Personal finance, from zero Lesson 29 / 60

Volatility and risk: the math that isn't scary

Standard deviation in plain language. Why '7% per year' hides huge year-to-year swings, and what to expect from a diversified equity portfolio.

“Stocks return 7% per year on average.”

This is both true and deeply misleading. The word “average” hides what actually happens: in reality, stocks returned +24% one year, −19% another, +11% another, −3% another, +31% another. The 7% is the geometric mean across decades, not what happens in any particular year.

Today’s lesson is about volatility — what it is, how to measure it, and what to realistically expect from your equity and bond holdings.

Volatility, in one sentence

Volatility is how much returns vary around their average.

Two investments can both have 7% average return, but one with volatility 5% looks like [5%, 9%, 6%, 8%, 7%] (calm) and another with volatility 20% looks like [−15%, 30%, −5%, 20%, 5%] (wild).

They have the same “expected return” (mathematical average). Their experience is vastly different.

Standard deviation

The most common measure of volatility is standard deviation (σ, sigma). Intuition: σ measures the “typical” distance of a data point from the mean.

For an asset with:

  • Mean return: 7% per year.
  • Standard deviation: 20%.

The rough interpretation (assuming returns are roughly normally distributed, which isn’t exactly true but useful):

  • ~68% of years, return is between mean − σ and mean + σ: between −13% and +27%.
  • ~95% of years, return is between mean − 2σ and mean + 2σ: between −33% and +47%.
  • ~99% of years, return is between −53% and +67%.

That’s a wide range. Global equity has historical σ around 15-20%. So any given year, a 20% loss is roughly a 1-in-6 event, and a 40% loss roughly a 1-in-40 event. Rare, not impossible.

Historical numbers, EU-focused

Rough annualized volatility of major asset classes (based on multi-decade data):

Asset classReal returnVolatility (σ)
Cash (short-term EUR deposits)0-0.5%1-2%
Short-term EUR government bonds1-2%3-5%
Long-term EUR government bonds2-3%7-12%
EUR corporate bonds2-3%5-9%
European equities4-6%18-22%
Global equities5-7%15-18%
Emerging market equities5-7%22-28%
Gold1-3%15-18%
Italian real estate1-2%10-15%

Source: multi-decade historical data from JP Morgan Long-Term Capital Market Assumptions, Credit Suisse Global Investment Returns Yearbook.

Numbers approximate; vary by sub-period. But the ranking is stable — equities are more volatile than bonds, and international diversification lowers volatility vs single-country.

What volatility feels like

Textbook numbers don’t capture the emotional experience. Some real historical examples:

  • 2008 global financial crisis: MSCI World lost ~42% peak-to-trough. Took 5 years to recover nominally, 7 years in real terms.
  • 2020 COVID: −34% in 5 weeks, then +70% in 9 months. Whiplash.
  • 2022: global equity −18%, bonds −13%. Both down — rare.

A typical 20-year investor will experience at least 1-2 bear markets of 30%+ drawdown. Plan for this. Don’t be surprised by it.

Sofia started investing in 2023. Her first real test will come. Not “if” — “when.”

Why volatility matters for planning

Three practical consequences:

1. Sequence of returns risk

For someone accumulating (still working, adding money), a market crash early-on is actually helpful — you buy at lower prices for longer.

For someone decumulating (retired, withdrawing), a market crash early in retirement can permanently reduce sustainability. Withdrawing during a crash locks in losses and leaves less capital to recover.

This is why many retirees gradually shift toward bonds: less volatility means less sequence-of-returns risk during withdrawal years.

2. Time horizon matters

Annual volatility doesn’t care about time horizon. 20-year annualized return volatility is much lower than 1-year. On decades-long horizons, equities tend to deliver positive real returns with high confidence. On 1-year horizons, they’re a coin flip.

Rough rule: match asset volatility to your actual need-the-money timeline. Cash for this month’s rent; bonds for money you need in 2-5 years; equities for money you won’t need for 10+ years.

3. Psychological tolerance

Even if you “can” tolerate a 40% drop financially, can you tolerate it psychologically? Many people can’t. They sell at the bottom.

The data is clear: retail investors who sell in crashes earn worse returns than the underlying funds they hold. The gap — called “behavior gap” — is often 2-3% per year, compounded over decades is enormous.

Self-knowledge is the defense. If you know you’d panic-sell at −30%, build a portfolio (more bonds) that doesn’t drop that much. Not the theoretically optimal portfolio — the one you can actually stick with.

Diversification and volatility

Combining assets with imperfect correlation reduces portfolio volatility below the average of components’ volatilities.

Simple example:

  • Asset A: 10% return, 20% volatility.
  • Asset B: 10% return, 20% volatility.
  • 50/50 mix if correlation = 1.0 (perfect): 20% volatility (no diversification).
  • 50/50 mix if correlation = 0.5: ~17% volatility.
  • 50/50 mix if correlation = 0.0: ~14% volatility.
  • 50/50 mix if correlation = −0.5: ~11% volatility.

In reality, stocks and bonds are often somewhat positively correlated (0.2-0.4), which still gives meaningful diversification. Gold and commodities have lower or negative correlation with equities at times. Real estate correlations vary.

A classic 60% stocks + 40% bonds portfolio typically has volatility around 10-12%, vs 15-18% for 100% stocks. The return is lower (about 5% real vs 7%), but the smoother ride often helps investor behavior.

Max drawdown

Volatility (σ) is about dispersion. Max drawdown is about worst-case trough.

Max drawdown = from any peak to any subsequent trough, what’s the biggest cumulative loss?

Historical max drawdowns:

  • MSCI World since 1970: −50% (2008).
  • S&P 500 since 1928: −85% (1929-1932).
  • Global 60/40 portfolio since 1970: −32% (2008).
  • EUR aggregate bonds since 1970: −15% (2022).

For planning, consider not just the typical-year volatility but the “what’s the worst drop I could face.” Keep enough non-equity assets that this drop doesn’t threaten life plans.

The “risk” beyond volatility

Volatility is just one kind of risk. Others:

  • Inflation risk. Bonds feel safe until 5% inflation eats them.
  • Longevity risk. Running out of money before running out of life.
  • Sequence risk. Bad returns early in retirement.
  • Concentration risk. Putting too much in one thing.
  • Behavioral risk. Panic-selling at the wrong time.

A portfolio optimized to minimize volatility (cash only) has zero equity volatility but maximum inflation + longevity risk.

Good planning considers all risks, not just the one easy to measure.

What to do with this lesson

Three things:

  1. Know your portfolio’s volatility. Sum σ across your holdings, roughly. 100% global equity is ~18%. 60/40 is ~12%. Cash is ~1%. Decide what you can tolerate.
  2. Stress-test yourself psychologically. Imagine your portfolio drops 40% in 6 months. Can you not sell? If yes, you can hold more equity. If no, hold more bonds.
  3. Plan for the inevitable bear market. Every 20-year horizon has at least one. Expect it. Plan for it. Don’t be surprised.

Sources

  • JP Morgan Asset ManagementLong-Term Capital Market Assumptions. Annual publication. https://am.jpmorgan.com/.
  • Credit Suisse / UBSGlobal Investment Returns Yearbook. https://www.ubs.com/ (retrieved 2025-02).
  • Dimson, Marsh, StauntonTriumph of the Optimists: 101 Years of Global Investment Returns, Princeton University Press, 2002.
  • Morgan HouselThe Psychology of Money, 2020 — excellent on behavioral aspects.

Next lesson: efficient markets and why you probably can’t beat them. EMH, the active vs passive debate, SPIVA data, and what it actually means for your strategy.

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