Minimum Capital Formula

Quick Reference

Capitale minimo necessario per tradare uno strumento mantenendo leverage ragionevole e position sizing flessibile.

Formula Standard

Min Capital = 4 × (Price × Multiplier × σ% × FX) / Target Vol%

Variabili

  • 4: Numero contracts per flessibilità
  • Price: Prezzo corrente strumento
  • Multiplier: Futures multiplier
  • σ%: Annual standard deviation
  • FX: Tasso cambio a home currency
  • Target Vol%: Target volatilità (es. 0.20 per 20%)

Perche "4 Contracts"?

Minimum position per volatility targeting flexibility: - 1 contract: No adjustment possible - 2 contracts: Solo ±50% adjustments - 4 contracts: Adjustments 25%, 50%, 75%, 100% - 4 = sweet spot tra flexibility e capital requirement

Esempio S&P 500 Micro

Parameters: - Price = 4500 - Multiplier = 5 - σ% = 16% (0.16) - FX = 1.0 (USD) - Target = 20% (0.20)

Calcolo:

Min Capital = 4 × (4500 × 5 × 0.16 × 1.0) / 0.20
            = 4 × 3,600 / 0.20
            = 14,400 / 0.20
            = $72,000

Ma: Per beginner con target 12%:

Min Capital = 14,400 / 0.12 = $120,000

Versione Semplificata

Per Starter System (1 contratto minimo):

Min Capital = (Price × Multiplier × σ%) / Target Vol%

Stesso esempio (1 contract):

Min Capital = 3,600 / 0.20 = $18,000

Trade-off: Capital piu basso, ma zero flexibility.

Per Diversi Prodotti

CFD (Per Contract)

Min Capital = 4 × (Size × Price × σ%) / Target Vol%

Esempio GBPUSD CFD: - Size = £10,000 - Price = 1.33 (to USD) - σ% = 10% - Target = 25%

Min Capital = 4 × (10,000 × 1.33 × 0.10) / 0.25
            = 4 × 1,330 / 0.25
            = $21,280

Margin Stocks

Min Capital = 4 × 10 × (Price × σ%) / Target Vol%

10 shares = minimum economico per commission.

Esempio Apple @ $150, σ = 30%, target 20%:

Min Capital = 40 × (150 × 0.30) / 0.20
            = 40 × 45 / 0.20
            = $9,000

Relationship a Leverage

Implied leverage con min capital:

Leverage = (4 × Price × Multiplier) / Min Capital
         = Target Vol% / σ%

Esempio S&P (σ 16%, target 20%):

Leverage = 20% / 16% = 1.25×

Low leverage → safe ma richiede molto capital.

Capital Requirements Comparison

Instrument Min Capital (20% target)
S&P 500 micro $72,000
NASDAQ micro $95,000
Gold micro $45,000
Crude Oil $85,000
GBPUSD future $125,000
2-year Bond $12,000

Observation: Low-vol instruments (bonds) = low capital, ma high costs risk-adjusted!

Starter System Approach

Minimum viable: - 1 instrument - 1 contract minimum - Conservative target (12%)

Formula:

Min Capital = (Price × Multiplier × σ%) / 0.12

S&P 500 micro:

Min = 3,600 / 0.12 = $30,000

Pero: Recommend starting con $50,000 per buffer.

Multi-Instrument Portfolio

Aggregate minimum:

Total Min = Σ(Min Capital per instrument) / IDM

Dove IDM = Instrument Diversification Multiplier.

Esempio 3 instruments (IDM ≈ 1.5): - S&P 500: $72k - Gold: $45k - Crude: $85k - Total naive: $202k - With IDM: $202k / 1.5 = $135k

Diversification riduce capital requirement!

Adjusting for Risk Tolerance

More conservative (target 12%):

Min Capital = Standard × (20% / 12%) = Standard × 1.67

More aggressive (target 40%):

Min Capital = Standard × (20% / 40%) = Standard × 0.50

But: Max recommended target = 50%, so min capital never < half standard.

Practical Considerations

Transaction Costs

Lower capital → higher % costs:

$10k capital, $50 annual costs = 0.5% $100k capital, $50 annual costs = 0.05%

Risk-adjusted identical, ma psychological difference.

Margin Requirements

Broker minimum può essere diverso:

Broker requires $5k margin per contract Formula says min capital $72k

Need: Max($72k, broker requirement)

Spesso formula > broker, which is safer.

When Capital Insufficient

Options se non hai min capital:

  1. Trade cheaper instruments: Micro futures invece di standard
  2. Lower target volatility: 12% invece di 20%
  3. Accept limited flexibility: Start con 1-2 contracts
  4. Use CFDs: Lower min capital (ma higher costs)
  5. Wait & save: Better che under-capitalized trading

Warning Signs Under-Capitalization

  • Leverage > 10×
  • Can't adjust positions smoothly
  • One bad day = margin call
  • Commission > 1% of capital
  • Constant stress about positions

Solution: Increase capital or reduce ambitions.

Errori Comuni

  • Starting too small: $5k per futures (disaster!)
  • Ignoring flexibility need: 1 contract, no adjustment room
  • Using max broker leverage: Margin call inevitable
  • Not accounting for costs: Small capital = costs eat returns
  • Overconfidence: "I'll start small and build" (usually fails)

Concetti Correlati

  • [[Position Sizing]] - usa minimum capital come base
  • [[Leverage]] - min capital determines safe leverage
  • [[Volatility Targeting]] - formula deriva da questo
  • [[Risk Adjusted Costs]] - smaller capital = higher % costs