Portfolio Calculations
This page explains how we calculate portfolio-level numbers from the inputs in The ETFs (expected return, volatility) and How They Move Together (correlations).
You don't need to understand the formulas to use HalalFolio. But if you're curious about why certain combinations reduce risk, this is how.
Portfolio Expected Return
This part is simple. The portfolio's expected return is the weighted average of each asset's expected return.
Example:
| ETF | Allocation | Expected Return |
|---|---|---|
| HLAL (U.S. Stocks) | 60% | 7% |
| GLDM (Gold) | 40% | 5% |
Portfolio Expected Return = (0.60 × 7%) + (0.40 × 5%) = 6.2%
Nothing surprising here. If you hold more of the higher-returning asset, your portfolio's expected return goes up.
Portfolio Volatility
This is where it gets interesting. Portfolio volatility is not a simple weighted average.
If you hold two assets with low correlation, the portfolio volatility can be significantly lower than either asset alone.
The intuition: When Asset A zigs, Asset B may zag. The movements partially cancel out. Your combined portfolio becomes smoother.
A Worked Example
Let's calculate both metrics for a simple 60/40 portfolio.
Inputs
| Asset | Weight | Expected Return | Volatility |
|---|---|---|---|
| U.S. Stocks (HLAL) | 60% | 7% | 15% |
| Gold (GLDM) | 40% | 5% | 15% |
Correlation between stocks and gold: 0.00 (they move independently)
Expected Return
(0.60 × 7%) + (0.40 × 5%) = 6.2%
Volatility
Variance = (0.60 × 0.15)² + (0.40 × 0.15)² + 2 × 0.60 × 0.40 × 0.15 × 0.15 × 0.00
= 0.0081 + 0.0036 + 0
= 0.0117
Volatility = √0.0117 = 10.8%
What Happens with High Correlation
If the correlation were +1.0 (perfect lockstep), the math changes:
Variance = (0.60 × 0.15)² + (0.40 × 0.15)² + 2 × 0.60 × 0.40 × 0.15 × 0.15 × 1.0
= 0.0081 + 0.0036 + 0.0108
= 0.0225
Volatility = √0.0225 = 15%
Where You See This in HalalFolio
When you build or view a portfolio, HalalFolio runs these calculations:
- Expected Return — shown as a percentage, calculated from weighted ETF returns
- Volatility — shown as a percentage, calculated using the correlation matrix
- Projections — future value estimates based on these assumptions
The model portfolios are designed with correlation in mind. Conservative portfolios have more sukuk and gold (low correlation with stocks). Growth portfolios lean heavily into equities (high correlation with each other, but higher expected return).
The Limits
These calculations are only as good as the inputs.
Estimation error: Expected returns are guesses. Volatility and correlations shift over time.
Fat tails: The math assumes a bell curve distribution. In reality, extreme events (2008, COVID) happen more often than the model predicts.
Correlation breakdown: During panics, correlations spike toward 1.0. Diversification can fail precisely when you need it most.
But imperfect math is still better than no math. It gives you a structured way to think about risk and return together.
Summary
For the inputs behind these calculations, see The ETFs and How They Move Together.