Diversification and portfolio risk: why mixing assets lowers volatility
The risk of a portfolio is not the average of the risks of its parts. It depends on how the parts move together, measured by correlation. This lesson explains correlation, the formula for the volatility of a two-asset mix, asset allocation and rebalancing, with a calculator that builds a stock and bond mix from real US market returns for 2000 to 2024 and shows how much volatility the mixing removed, and why it removed little in 2022.
- Level
- Beginner
- Reading time
- About 26 minutes
- Know this first
- Risk and return
By the end you will be able to:
- explain correlation and why it determines how much diversification helps
- calculate the standard deviation of a two-asset mix
- build a stock and bond mix and read its return, volatility and worst year
- explain why the benefit of diversification changes between periods
- describe asset allocation and rebalancing, and work out the trades needed to rebalance
Not all the eggs in one basket
The SEC's investor site defines diversification as the practice of spreading money among different investments to reduce risk, and asset allocation as dividing an investment portfolio among different asset categories. The reasoning is that, historically, the returns of the three major asset categories, stocks, bonds and cash, have not moved up and down at the same time, so a loss in one may be offset by a gain in another.
The last lesson measured the risk and return of stocks and Treasury bonds one at a time. This lesson measures them together. The key quantity is not how risky each asset is alone, but how the two move relative to each other. The lesson on the cost of equity explains the related split between risk that diversification removes and market risk that it cannot.
Correlation: do two assets move together?
The correlation of two series of returns is a number between −1 and +1. At +1 they move in perfect step, at 0 they are unrelated, and at −1 one rises exactly when the other falls. The lower the correlation, the more a mix of the two smooths out the ride.
An invented example makes the extreme case visible. Company X sells umbrellas and Company Y sells sunscreen. Over four years X returns +20%, −10%, +20% and −10%, while Y returns −10%, +20%, −10% and +20%. Each is volatile on its own, with a standard deviation of 17.32%. But a portfolio that puts half in each earns exactly +5% every year, because one always offsets the other. Its standard deviation is zero. Real assets are never perfectly opposite, but the example shows the mechanism.
For two assets the standard deviation of a mix follows a formula:
If the correlation is +1 the formula collapses to the weighted average of the two standard deviations, so there is no benefit. Any correlation below +1 makes the mix less volatile than that average, and the lower the correlation the larger the gap. Take 50% in an asset with a standard deviation of 20%, 50% in another with 10%, and a correlation of 0.5. The variance is 0.25 × 400 + 0.25 × 100 + 2 × 0.25 × 0.5 × 20 × 10 = 175, so the mix has a standard deviation of 13.23%, below the weighted average of 15%.
Build a stock and bond mix
This calculator uses the same real data as the last lesson: annual returns of the S&P 500 including dividends and of the 10-year US Treasury bond, 2000 to 2024. Set the share held in stocks, the last year and the number of years. The mix is rebalanced to the chosen weights at the start of every year, so each year's return is the weights times the two returns. The left page shows how the mix performed. The right page shows the correlation between the two assets in that period and how much volatility the mixing removed.
From 2015 to 2024, a mix of 60% stocks and 40% bonds, rebalanced each year, returned 8.04% a year compounded with a standard deviation of 12.05% and a worst year of −17.96%. Stocks alone returned 12.98% with a standard deviation of 16.22%, and bonds alone 0.26% with 8.05%. The two had a correlation of 0.64, so the mix's standard deviation is 0.90 percentage points below the weighted average of the two (12.95%).
