Why Volatility Is the Price of Higher Returns

Volatility is the price of higher returns only in a limited sense. From 1928 to 2025, the broad US asset classes with higher average returns generally also swung harder, because investors demand extra expected return for holding risk they cannot diversify away. Volatility on its own is not what gets paid, though: company-specific swings carry no premium, the most volatile US stocks did worse than calm ones over 1968–2008, and the extra return is an expectation that can fail to arrive for a decade or more.

Key takeaways

In Damodaran's 1928–2025 data, the S&P 500 averaged 11.85% a year with a standard deviation of 19.40%, against 3.41% and 3.04% for three-month Treasury bills.
Theory says only market-wide (systematic) risk carries a premium; company-specific risk can be diversified away, so the market does not pay for it.
The premium is not guaranteed: 10-year Treasuries beat the S&P 500 in 13 of the 89 rolling 10-year periods since 1928, including 1999–2008.
Volatility drags on compounding: a 10% average return that alternates between +30% and −10% compounds at only 8.17% a year.
The premium shifts with prices and interest rates; in May 2026 the Federal Reserve put one estimate near a 20-year low.

What 98 years of US returns show

Aswath Damodaran of NYU Stern publishes annual US returns back to 1928 in his historical returns spreadsheet (histretSP.xls), now updated through 2025. The figures below were recomputed from its annual series for 3-month T-bills, 10-year Treasuries, Moody's Baa corporate bonds and the S&P 500 with dividends.

The arithmetic mean is the simple average of yearly returns; the geometric mean is the compound rate that actually turned a starting sum into the ending sum. Standard deviation measures how widely yearly returns scattered around their average, which is what "volatility" means here.

1928–2025, nominal	Arithmetic mean	Geometric mean	Standard deviation	Worst year	Years with a loss
3-month T-bills	3.41%	3.37%	3.04%	+0.03% (2014)	0 of 98
10-year Treasury	4.82%	4.53%	7.90%	−17.8% (2022)	20 of 98 (20%)
Baa corporate bonds	6.90%	6.63%	7.65%	−15.7% (1931)	16 of 98 (16%)
S&P 500	11.85%	10.02%	19.40%	−43.8% (1931)	26 of 98 (27%)

Inflation changes the picture for the "safe" end. Real returns below remove each year's CPI inflation using the spreadsheet's method, (1 + nominal) ÷ (1 + inflation) − 1. Prices rose about 18.7-fold over the period, or 3.04% a year compounded.

1928–2025, after inflation	Arithmetic mean	Geometric mean	Standard deviation	Worst year	Years with a real loss
3-month T-bills	0.40%	0.33%	3.82%	−15.0% (1946)	40 of 98 (41%)
10-year Treasury	1.83%	1.45%	8.86%	−22.8% (2022)	42 of 98 (43%)
Baa corporate bonds	3.86%	3.49%	8.80%	−20.4% (2022)	31 of 98 (32%)
S&P 500	8.61%	6.78%	19.30%	−38.1% (1931)	31 of 98 (32%)

The broad pattern holds: the asset with the widest swings earned the most, and T-bills, which never had a losing year in nominal terms, earned almost nothing after inflation. The ordering is not perfect, however. Baa corporate bonds earned about 2 percentage points a year more than 10-year Treasuries with slightly lower measured volatility, a sign that standard deviation alone is not what investors are paid for. One caution: the spreadsheet rebuilds bond returns from yield changes rather than actual bond portfolios, so default losses are not deducted and the Baa figure likely overstates what holders earned.

Growth of $10,000, illustrative

Illustrative example: $10,000 placed in each series at the start of the period, with all income reinvested and no taxes, fees or trading costs. Real values are in start-of-period purchasing power.

Series	1928–2025 nominal	1928–2025 real	1999–2008 nominal	1999–2008 real
3-month T-bills	$257,830	$13,757	$13,721	$10,698
10-year Treasury	$771,756	$41,178	$18,939	$14,766
Baa corporate bonds	$5,395,241	$287,869	$18,680	$14,564
S&P 500	$115,700,909	$6,173,344	$8,722	$6,800

Over 98 years, stocks ended with roughly 150 times as much as 10-year Treasuries. Over the ten years from 1999 through 2008, the order flipped: the S&P 500 lost 1.36% a year (3.78% a year after inflation), while 10-year Treasuries gained 6.59% a year.

Why investors demand a premium

A risk premium is the extra expected return an asset must offer over a near-riskless one to persuade investors to hold it. As the SEC's investor education page on risk puts it, as risks rise, investors generally seek higher returns to compensate. Prices enforce this: if a risky asset were priced to return no more than a T-bill, few people would hold it, its price would fall, and the lower price would raise its expected return until buyers appeared.

