Editing Openai/694a9127-1940-8001-9b22-f125f741a780 (section)

=== 🧮 MODULE 20 — KELLY-FRACTION ADAPTIVE RISK (INSTITUTIONAL SAFE) ===

==== 🎯 Objective ====

Continuously size risk based on edge strength, but:
* Cap aggression
* Respect drawdown
* Respect regime & correlation filters
* Never go full Kelly (too volatile)

==== 1️⃣ Kelly Math (R-Based, Robust) ====

Classic Kelly:

f∗=bp−qbf^* = \frac{bp - q}{b}f∗=bbp−q
Where:
* bbb = reward-to-risk (RR)
* ppp = win probability
* q=1−pq = 1 - pq=1−p

We derive p and b from live trade history, not assumptions.

==== 2️⃣ Data Buckets (Context-Aware Kelly) ====

We reuse expectancy context, because Kelly must be conditional.

<syntaxhighlight lang="pinescript">var array<string> k_keys   = array.new_string()
var array<int>    k_wins   = array.new_int()
var array<int>    k_losses = array.new_int()
var array<float>  k_rsum   = array.new_float()

</syntaxhighlight>

==== 3️⃣ Kelly Key (Same Context as Expectancy) ====

<syntaxhighlight lang="pinescript">kelly_key(string session, string regime, string htf_bias, string side) =>
    session + "|" + regime + "|" + htf_bias + "|" + side

</syntaxhighlight>

==== 4️⃣ Update Kelly Stats (After Trade Close) ====

Call once per closed trade:

<syntaxhighlight lang="pinescript">update_kelly(string key, float trade_r) =>
    idx = array.indexof(k_keys, key)

    if idx == -1
        array.push(k_keys, key)
        array.push(k_wins, trade_r > 0 ? 1 : 0)
        array.push(k_losses, trade_r <= 0 ? 1 : 0)
        array.push(k_rsum, trade_r)
    else
        array.set(k_wins, idx,
            array.get(k_wins, idx) + (trade_r > 0 ? 1 : 0))
        array.set(k_losses, idx,
            array.get(k_losses, idx) + (trade_r <= 0 ? 1 : 0))
        array.set(k_rsum, idx,
            array.get(k_rsum, idx) + trade_r)

</syntaxhighlight>

==== 5️⃣ Kelly Fraction Calculation (CAPPED & SAFE) ====

<syntaxhighlight lang="pinescript">calc_kelly_fraction(string key) =>
    idx = array.indexof(k_keys, key)
    if idx == -1
        0.0
    else
        wins   = array.get(k_wins, idx)
        losses = array.get(k_losses, idx)
        total  = wins + losses

        if total < 20
            0.0
        else
            p = wins / total
            avg_r = array.get(k_rsum, idx) / total
            b = math.max(avg_r, 0.1)

            raw_kelly = (b * p - (1 - p)) / b

            // HARD SAFETY CAPS
            math.clamp(raw_kelly, 0.0, 0.25)

</syntaxhighlight>

🔒 Important
* Minimum sample size
* Kelly ≤ 25%
* Negative edge → zero risk

==== 6️⃣ Fractional Kelly (Prop-Safe) ====

Never use full Kelly.

<syntaxhighlight lang="pinescript">KELLY_FRACTION = 0.30   // 30% Kelly (recommended)

</syntaxhighlight>

<syntaxhighlight lang="pinescript">kelly_mult = calc_kelly_fraction(k_key) * KELLY_FRACTION

</syntaxhighlight>

==== 7️⃣ Final Risk Composition (CRITICAL) ====

Your final risk per trade becomes:

<syntaxhighlight lang="pinescript">base_risk = get_risk_pct(regime)

// Apply system modifiers
risk_pct =
     base_risk
   * equity_risk_mult
   * corr_risk_mult
   * htf_risk_mult(htf_bias, side)

// Apply Kelly LAST
risk_pct := risk_pct * (1 + kelly_mult)

// Absolute hard cap (prop-safe)
risk_pct := math.min(risk_pct, 1.0)

</syntaxhighlight>

✔ Kelly only amplifies edge
✔ Never increases risk during drawdown
✔ Automatically shrinks to zero when edge disappears

==== 8️⃣ Master Safety Override ====

If any of these are true → Kelly ignored:

<syntaxhighlight lang="pinescript">if trading_paused or equity_regime() == "cold" or corr_regime == "high"
    kelly_mult := 0.0

</syntaxhighlight>

==== 9️⃣ Where to Call Updates (Summary) ====

After each closed trade:

<syntaxhighlight lang="pinescript">k_key = kelly_key(session, regime, htf_bias, side)

update_kelly(k_key, trade_r)
update_expectancy(exp_key, trade_r)
update_regime_stats(regime, trade_r)
update_equity(trade_r)
update_drawdown()

</syntaxhighlight>