Measuring Portfolio Risk: Volatility, Beta, Sharpe and Drawdown

None of these four numbers measures risk. They measure different shadows of it, they disagree with each other, and only one of them has ever made anybody sell at the bottom. Learn all four. Then watch that one.

Volatility: the spread, worked by hand

Volatility is the standard deviation of returns. Take five annual results: plus 12 percent, minus 8, plus 18, plus 4, minus 2. The average is (12 - 8 + 18 + 4 - 2) / 5 = 4.8%.

Square each deviation from that average and add them: 7.2^2 + (-12.8)^2 + 13.2^2 + (-0.8)^2 + (-6.8)^2 = 436.8. Divide by n - 1, which is 4, for a variance of 109.2, then take the square root: 10.45%.

So the portfolio has averaged 4.8 percent a year and swung about 10.4 percent around that, which means in a typical year the result landed somewhere between minus 5.6 and plus 15.2 percent, one standard deviation either side.

Why volatility flatters a portfolio

Two problems, and both of them matter to you.

The first is that standard deviation treats a 15 percent gain and a 15 percent loss as equally risky, because it measures spread in both directions. Nobody has ever called their partner in a panic about an unexpected gain.

The second is that the arithmetic assumes a tidier distribution of returns than markets produce, and the truly bad months arrive more often, and land harder, than a volatility figure implies. Treat it as a rough gauge. It describes how bumpy the ride has been. It says nothing about the worst case.

Beta: how much of the movement was just the market

Beta compares a portfolio’s moves with a benchmark index. Usually the S&P 500. A beta of 1.0 means it has tracked the market, a beta of 1.3 means it has amplified the market’s moves by about 30 percent in both directions, and a beta of 0.7 means it moved about 70 percent as much.

The use is immediate. A portfolio with a beta of 1.2, in a market that falls 10 percent, would be expected to fall about 12 percent from that market move alone. On $200,000 that is a $24,000 fall where you planned for $20,000, and the extra $4,000 is the part you did not budget for.

You can approximate your own by weighting each holding’s beta: a portfolio that is 70 percent in a fund with a beta of 1.1 and 30 percent in one with a beta of 0.2 comes out at 0.7 x 1.1 + 0.3 x 0.2 = 0.83.

Where beta earns its keep is checking a portfolio against its own description: a retiree who believes she holds something conservative, and whose holdings carry a combined beta of 1.15, owns a more aggressive portfolio than her plan says she does.

What beta cannot see is concentration. Five companies can produce a beta near 1.0 while being vastly riskier than the index, because most of that risk is company specific, the kind diversification exists to remove, and beta is blind to it and says nothing when it bites.

Sharpe: what the movement bought you

Sharpe = (portfolio return - risk-free rate) / portfolio volatility

Compare two portfolios over the same twelve months, in a year when cash pays 4 percent.

Portfolio	Return	Volatility	Excess return	Sharpe
A, aggressive	9%	12%	5%	0.42
B, balanced	7%	6%	3%	0.50

Portfolio A made more money. Portfolio B was paid better for the risk it took, earning 0.50 percentage points of excess return per point of volatility against A’s 0.42, so which one you want depends entirely on whether you can hold A through its worse quarters. That is a question about you.

Two rules before you use it. Only compare Sharpe ratios measured over the same period, because the risk-free rate moves and a ratio from a 5 percent cash era does not compare with one from a zero rate era. And treat small differences as noise. These are estimates drawn from limited history. The Sharpe ratio calculator handles the arithmetic on your own figures.

Drawdown: the number that decides whether you sell

Maximum drawdown is the largest fall from a peak to the trough that followed it, and of the four it is the only one that describes what owning the thing actually felt like.

Its importance comes from an asymmetry that catches people out every time: recovering from a loss takes a bigger percentage gain than the loss itself, because the gain is earned on a smaller base.

gain needed = 1 / (1 - loss) - 1

A $100,000 portfolio falls 25 percent and is worth $75,000. Getting back to $100,000 means making $25,000 on a $75,000 base, and 25,000 / 75,000 = 33.3%. The formula agrees: 1 / 0.75 - 1 = 0.333.

The recovery table, and where the curve turns cruel

Drawdown	Gain needed to recover	On $100,000 you are left with
10%	11.1%	$90,000
20%	25.0%	$80,000
25%	33.3%	$75,000
30%	42.9%	$70,000
40%	66.7%	$60,000
50%	100.0%	$50,000
60%	150.0%	$40,000

Past 30 percent the curve steepens badly. Staying out of the deep hole is worth more to a household than an extra point of return in the good years, and that single fact is the whole argument for owning bonds at all. The drawdown recovery calculator extends the table. It also adds the years a recovery takes at a given return.

Reading the four together

Measure	What it answers	What it is blind to
Volatility	How widely results have been spread	Direction, and rare extreme events
Beta	How much of the movement came from the market	Company and sector concentration
Sharpe ratio	What the risk was paid	Strategies that lose rarely and badly
Max drawdown	The worst experience of holding it	Whether a worse one is still possible

Run them in that last order when you review a portfolio. Drawdown tells you whether the thing is survivable for you, volatility and Sharpe tell you whether you are being paid for the ride, and beta tells you whether the portfolio behaves the way its name and its marketing claim. A fund sold as defensive with a beta of 1.1 has been mislabelled. The brochure does not get a vote.

Correlation belongs beside all four. A portfolio’s volatility depends on how its parts move against each other, and that relationship does more work than the individual volatilities do, which is what the correlation matrix shows for real funds and sectors.

Every one of them looks backwards

They are computed from history. The history you have may not contain the event that is coming for you: bond funds measured across a calm decade looked far safer than the duration arithmetic said they were, right up until rates moved.

They also miss risks that never show up as movement. A single stock can trade quietly for years and lose most of its value on one announcement, and strategies that collect small premiums post beautiful Sharpe ratios for years before meeting the event they were exposed to the whole time.

The risk that shows up in none of them

Not one of these numbers measures the thing that actually goes wrong in household portfolios, which is running out of money at the wrong time, and a portfolio with immaculate statistics that is too small, or too cautious, to fund a thirty year retirement has failed, whatever its Sharpe ratio says. That question belongs to retirement portfolio basics and to the mix you chose in asset allocation.

Give this ten minutes this week. Find the worst twelve months your portfolio has lived through, write the loss as a dollar figure on a piece of paper, and ask yourself honestly whether you would have held on. If the answer is no, the fix is a lower stock weight and a rebalancing rule, applied now while it is cheap and easy, months before the next decline arrives.