{Strike } X^2)\]
Valuation (Mark-to-Market): \[\text{Value}_t = N_{\text{Var}} \times PV_t \times \left( \frac{t}{T}(\text{RealizedVol}^2) + \frac{T-t}{T}(\text{ImpliedVol}^2) - X^2 \right)\] This formula uses a weighted average of realized variance (from the past) and implied variance (for the future).

Example: Variance Swap

Scenario: A short position with a $50k Vega Notional, a Strike of 20%. The Realized Volatility is 16%, and the New Implied Volatility is 19%.
Step 1: Calculate $N_{\text{Var}} = 50,000 / (2 \times 20) = 1,250$.
Step 2: Calculate the weighted variance (e.g., half realized, half implied).
Step 3: Compare this to the strike variance ($20^2 = 400$).
Step 4: A short position profits if the Weighted Variance is less than the Strike Variance.

LOS: Demonstrate the use of derivatives in asset allocation, rebalancing, and inferring market expectations.

Asset Allocation with Derivatives

Rebalancing Asset Allocation

Strategy: Derivatives, particularly futures, can be used to efficiently shift asset allocations (e.g., from stocks to bonds) without the need to sell physical assets (often referred to as an “Overlay” strategy).
Process:
1. Determine the specific amount to shift (e.g., reduce stock exposure by $100M, increase bond exposure by $100M).
2. Short Equity Futures: To reduce stock exposure. For the portion being removed, the Target Beta ($\beta_T$) is 0. \[N_{\text{stock}} = \frac{0 - \beta_S}{\beta_f} \times \frac{\text{Amount}}{\text{Futures Value}}\]
3. Long Bond Futures: To increase bond exposure. For the portion being added, a Target BPV ($BPV_T$) is established. \[N_{\text{bond}} = \frac{BPV_{Target} - 0}{BPV_{CTD}} \times CF\]

Inferring Market Expectations

Fed Funds Futures:
- Prices are quoted as $100 - \text{Effective Fed Funds Rate}$.
- Used to infer the market’s perceived probability of FOMC rate hikes or cuts.
- Probability Formula (for a rate hike): \[P(\text{Hike}) = \frac{\text{Effective Rate Implied} - \text{Current Rate}}{\text{Rate assuming Hike} - \text{Current Rate}}\]
Other Inferences:
- CPI Swaps: Provide insights into inflation expectations.
- VIX Futures: Reflect market expectations for future volatility.