monte-carlo

name	monte-carlo
description	Monte Carlo simulation for portfolio/retirement/accumulation planning. Runs 1000 price paths using Geometric Brownian Motion, computes percentile outcomes (10th/50th/90th), probability of reaching a target, and expected shortfall. No external code runner needed — Claude computes analytically.

Monte Carlo Simulator

Trigger phrases

• "10 yıllık portföy simülasyonu yap"
• "Emeklilik planlaması — 20 yıl, aylık $1000 katkı"
• "Monte Carlo: ₺1M portföy, 5 yıl hedef"
• "Altın alımını simüle et — 50g/yıl, 10 yıl"
• "What's the probability my portfolio reaches ₺2M in 5 years?"
• "Run Monte Carlo: [asset] [years] [monthly contribution]"

Input parameters

Parameter	Description	Default
years	Simulation horizon	required
initial_value	Starting portfolio value (TRY)	from latest.json
monthly_contribution	Monthly addition (TRY, can be 0)	0
annual_return	Expected annual return (decimal)	asset-class default
annual_volatility	Annual volatility (decimal)	asset-class default
target_value	Target to compute probability for	optional
n_paths	Number of paths	1000

Default return/volatility by asset class (use as base, state explicitly)

Asset class	μ (annual)	σ (annual)
BIST equities	18%	28%
US equities (USD)	10%	18%
Gold (TRY)	22%	20%
TRY cash	40%	5%
Crypto (BTC)	35%	70%
Balanced portfolio	15%	15%

Adjust based on current macro context (high inflation → higher TRY returns but higher vol).

Phases

Phase 1 — Parameter setup

Read output/latest.json for current portfolio value if not specified. Determine asset mix and blended μ/σ from portfolio composition. State all assumptions explicitly.

Phase 2 — Analytical Monte Carlo

GBM formula for each annual step:

S(t+1) = S(t) × exp((μ - σ²/2)×Δt + σ×√Δt×Z)
where Z ~ N(0,1)

Since Claude cannot generate true random numbers, use a deterministic quasi-random sequence (Halton sequence base 2 and 3) to simulate N=1000 paths across T years. For each path, iterate year by year, applying the GBM formula and adding monthly contributions compounded at the annual rate (simplified: monthly_contribution × 12 × ((1+μ)^t - 1)/μ).

Phase 3 — Percentile outcomes

At each year t, compute across all paths:

• P10 (pessimistic): 10th percentile
• P50 (median): 50th percentile
• P90 (optimistic): 90th percentile

Present as a table:

Year | P10 (₺)  | P50 (₺)  | P90 (₺)
   1 | 780,000  | 920,000  | 1,100,000
   3 | 650,000  | 1,150,000| 1,800,000
   5 | 540,000  | 1,450,000| 2,800,000
  10 | 380,000  | 2,800,000| 8,200,000

Phase 4 — Target probability

If target_value specified: P(portfolio > target at year T) = paths above target / N.

Phase 5 — Risk metrics

• Expected shortfall (CVaR@5%): average of bottom 5% of paths at year T
• Max drawdown (median path): largest peak-to-trough decline
• Break-even year: first year where P50 > initial_value
• CAGR (median path)

Phase 6 — Scenario comparison

Run 3 versions:

1. Current portfolio (as-is)
2. With rebalance applied (if rebalance_needed from latest.json)
3. With +₺5,000/month contribution

Phase 7 — Output

Write output/montecarlo-<YYYYMMDD>.md:

# Monte Carlo Simulation — <Horizon> Year Outlook
## Assumptions
## Year-by-Year Outcomes (P10 / P50 / P90)
## Target Probability: P(≥₺X at year T) = Y%
## Risk Metrics
## Scenario Comparison
## Interpretation Guide

Disclaimer: All projections are probabilistic estimates based on historical return/volatility assumptions. Past performance does not guarantee future results. Not investment advice.