Return Stacking

https://www.returnstacked.com/a-different-way-to-outperform-benchmarks/?_hsenc=p2ANqtz-9EGAoITOVzRwnxEaD_V9QByHTc72lRjWC0j6rrLKcM2Kk3z0bTIPHiTgDcF5za3KitUsoZHw1aQG_KM9eaMlm0AuPnTQ&_hsmi=317353322#utm_campaign=Welcome%20New%20Contacts%207%20Nurture%20Emails&utm_medium=email&utm_content=317353322&utm_source=hs_automation

key idea behind alternative beta stacking: find alternative betas to stack that:

• have historically deliveredp positive excess returns
• low correlation with sp500
• lowly correlated each other

2 examples of strategies that have these characteristics (historically):

• managed future trend following: taking long and short positions in commodities, currencies, IR and equities using quantitative and systematic methods to find trends

• guture yield (carry) strategy => return accrues to the investor is there's no chane in price (coupon and dividens are such an example). currency and commodity can do the same.

  • with fx. we can buy a currrency with low IR and puschase short-term bills demonitated in a currency with higher rates
  • commodity carry: long position where the roll yield is positive (backwardation) and short where the roll yield is negative (contango)

Quantitative Study Plan: Return Stacking and Derivatives

Chapter 1: The Mathematics of Derivative Pricing

• The No-Arbitrage Principle: Defining the fundamental law of quantitative finance.
• The Cost of Carry Model: Deriving the continuous-time futures pricing formula: $F=S\cdot e^{(r-q)T}$.
• Interest Rates ($r$) and Dividends ($q$): Quantifying their exact impact on the futures basis.

Chapter 2: Mechanics and Leverage of Futures Contracts

• Notional Value vs. Margin: Mathematical definitions of initial and maintenance margin.
• The Mark-to-Market Process: Daily settlement equations and cash drag.
• Quantifying Leverage: Calculating the precise leverage factor ($L=\text{Notional}/\text{Equity}$) and its impact on geometric vs. arithmetic returns.

Chapter 3: The Term Structure and Roll Yield

• Contango and Backwardation: Mathematical definitions of the futures curve shape.
• Calculating Roll Yield: Formulating the specific gain or drag when rolling from the prompt month to the next: $\text{Roll Yield}=\ln (F_{T2}/F_{T1})$.
• Convenience Yield: Modeling the underlying physical or theoretical benefit of holding the asset.

Chapter 4: Modern Portfolio Theory (MPT) and Capital Efficiency

• The Efficient Frontier: Mapping risk and return using variance and expected value.
• The Capital Allocation Line (CAL): Extending the frontier using a risk-free borrowing rate.
• Sharpe and Sortino Ratios: Calculating risk-adjusted returns before and after leverage.

Chapter 5: The Mathematics of Return Stacking

• The Stacked Return Equation: Formulating the total portfolio return: $R_p=w_1{R}_1+w_2{R}_2-c_f$.
• Covariance and Correlation Matrices: Modeling how the core asset and the stacked asset interact mathematically.
• Volatility Drag: Calculating the erosion of compounded returns in a levered, high-volatility portfolio using Itô's Lemma.

Chapter 6: Financing Costs and the Implied Rate

• Extracting the Implied Rate: Reverse-engineering the financing cost embedded in the futures basis.
• SOFR and Short-Term Rates: Modeling the impact of central bank rates on the cost of carry.
• Net Return Optimization: Finding the mathematical breakeven point where the stacked asset's expected return justifies the financing cost.

Chapter 7: Risk Modeling in Levered Portfolios

• Value at Risk (VaR): Parametric and historical calculations for maximum expected loss.
• Conditional VaR (Expected Shortfall): Quantifying the tail risk beyond the VaR threshold.
• Margin Call Probability: Using stochastic calculus to model the probability of account equity falling below maintenance margin.

Chapter 8: Alternative Instruments: Options vs. Swaps

• Black-Scholes-Merton Overview: The differential equation for option pricing.
• The "Greeks" (Delta, Gamma, Theta): Why options introduce non-linear risks compared to the linear (Delta = 1) nature of futures.
• Total Return Swaps (TRS): The mathematics of institutional over-the-counter (OTC) stacking alternatives.

Chapter 9: The "Second Engine": Trend Following Math

• Time-Series Momentum: Mathematical definitions of trend models (e.g., Moving Average Crossovers).
• Whipsaw Drag: Quantifying the loss function when standard deviation spikes and autocorrelation turns negative.
• Risk Parity: Sizing positions mathematically based on inverse volatility.

Chapter 10: Portfolio Optimization and Real-World Constraints

• Tracking Error: Calculating the standard deviation of the difference between the stacked portfolio and a benchmark.
• Rebalancing Algorithms: The math behind tolerance bands and the transaction costs of restoring the target leverage ratio.