Monte Carlo Simulation for Investment Risk Assessment

Introduction

Monte Carlo simulation is a powerful computational technique that uses random sampling to obtain numerical results for problems that might be deterministic in principle. In investment risk assessment, it provides a probabilistic framework for understanding potential outcomes.

Methodology

1. Variable Identification

Identify all key variables that affect investment returns:

Market returns (equity, fixed income, commodities)

Interest rates

Currency exchange rates

Inflation rates

Default probabilities

2. Distribution Fitting

For each variable, fit an appropriate probability distribution using historical data:

Normal distribution for log returns

Student-t for fat-tailed distributions

Copulas for modeling dependencies

3. Simulation Engine

Generate 10,000+ scenarios using correlated random variables:

For each simulation i = 1 to N:

Generate correlated random variables Z

Calculate portfolio value P(i)

Store result

4. Risk Metrics Calculation

**Value at Risk (VaR)**: The maximum loss at a given confidence level

**Conditional VaR (CVaR)**: Expected loss beyond VaR

**Maximum Drawdown**: Largest peak-to-trough decline

Application: Egyptian Market Portfolio

We applied this methodology to a diversified Egyptian portfolio:

40% Egyptian equities (EGX30)

30% Government bonds

20% Real estate

10% USD-denominated assets

Results (95% Confidence)

1-Year VaR: -18.5%

CVaR: -24.2%

Probability of positive return: 67.3%

Expected return: +8.7%

Stress Testing Scenarios

We additionally modeled three stress scenarios:

1. Currency shock: 30% devaluation

2. Interest rate spike: +500bps

3. Combined stress: Both scenarios simultaneously

Conclusion

Monte Carlo simulation provides investment decision-makers with a nuanced understanding of portfolio risk that traditional methods cannot match.