Four experiments. First, at the starting settings the 60% stock mix compounded at 8.04% with a standard deviation of 12.05%, against 12.98% and 16.22% for stocks alone. The mix gave up some growth for a lower standard deviation, and the correlation between the two assets was 0.64. Second, set the last year to 2009 and the history to 10 years. The correlation drops to −0.86 and the mix's standard deviation falls to 9.53%, far below stocks alone at 20.86%. The mix also compounded at 2.93% while stocks alone returned −0.95%. Third, drag the stock share from 0% to 100% in that period and watch the standard deviation fall first and then rise: some bonds cut the risk below that of either asset on its own. Fourth, set the last year to 2022 and the history to 5 years. The correlation is high at 0.71, because stocks and bonds fell together in 2022, and the risk removed shrinks.
The same 60/40 mix over three non-overlapping windows:
| Ten-year window | 2000 to 2009 | 2010 to 2019 | 2015 to 2024 |
|---|---|---|---|
| US stocks, compounded a year | −0.95% | 13.44% | 12.98% |
| Treasury bonds, compounded a year | 6.26% | 4.13% | 0.26% |
| Correlation of the two | −0.86 | −0.23 | 0.64 |
| 60/40 mix, compounded a year | 2.93% | 9.94% | 8.04% |
| 60/40 mix, standard deviation | 9.53% | 7.17% | 12.05% |
| 60/40 mix, worst year | −13.89% | −2.55% | −17.96% |
The benefit of diversification was large in one window and small in another. It depends on how the assets happen to move, and the correlation changes over time. In 2008, stocks returned −36.55% and bonds +20.10%, so a 60/40 mix lost −13.89%. In 2022 both lost about 18% and the mix lost −17.96%, hardly any protection.
Allocation and rebalancing
The calculator rebalances every year, and that is a choice the investor makes. The SEC defines rebalancing as bringing the portfolio back to its original asset allocation mix. Without it, the winners grow into a larger share and the portfolio drifts toward more risk. Suppose $10,000 is split 60/40, with $6,000 in stocks and $4,000 in bonds. If stocks rise 20% and bonds are flat, stocks are worth $7,200 and the total is $11,200, so stocks are now 64.29% of the portfolio. Rebalancing means selling $480 of stocks and buying $480 of bonds to return to $6,720 and $4,480. Rebalancing has costs, such as trading fees and tax, which a later lesson covers.
The mix itself is a matter of goals, time and how much of a fall the investor can tolerate. The SEC notes that asset allocation has a major impact on whether you will meet your financial goal. This page cannot say what mix is right for anyone.
What diversification cannot do
- It does not remove market-wide losses. The SEC notes that all investments involve some risk and you could lose some or all of your money. In 2022 a stock and bond mix fell.
- Correlations change. They differ between periods, so a past low correlation is not a promise.
- Two assets are a toy. A real portfolio holds many assets, such as shares in different countries, property and cash.
- Windows are short. The calculator uses five to ten years of annual data. Correlations estimated from so few points are rough.
- Returns here are before costs and taxes. Rebalancing and fund fees reduce what an investor keeps.
- Many names are not many risks. Owning twenty stocks in the same industry can still leave one risk.
Common mistakes
Counting holdings instead of risks
Ten funds that hold the same shares are one bet. What matters is how different the underlying returns are.
Assuming bonds always cushion stocks
They did in 2008 and did not in 2022. Check what each asset is exposed to.
Thinking diversification guarantees a gain
It reduces the swings from any one holding. It does not remove the chance of a loss.
Never rebalancing
Left alone, a portfolio drifts toward whatever has done best and carries more risk than intended.
Reading a past correlation as fixed
The correlation of stocks and bonds in the data above runs from strongly negative to clearly positive depending on the period.
Try it yourself
1. Asset X returns +20%, −10%, +20%, −10%, and Asset Y returns −10%, +20%, −10%, +20%. What does a 50/50 mix return each year?
Show the working
Year one: 0.5 × 20 + 0.5 × (−10) = +5%. Year two: 0.5 × (−10) + 0.5 × 20 = +5%. It is +5% every year, so the mix has no volatility at all, because the two series are perfectly negatively correlated.
2. Half the money is in an asset with a standard deviation of 20% and half in one with 10%, and the correlation is 0.5. What is the standard deviation of the mix?
