Correlated Market Factors

Why correlations matter

In a diversified 60/40 portfolio with independent returns:

• In a bad year for stocks, bonds might be up, down, or flat — random.
• Portfolio volatility is the square root of weighted variance.
• "Diversification" is maximized.

In reality:

• In a bad year driven by inflation (2022), stocks and bonds both decline. A 60/40 portfolio drops meaningfully more than independent-random would predict.
• In a flight-to-safety crisis (2008), stocks crash and high-quality bonds rally. Diversification works better than independence predicted.
• In a deflationary shock, everything rallies except risk assets — bonds and cash outperform.

Different market regimes produce different correlations. Static independent-return models miss this.

The six factors in Horizons

Horizons' Monte Carlo models six market factors, each with specific distribution parameters:

1. Aggressive-strategy returns. Stock-heavy portfolios. Mean ~7% real, SD ~15%.

2. Moderate-strategy returns. Balanced. Mean ~5% real, SD ~10%.

3. Conservative-strategy returns. Bond-heavy. Mean ~3% real, SD ~6%.

4. Interest rates. Short-term rates. Mean ~3% nominal, SD ~1.5%, AR(1) persistence.

5. Inflation. CPI. Mean ~2.5%, SD ~1%, AR(1) persistence.

6. Housing appreciation. Mean ~3.5% nominal, SD ~6%.

Each factor has correlations with the others, informed by historical relationships.

The correlation structure

Approximate correlations among the factors (positive or negative):

• Aggressive & Moderate & Conservative: all strongly positive (same broad market).
• Rates & Inflation: strongly positive (central banks raise rates in inflationary environments).
• Rates & Conservative returns: strongly negative (rising rates hurt bonds).
• Inflation & Aggressive returns: negatively correlated in some regimes (high inflation hurts valuations).
• Housing & Aggressive: moderately positive (general economic conditions).
• Housing & Rates: moderately negative (lower rates boost housing demand).

These aren't fixed numbers; they vary across periods. Horizons uses blended historical averages that capture typical relationships.

AR(1) persistence

Some variables have "memory" — last year's value influences this year's. Interest rates and inflation in particular:

• A year of 6% inflation is typically followed by another year of elevated inflation, not an immediate snap back to 2%.
• Interest rates set by central banks move in deliberate cycles, not random walks.

AR(1) models this: this year's value = ρ × last year's value + (1−ρ) × mean + noise. With ρ = 0.9, 90% of last year's deviation persists.

This matters because plans that assume fast mean reversion may underestimate the damage of a sustained high-inflation period.

Why it matters for plans

Correlated factors produce more realistic risk assessments:

60/40 portfolio in a high-inflation year. Independent model: bonds might be flat while stocks drop, softening the blow. Correlated model: stocks and bonds both fall, exacerbating drawdown. The real 2022 experience.

Retiree withdrawing during a crisis. Independent model: portfolio might have one asset class to draw from without pain. Correlated model: everything drops together; drawdowns compound withdrawals.

Home as part of net worth. Independent model: home might rally when stocks fall, buffering. Correlated model: recessions hit housing and stocks together (2008).

Regime changes

Markets go through regimes — periods with consistent correlation structures that then shift. Historical data includes multiple regimes:

• 1980s–2000: disinflation era, strong stock-bond negative correlation, "Great Moderation."
• 2000–2007: housing bubble era.
• 2008–2009: financial crisis, flight-to-safety dominated.
• 2010–2019: low-rate, low-inflation era, stocks up consistently.
• 2020: COVID dislocations.
• 2022: inflation shock, stocks and bonds down together.

Using long-run averages is reasonable for planning, but real experience will include regime-specific conditions that the model doesn't fully capture.

Tail correlations

A specific problem: correlations often become more extreme during market stress. In normal years, stocks and bonds have moderate correlation. In crises, correlations can spike to 1.0 (everything moves together, usually down).

This "tail dependence" isn't well-modeled by standard multivariate normal distributions. Advanced copula-based models handle it better but add complexity. Horizons uses a blended approach that produces realistic tail behavior.

What to read in the output

When looking at your Horizons Monte Carlo:

• Fan chart in moderate scenarios reflects typical correlation structure.
• Worst trials often represent scenarios where inflation rose, rates rose, stocks fell, and the retiree kept withdrawing — correlated disaster.
• Best trials represent benign environments — low inflation, low rates, strong stock returns, housing appreciation.

How Horizons uses this

Horizons' factor model draws correlated shocks each year across all six factors, applies them to your specific portfolio composition, and propagates the results through your forecast. The output is a realistic distribution of outcomes that captures the joint risk structure of real markets, not just the marginal volatility of each asset class.