Risk and what it costs.

Volatility

How much a return bounces around its average. The standard measure of risk, and an incomplete one.

Volatility is the dispersion of returns, usually quoted as an annual standard deviation. A portfolio returning 7% with 16% volatility will spend most years somewhere between minus 9 and plus 23, and occasionally well outside that.

It is useful because it is measurable and it compounds against you: two portfolios with the same average return but different volatility do not end up in the same place, because losses require larger gains to undo. It is incomplete because it treats an upside surprise as identical to a downside one, and because the thing that actually ruins people is not variance, it is being forced to sell during the bad part.

What it does to a withdrawal plan: what a million dollars actually pays.

Volatility drag

The gap between the average return and the return you actually compound at. Roughly half the variance, every year.

An investment that gains 60% one year and loses 40% the next has averaged 10% a year and lost 4% of your money. The average is a statistic about the returns. What you keep depends on the returns multiplied together, and a loss always needs a larger gain to undo it.

The rule of thumb is that the typical compound return is the average minus half the variance. With an 8% expected return and 20% volatility, the typical outcome compounds at 5.9% a year. At 50% volatility it is -4.7%: the same expected return, and the typical holder loses money.

It is why concentrated positions cost more than their average suggests, and why daily-reset leveraged funds do not deliver their stated multiple over time: leverage multiplies the average and squares the drag.

The full treatment: the average return is not the return you get.

Beta

How much a holding moves when the market moves. One means it tracks; above one means it amplifies.

Beta separates the part of a stock's movement explained by the market from the part specific to the company. A beta of 1.1 means that when the market rises 10%, this stock has historically risen about 11%, before anything company-specific happens on top.

It matters because market risk is compensated and company-specific risk is not. You are paid for bearing the first because it cannot be diversified away. You are not paid for the second, because it can be removed for free by owning more companies, which is the entire argument against concentration.

Why the uncompensated half costs you: your employer already owns enough of you.

Drawdown

The fall from a peak to the following trough, measured in percent. What risk actually feels like.

Volatility is a statistic. A drawdown is an experience. It is the number that determines whether a plan survives contact with its owner, because it measures the worst it got rather than how much it wobbled on average.

The arithmetic of recovery is the part people underestimate. A 20% fall needs a 25% gain to get back. A 50% fall needs 100%. That asymmetry is why avoiding large drawdowns matters more than capturing the last increment of return, and why leverage is so dangerous even when the expected return is positive.

What to do while one is happening: the price of admission.

Diversification

Owning enough different things that no single one can decide the outcome. The only free lunch in finance.

It is free in a specific, literal sense: it reduces risk without reducing expected return, which nothing else does. Every other risk reduction costs you something, usually return, sometimes liquidity.

The effect is largest where concentration is highest. Moving a portfolio from fully diversified to half in a single stock costs $95,166 at the median on $200,000 over 10 years, and raises the chance of ending below where you started from 13.1% to 35.8%, while the good case barely moves.

The arithmetic in full: employer stock concentration, and the base rate in index funds are the right answer.

Correlation

Whether two things move together. Diversification only works when they do not.

Owning twenty holdings that all rise and fall together is one position wearing twenty names. What reduces risk is not the count but the independence, and independence is not constant.

The cruel property of correlation is that it rises in crises. Assets that behaved differently for a decade can move as one in a bad month, which is precisely when you needed them not to. A diversification benefit measured in calm conditions overstates what you will get when it matters.

The version that affects most people has nothing to do with markets. If your employer's shares fall, your bonus, your next grant and your job security are all impaired in the same quarter. That is a correlation, and it is the one worth managing first.

The correlation nobody models: your employer already owns enough of you.

Path dependency

When the order of returns changes the outcome, not just the average. True whenever money moves in or out.

If you neither add nor withdraw, only the average return matters and the order is irrelevant. The moment you are contributing or drawing down, order decides everything, because a bad year hits a different amount of money depending on when it lands.

For a saver this works in your favor: early falls buy more shares. For a retiree it is the central risk, because an early bad run permanently shrinks the base that has to last. Two retirements with identical average returns and different orderings do not end the same way.

The full treatment: the order your returns arrive in.

Concentration risk

The risk you are not paid to take. What happens when one holding is large enough to decide the outcome.

Market risk is compensated because it cannot be removed. Company-specific risk is not compensated, because it can be removed for free by owning more companies. A concentrated portfolio therefore carries extra risk with no extra expected return attached, which is the one trade in finance that is unambiguously bad.

The cost is measurable. Moving a $200,000 portfolio from fully diversified to half in a single stock costs $95,166 at the median over 10 years, and raises the probability of ending below where you started from 13.1% to 35.8%. The good case barely improves, which is the point: the distribution gets wider at the bottom and not at the top.

It shows up in places that do not look like a portfolio decision. Employer stock concentrates your investments in the same company that pays your salary, so one event takes both. A house is a large, leveraged, undiversified position in one street. Counting those is the difference between a diversified portfolio and a diversified brokerage account.

The arithmetic in full: your employer already owns enough of you. Run your own numbers: the concentration risk worksheet.