In the 1928–2025 data, stocks beat T-bills by 8.44 percentage points a year on an arithmetic basis and 6.65 points a year compounded. Gaps of this size are hard to explain. Rajnish Mehra and Edward Prescott, in "The Equity Premium: A Puzzle" (Journal of Monetary Economics, 1985), found that a class of general equilibrium models could not reconcile the large average return on US stocks with the small average return on Treasury bills over 1889–1978. This equity premium puzzle means the premium is an observed fact that theory struggles to size, not a constant it produces.

Only market-wide risk is paid

The Capital Asset Pricing Model (CAPM), set out by William Sharpe in "Capital Asset Prices" (Journal of Finance, 1964), explains which risk earns the premium. The 1990 Nobel announcement for Sharpe, Markowitz and Miller credits Markowitz with the insight that what matters is not an asset's risk in isolation but its contribution to the risk of the whole portfolio. Sharpe's CAPM builds on it: an asset's risk premium varies in direct proportion to its beta, a measure of how it moves with the market.

The split works like this. Systematic risk comes from recessions, rate shocks and panics that hit nearly everything at once; holding more securities cannot remove it. Idiosyncratic risk comes from one company's lawsuit, product failure or fraud; spread across many holdings, those shocks largely cancel out. Because idiosyncratic risk can be shed at little cost, the market has no reason to pay anyone for carrying it.

The Baa-versus-Treasury comparison shows the idea in miniature. In the 12 years since 1928 when the S&P 500 fell more than 10%, 10-year Treasuries returned an average of +3.5% while Baa corporate bonds averaged −0.4%. Baa bonds' yearly returns had a correlation of 0.40 with stocks, against 0.02 for Treasuries.

Volatility was similar, but Baa losses tended to arrive when the rest of a portfolio was also losing, which is consistent with their higher return. Twelve years is a small sample, though, and 2022, when stocks and both bond series fell together, shows the pattern is not fixed.

Where the trade-off breaks down

The title's claim holds for broad, undiversifiable risk over long periods. It fails in at least three ways.

Expected is not realized

A premium is a higher expected return, not a scheduled payment. Counting every rolling window in the 1928–2025 data, 10-year Treasuries ended ahead of the S&P 500 in 13 of 89 ten-year periods (15%), clustered around 1928–1940, 1965–1978 and 1998–2011. T-bills beat stocks in 13 of those 89 windows too.

Over 20 years the shortfall became rare but did not vanish: Treasuries beat stocks in 1 of 79 twenty-year windows (1929–1948). Over the 19 years from 2000 through 2018, $10,000 in 10-year Treasuries grew to about $25,090, against about $24,440 in the S&P 500.

Even the long-run average is uncertain. The yearly stock-minus-bill premium of 8.44 points has a standard error of about 2.0 points, so two standard errors either side spans roughly 4.5 to 12.4 points. A 98-year record cannot pin the premium down precisely, a point the spreadsheet's own notes make about its averages.

Calmer stocks did not earn less

If volatility itself were paid, the most volatile stocks would have earned the most. They did not. Malcolm Baker, Brendan Bradley and Jeffrey Wurgler, in "Benchmarks as Limits to Arbitrage" (Financial Analysts Journal, 2011), report that from January 1968 to December 2008 a dollar in their lowest-volatility US stock portfolio grew to $59.55, while a dollar in the highest-volatility portfolio was worth $0.58, before transaction costs. They attribute part of this to fund managers judged against fixed benchmarks, who have little incentive to exploit the gap.

Andrea Frazzini and Lasse Heje Pedersen, in "Betting Against Beta" (Journal of Financial Economics, 2014), find that high-beta assets have earned lower risk-adjusted returns in US stocks, 20 international stock markets, Treasury bonds, corporate bonds and futures. Their explanation is that investors who face limits on borrowing (leverage and margin constraints) buy high-beta assets to get more market exposure, bidding up their prices.

Single stocks: more swing, no extra pay

A single stock carries market risk plus its own company risk, so it swings more than an index while, by the CAPM logic above, earning no premium for the extra part. Hendrik Bessembinder's "Do Stocks Outperform Treasury Bills?" (Journal of Financial Economics, 2018) shows how lopsided the result can be: the majority of US common stocks in the CRSP database since 1926 had lifetime buy-and-hold returns below one-month Treasury bills, and the best-performing 4% of companies accounted for the entire net gain of the US stock market over that time.

Volatility drag on compounding

Volatility also costs something directly. A 50% loss needs a 100% gain to recover, so swings pull the compound rate below the simple average. A widely used approximation sizes the gap:

G ≈ A − σ² / 2

G = geometric (compound) annual return
A = arithmetic (simple average) annual return
σ = standard deviation of annual returns (as a decimal)

Illustrative example: three hypothetical assets each average exactly 10% a year over 20 years, starting with $10,000.

