robinhood-options-mobile

Beta-Weighted Portfolio Delta & Cross-Asset Greeks Engine

RealizeAlpha includes an institutional-grade quantitative risk engine that calculates Beta-Weighted Portfolio Delta ($\Delta_\beta$) and aggregate cross-asset Greeks (Gamma, Vega, Theta) across equities, options, futures, cryptocurrencies, and forex.

---

1. Overview & Theoretical Foundation

Standard portfolio delta sums raw delta values across options contracts ($\sum \Delta_i$), but raw delta suffers from the apples-to-oranges fallacy: 100 deltas of an ultra-volatile tech stock (e.g., NVDA, beta $\beta = 2.1$) represent vastly different dollar exposure than 100 deltas of a defensive consumer staple (e.g., KO, beta $\beta = 0.55$) or a 3x leveraged ETF (e.g., TQQQ, beta $\beta = 3.0$).

Beta-weighting normalizes every position in a multi-asset portfolio against a single liquid benchmark index (by default SPY, with 1-tap switching to QQQ, DIA, or IWM). This translates disparate holdings into equivalent benchmark index shares:

\[\Delta_{\beta, \text{pos}} = \Delta_{\text{pos}} \times \left(\frac{S_{\text{pos}}}{S_{\text{benchmark}}}\right) \times \beta_{\text{pos}}\]

Where:

• $\Delta_{\text{pos}}$ is the position’s directional sensitivity:
  • Equities: Number of shares held (long $> 0$, short $< 0$).
  • Options: Contract count $\times 100 \times \text{Delta}$ per contract.
  • Futures: Contracts $\times$ Multiplier $\times$ Delta (e.g., /ES = 50x, /NQ = 20x, /YM = 5x).
  • Forex / Crypto: Quantity held $\times$ Asset price $\times$ Benchmark sensitivity.
• $S_{\text{pos}}$ is the current spot/market price of the underlying asset.
• $S_{\text{benchmark}}$ is the price of the benchmark index (e.g., SPY at $500).
• $\beta_{\text{pos}}$ is the asset’s beta relative to the benchmark index ($\frac{\text{Cov}(R_{\text{pos}}, R_{\text{bench}})}{\text{Var}(R_{\text{bench}})}$).

True Dollar Market Risk ($ Delta per 1% Move)

The dollar risk per 1% move in the benchmark is computed directly as:

\[\$ \Delta_{1\%} = \Delta_{\beta, \text{portfolio}} \times S_{\text{benchmark}} \times 0.01\]

If a portfolio has $\Delta_{\beta-SPY} = +250$ with SPY at $500, a +1% rally in the S&P 500 will generate an expected gain of:

\[\$ \Delta_{1\%} = 250 \times 500 \times 0.01 = +\$1,250.00\]

---

2. Cross-Asset Coverage & Multipliers

The analytics engine (AnalyticsUtils.calculateBetaWeightedGreeks) natively aggregates risk across five major asset classes:

Asset Class	Position Type	Spot Valuation	Beta Fallback Source	Formula
Equities	InstrumentPosition	Last trade quote / average buy price	Fundamental beta or fallback: 1.0 (default), 3.0 (3x bull), -3.0 (3x bear)	$\text{Shares} \times \left(\frac{S}{S_B}\right) \times \beta$
Options	OptionAggregatePosition	Underlying instrument quote	Underlying fundamental beta or asset fallback	$\text{Contracts} \times 100 \times \Delta \times \left(\frac{S}{S_B}\right) \times \beta$
Futures	FuturesPositionStore	Product contract quote / trade price	/ES: 1.0, /NQ: 1.25, /YM: 0.95, /RTY: 1.15, /CL: 0.35, /GC: 0.10	$\text{Contracts} \times \text{Multiplier} \times \left(\frac{S}{S_B}\right) \times \beta$
Crypto	ForexHolding	Currency pair quote (BTC, ETH, SOL)	BTC: 1.6, ETH: 1.8, SOL: 2.0, other crypto: 1.4	$\text{Qty} \times \left(\frac{S}{S_B}\right) \times \beta_{\text{crypto}}$
Forex	ForexHolding	Fiat currency quote (EUR, GBP, JPY)	Fiat currencies: 0.15	$\text{Qty} \times \left(\frac{S}{S_B}\right) \times 0.15$

