Standard Deviation and Volatility

The number

The standard deviation of annual returns for common asset classes (historical approximations):

• Cash: ~1%
• U.S. intermediate bonds: ~5–6%
• U.S. large-cap stocks: ~15–17%
• U.S. small-cap stocks: ~20–22%
• Emerging market stocks: ~25–30%
• Individual stocks: 30%+ commonly, sometimes much higher

A stock index with 17% volatility and 10% average return will, in most years, produce a return between roughly −7% and +27% — that's one standard deviation around the mean.

What it tells you

Under the assumption that returns are roughly normally distributed:

• 68% of years will fall within one standard deviation of the mean.
• 95% of years will fall within two standard deviations.
• 99.7% of years will fall within three standard deviations.

For a stock portfolio with 10% mean and 17% SD:

• 68% of years: −7% to +27%
• 95% of years: −24% to +44%
• 99.7% of years: −41% to +61%

Real market returns have slightly fatter tails than a normal distribution — extreme events happen more often than the bell curve predicts. 2008, 2020 flash crash, 2022 bond collapse. But the framework is still useful for building intuition.

Volatility is symmetric — portfolios aren't

A common mistake: assuming a portfolio that gains 10% one year and loses 10% the next breaks even. It doesn't.

$100 → 10% gain → $110 → 10% loss → $99.

That gap gets larger as volatility increases:

• +30%, −30%: $100 → $130 → $91 (9% loss).
• +50%, −50%: $100 → $150 → $75 (25% loss).

This is called volatility drag, and it's the reason that high-volatility strategies underperform their arithmetic averages. A fund that averages 10% per year with 25% volatility has a geometric (actual compounded) return closer to 7%.

Sharpe ratio

The Sharpe ratio measures return per unit of risk: (return − risk-free rate) / standard deviation. Higher is better. It's how sophisticated investors compare strategies with different volatility profiles. A strategy earning 10% with 15% volatility (Sharpe ≈ 0.5 if risk-free rate is 2.5%) is roughly as attractive as one earning 15% with 25% volatility (same Sharpe).

The Monte Carlo connection

Horizons' Monte Carlo engine uses volatility directly: each trial draws returns from distributions with the right mean and standard deviation for each strategy, plus correlations between factors. When you see a wide fan chart, you're seeing high volatility. When you see a tight chart, you're seeing lower volatility — which usually means a more conservative portfolio or shorter horizon.

Can you reduce volatility?

Yes, through diversification and allocation:

• Adding bonds to a stock portfolio lowers volatility more than it lowers return.
• International diversification reduces country-specific risk.
• Factor tilts (value, small-cap, quality) sometimes reduce volatility relative to cap-weighted indexes.

The historical 60/40 portfolio (60% stocks, 40% bonds) has volatility around 10% — meaningfully less than a pure stock portfolio while still capturing most of the long-run return.

How Horizons uses this

Each investment strategy in Horizons has an expected return and a volatility. Monte Carlo draws from that distribution 200+ times to generate the fan chart you see. The risk-of-ruin number is essentially counting how many of those trials end with the portfolio at zero — a direct translation of volatility into plan survival probability.