Show the working
Variance = 0.25 × 20² + 0.25 × 10² + 2 × 0.5 × 0.5 × 0.5 × 20 × 10 = 100 + 25 + 50 = 175. The square root is 13.23%, below the weighted average of 15%.
3. In question 2, what would the standard deviation be if the correlation were +1?
Show the working
The variance would be 100 + 25 + 2 × 0.25 × 1 × 200 = 225, and the square root is 15%, which equals the weighted average. With a correlation of +1 there is no diversification benefit.
4. In 2008 stocks returned −36.55% and bonds returned +20.10%. What did a 60/40 mix return?
Show the working
0.6 × (−36.55) + 0.4 × 20.10 = −21.93 + 8.04 = −13.89%.
5. A $10,000 portfolio is 60% stocks and 40% bonds. Stocks rise 20% and bonds are flat. What share is now in stocks, and how much must be sold to rebalance to 60/40?
Show the working
Stocks are 6,000 × 1.2 = $7,200 and bonds $4,000, a total of $11,200. The stock share is 7,200 ÷ 11,200 = 64.29%. The 60% target is 0.6 × 11,200 = $6,720, so $480 of stocks is sold and $480 of bonds bought.
Where this is used
- A financial planner sets a mix of stocks, bonds and cash that matches a client's goals and tolerance for loss.
- A pension fund tests how its mix would have behaved in past crises such as 2008 and 2022.
- A fund manager looks at the correlation of a new holding with the existing portfolio before buying.
- A saver with a single employer's shares asks how much of their wealth rides on one company.
Key terms
- Diversification
- Spreading money among different investments to reduce risk.
- Asset allocation
- Dividing a portfolio among different asset categories such as stocks, bonds and cash.
- Correlation
- A number from −1 to +1 showing how closely two returns move together.
- Weight
- The share of a portfolio held in one asset.
- Portfolio standard deviation
- The volatility of the combined portfolio, which depends on the weights, the individual volatilities and the correlation.
- Rebalancing
- Bringing a portfolio back to its original asset allocation.
- Market risk
- Risk that affects the whole market and cannot be removed by diversifying.
Questions people ask
How many stocks are needed to be diversified?
There is no single number. What matters is how different the holdings' returns are, and a broad fund can hold hundreds in one purchase.
Why did the mix lose in 2022?
Both stocks and Treasury bonds fell that year, so mixing them removed little. The data show it, but this lesson does not explain the cause.
Does diversification lower the expected return?
Mixing in a lower-returning asset lowers the average return, as the calculator shows, but it lowers the volatility too. Whether the trade is worth it depends on the investor.
Is a negative correlation good?
For diversification, yes, since the mix is steadier. But it rarely stays negative, as the 2015 to 2024 window shows.
Sources and review
- US Securities and Exchange Commission, Investor.gov, Beginners' guide to asset allocation, diversification, and rebalancing, for the definitions of diversification, asset allocation and rebalancing, and the point that stocks, bonds and cash have historically not moved up and down at the same time.
- Aswath Damodaran, NYU Stern, Historical returns on stocks, bonds and bills: 1928-2024 (last updated 5 January 2026), for the annual returns of the S&P 500 including dividends and of the 10-year US Treasury bond for 2000 to 2024. The page names its data source as multiple data services.
- Aswath Damodaran, NYU Stern, Annual returns on stock, T.bonds and T.bills: 1928 - current (last updated 5 January 2019), an older edition of the same dataset, used to check the 2000 to 2018 values.
How the numbers were checked: the portfolio returns, standard deviations and correlations were recomputed in plain code, the standard deviation formula was confirmed against the direct calculation on the yearly mix returns, and the calculator, which runs separately, was compared with that code for every combination of settings it allows. The returns come from the dataset cited above. The umbrella and sunscreen companies are invented for teaching.