Aggregate Greeks Aggregation

• Beta-Weighted Delta ($\Delta_\beta$): Sum of equivalent benchmark shares across all positions.
• Portfolio Gamma ($\Gamma$): Aggregate rate of change of delta per $1 move in option underlyings: \(\Gamma_{\text{portfolio}} = \sum \text{Contracts}_i \times 100 \times \Gamma_i\)
• Portfolio Vega ($\nu$): Aggregate dollar change per 1% change in implied volatility: \(\text{Vega}_{\text{portfolio}} = \sum \text{Contracts}_i \times 100 \times \nu_i\)
• Portfolio Theta ($\Theta$): Aggregate daily calendar decay in dollars: \(\text{Theta}_{\text{portfolio}} = \sum \text{Contracts}_i \times 100 \times \Theta_i\)

---

3. UI Component Architecture (PortfolioGreeksCard)

The PortfolioGreeksCard widget in lib/widgets/portfolio/portfolio_greeks_card.dart provides an interactive, institutional-grade analytics dashboard embedded in the Portfolio Risk Section (RiskSectionPage):

Key Visual Elements

1. Dual-View Segmented Toggle:
   • Beta-Weighted View: Shows normalized benchmark-equivalent shares, dollar risk per 1% move, asset class contributions, and top delta drivers.
   • Raw Greeks View: Classic sum of contract Greeks for traders focusing purely on raw options inventory.
2. Benchmark Selector Chips:
   • Supports quick 1-tap switching between SPY (S&P 500), QQQ (Nasdaq 100), DIA (Dow Jones), and IWM (Russell 2000).
   • Dynamically recalculates all equivalent shares, driver impacts, and stance badges in real-time.
3. Portfolio Stance Badge:
   • Bullish: $\Delta_\beta > +10$ benchmark shares (Green badge).
   • Bearish: $\Delta_\beta < -10$ benchmark shares (Red badge).
   • Neutral / Delta-Neutral: $-10 \le \Delta_\beta \le +10$ benchmark shares (Grey/Neutral badge).
4. Delta by Asset Class Chips:
   • Visual chips showing sub-totals for Stocks, Options, Crypto, and Futures.
5. Top Delta Drivers Breakdown:
   • Sorted list showing the highest-impact positions driving market exposure, displaying raw shares/contracts, spot price, beta, and net $\Delta_\beta$.
6. Educational Modal Bottom Sheet:
   • Integrated info button (Icons.info_outline) displaying complete mathematical formulations, greek interpretations, and guidance on delta hedging strategies.

---

4. Integration & State Management

In RiskSectionPage (lib/widgets/portfolio/risk_section_page.dart), the card is connected to the application’s global state and stores:

PortfolioGreeksCard(
  positions: options,
  equityPositions: portfolio.positions,
  futuresStore: futuresStore,
  forexStore: forexStore,
  benchmarkSymbol: controller.selectedBenchmark,
  benchmarkPrice: controller.benchmarkQuote?.lastTradePrice ?? 500.0,
  onBenchmarkChanged: (newBenchmark) {
    controller.selectBenchmark(newBenchmark);
  },
)

If the controller or live quote is temporarily loading, safe fallback pricing ensures calculation stability without throwing null exceptions.

---

5. Verification & Testing

The engine is validated with unit and widget tests:

• test/beta_weighted_greeks_test.dart:
  • Validates single equities and inverse ETF negative beta dampening.
  • Validates option contracts with underlying spot price weighting.
  • Validates multi-asset portfolios spanning stocks, options, /ES futures, and BTC crypto.
  • Validates benchmark switching between SPY and QQQ.
  • Validates zero/unpriced position handling.
• test/portfolio_greeks_card_test.dart:
  • Validates empty state rendering.
  • Validates beta-weighted view rendering, hero metrics, Greek tiles, asset chips, and top drivers.
  • Validates interactive benchmark switching and segmented view switching.
  • Validates educational guide bottom sheet presentation and scrollability.