Finance
Portfolio Loss Simulation Calculator
Run a reproducible two-asset Monte Carlo loss simulation with weights, volatility, correlation, a decision threshold, and tail-loss summaries.
SEEDED MONTE CARLO
Explore correlated two-asset loss paths and reproduce the run
This calculator is for allocation questions where two return sources move together imperfectly. It generates thousands of paired shocks, combines them at the selected weight, and stores the seed so an exported result can be rerun exactly.
CURRENT DECISION RECORD
Simulated loss bands
Every row is generated from the current inputs and reused by Copy, TXT, and the page-specific PDF.
| Loss interval ($) | Trials | Share of trials (%) |
|---|
CURRENT CALCULATION PROCESS
Formula, substitution, intermediate values, and reconciliation
rA = muA x t + sigmaA x sqrt(t) x zA; zB = rho x zA + sqrt(1-rho^2) x zIndependent; loss = -V x (w x rA + (1-w) x rB)
Waiting for valid inputs.
HOW TO RUN THE EXPERIMENT
Five steps for a reproducible simulation
- Set the current portfolio value and the actual weight assigned to Asset A.
- Enter separate return and volatility assumptions for both assets.
- Estimate correlation on a period and frequency consistent with the volatility inputs.
- Choose a horizon, trial count, seed, and loss threshold linked to the decision.
- Export the seed and inputs, then challenge the result with alternate correlations and stress assumptions.
FOUNDATIONS
Five simulation concepts that affect the answer
Paired shocks
Each trial draws one shock for Asset A and constructs Asset B's shock from a correlated and an independent component.
Weight closure
Asset B weight is exactly 100% minus Asset A weight, so every trial represents a fully allocated two-asset portfolio.
Seeded randomness
The seed initializes the pseudo-random sequence. Equal inputs and equal seed produce equal output.
Empirical percentile
Simulated VaR is selected from sorted trial losses; it is not inserted from a closed-form normal quantile.
Monte Carlo error
A finite run has sampling noise. Increasing iterations reduces, but never removes, uncertainty caused by the assumed model.
DEEP ANALYSIS
Three levers worth testing separately
Correlation shock
Correlation has little effect on each asset alone but can materially change the combined tail. A prudent review reruns the same seed at normal and stressed correlations so random-sequence differences do not obscure the comparison.
Allocation sensitivity
Changing Asset A weight changes expected return and shock exposure together. Compare allocations using the same value, horizon, iterations, and seed, then inspect both average loss and expected shortfall.
Convergence check
Run 5,000, 20,000, and 100,000 trials with the same assumptions. If the tail estimate still moves enough to change the decision, report a range instead of a falsely precise point estimate.
DECISION CASES
Two realistic simulation uses
Equity and bond liquidity sleeve
A nonprofit holds 60% global equity and 40% intermediate bonds and must fund payroll in 20 trading days. It simulates the sleeve at ordinary correlation, then at a positive stress correlation. The relevant result is whether the threshold breach rate remains tolerable in both runs.
Manager comparison under controlled randomness
An allocator compares a high-volatility return source with a lower-volatility alternative. It holds the seed and all other settings fixed, changes only the Asset A assumptions, and saves both PDFs so the committee can attribute the tail difference to the proposed manager rather than to a new random draw.
TERMS
Monte Carlo portfolio glossary
- Iteration
- One complete simulated pair of asset returns and the resulting portfolio loss.
- Random seed
- The integer that initializes the deterministic pseudo-random sequence used by the run.
- Correlation
- The linear association imposed between standardized shocks to the two assets.
- Box-Muller transform
- A method that converts uniform pseudo-random numbers into standard normal shocks.
- Empirical quantile
- A percentile selected from the ordered simulated losses rather than a theoretical formula.
- Monte Carlo error
- The finite-sample variation in an estimate that remains even when assumptions are unchanged.
EVIDENCE RECORD
What makes the run auditable
Preserve the seed, code version, iteration count, valuation date, portfolio weights, estimation windows for both assets, correlation method, horizon, threshold rationale, and each sensitivity run. A screenshot without the seed and assumptions is not a reproducible simulation record.
LIMITS
Simulation boundaries
- Both asset shocks are normal with constant return, volatility, and correlation.
- The model has two linear assets, no rebalancing, transaction costs, taxes, derivatives, or liquidity feedback.
- Extreme loss frequency can be understated when observed returns have fat tails or volatility clustering.
- The histogram uses broad decision bands and should not be read as a smooth fitted density.
Disclaimer: The simulation is a controlled experiment under stated assumptions, not a probability guarantee or investment recommendation.
SOURCES
Simulation and investor-risk references
FAQ
Questions specific to this two-asset simulation
Why does changing the seed change the result?
It selects a different finite set of shocks. Large differences across seeds suggest the trial count is too small for the precision the decision requires.
Does 100,000 iterations make the assumptions correct?
No. More trials reduce numerical sampling noise but do not repair incorrect return, volatility, correlation, or distribution assumptions.
What happens at correlation 1?
The independent component for Asset B becomes zero, so both standardized shocks move together. Different volatilities and returns still produce different asset returns.
What happens at correlation -1?
Asset B's standardized shock is the exact opposite of Asset A's. Depending on weights and volatilities, shock risk may offset substantially.
Why can a loss band include negative dollars?
The page uses a loss convention. A negative loss is a portfolio gain in that trial.
Can this model represent options or stop-loss rules?
No. It combines two linear asset returns. Nonlinear payoffs and path-dependent trading rules need a purpose-built simulation.