Yearly pattern	Arithmetic mean	Standard deviation	Compound rate (exact)	Formula estimate	Value after 20 years
+10% every year	10%	0%	10.00%	10.0%	$67,275
+30%, −10%, repeating	10%	20%	8.17%	8.0%	$48,068
+50%, −30%, repeating	10%	40%	2.47%	2.0%	$16,289

Same average, very different wealth: the steady asset ends $19,207 ahead of the moderate one and $50,986 ahead of the most volatile. The exact compound rate for an alternating pair is √((1 + up) × (1 − down)) − 1, so √(1.30 × 0.90) − 1 = 8.17%.

The real data fit the formula closely. For the S&P 500, 11.85% − (0.194² ÷ 2) ≈ 9.97%, against an actual compound rate of 10.02%. The compound rate sat 1.8 points below the simple average. A riskier asset therefore ends ahead only if its extra average return exceeds the extra drag its swings impose: against 10-year Treasuries, stocks' 7.0-point arithmetic lead shrank to 5.5 points compounded.

Why the premium is not fixed

The premium investors can expect depends on the price they pay. When prices rise faster than expected earnings, the built-in compensation for risk shrinks; when prices fall or safe yields drop, it widens. Fernando Duarte and Carlo Rosa of the New York Fed combined twenty models in "The Equity Risk Premium: A Review of Models" (Staff Report 714, February 2015) and found the estimated premium reached about 12% in 2012 and 2013, a level not seen since the 1970s, which they attributed to unusually low Treasury yields.

The Federal Reserve's Financial Stability Report tracks a simpler version, the S&P 500's forward earnings-to-price ratio minus the expected real 10-year Treasury yield, which the Fed calls a crude measure. In the May 2026 report, using data as of April 23, 2026, that estimate was near a 20-year low, and the forward price-to-earnings ratio remained well above its historical median. A thin measured premium says how little extra compensation current prices offer by that yardstick, not when, or whether, prices will move.

Frequently asked questions

Is volatility the same thing as risk?

No. Standard deviation measures how much returns scatter from year to year, but the SEC's investor education site also lists business, inflation, interest-rate and liquidity risk. It notes that the main concern with cash equivalents is inflation eroding their returns, a risk that barely registers as volatility. Volatility is a convenient, measurable stand-in for risk, not a complete description of it.

What is beta, and how does it differ from volatility?

Beta measures how much an asset tends to move with the market portfolio, based on the covariance between the two. In the CAPM description from the 1990 Nobel announcement, a stock with a beta above 1 adds more than average to a market portfolio's risk and one below 1 adds less. A stock can be highly volatile yet have a low beta if most of its swings come from company-specific news.

How often do large-company stocks lose money in a year?

The SEC's investor education site says about one year in three for large-company stocks as a group. In Damodaran's 1928–2025 S&P 500 series, the count was 26 losing years out of 98, a little more than one in four. Measured after inflation, 31 of the 98 years were losers, close to one in three.

Why are T-bills treated as risk-free if they lose to inflation?

Models such as the CAPM need a benchmark with a known payoff; the Nobel summary of Sharpe's work names Treasury bills as its example. "Risk-free" refers to the nominal payment, not purchasing power: in Damodaran's data T-bills never had a losing year in dollars, yet lost to inflation in 40 of 98 years, worst in 1946 at −15.0% after inflation.

Does the low-volatility pattern mean calm stocks always win?

No. Frazzini and Pedersen report that their betting-against-beta factor earned low returns in periods when funding constraints tightened, so the pattern has had bad stretches even within their sample. Both studies describe historical portfolios, before transaction costs in Baker, Bradley and Wurgler's case, and possible explanations; neither shows that a low-volatility strategy will outperform in future.

Checking a risk–return claim

When a fund, chart or article links higher risk to higher returns, a few questions separate the sound version of the idea from the misleading one:

Which risk? Is the extra volatility broad market exposure, which has historically carried a premium, or concentration in a few holdings, which has not?
Which average? Is the return arithmetic or geometric? Only the compound (geometric) rate matches ending wealth.
Which window? Check the start and end dates; the 1999–2008 result above came from the same assets as the 1928–2025 one.
Before or after inflation? A return that looks safe in dollars can still lose purchasing power.
What rate goes into projections? The Investment Growth calculator takes one assumed annual return and compounds it monthly at one-twelfth of that rate, so an entry of 10% (with the fee option off) grows at about 10.5% a year. Entering a compound rather than an arithmetic return, and trying two or three rates, keeps projections closer to the historical record.