Does Adding Gold Reduce Portfolio Risk?
A 2010–2025 case study shows why downside risk can tell a different story from conventional volatility
Abstract
This analysis compares a portfolio invested entirely in the S&P 500 with two portfolios that began with 90 percent in the S&P 500 and 10 percent in gold. It examines both whether gold improved risk-adjusted performance and whether semivariance—which measures only downside outcomes—better captures gold’s potential diversification benefit.
Key Findings
Gold slightly reduced returns but also reduced risk.
Semivariance showed a larger reduction in downside risk than standard deviation showed in overall volatility.
Annual rebalancing was essential to preserving the diversification benefit.
Investors often add gold to a stock portfolio on the theory that it will provide protection when equities perform poorly. Conventional portfolio analysis tests that theory using variance or standard deviation, which treat unexpectedly large gains and unexpectedly large losses as equivalent forms of volatility.
Semivariance provides a different test. It measures only returns below a specified target and therefore focuses on outcomes investors regard as harmful.
To illustrate the difference, I compared three portfolios over the 16 complete calendar years from 2010 through 2025:
A portfolio invested entirely in the S&P 500.
A portfolio invested 90 percent in the S&P 500 and 10 percent in gold, rebalanced annually.
A portfolio that began with the same 90/10 allocation but was never rebalanced.
The calculations use the total returns of SPY as a proxy for the S&P 500 and GLD as the gold investment, with distributions reinvested. Each portfolio began with $10,000 on January 1, 2010.
Variance Versus Semivariance
Standard deviation measures how widely returns vary around their average. It treats a return far above the average as just as risky as a comparably large return below the average.
That may be mathematically convenient, but it does not necessarily correspond to how investors think about risk. Investors generally welcome unusually large gains and dislike unusually large losses.
Semivariance measures only returns below a chosen threshold. In this example, the threshold is zero, meaning that only negative calendar-year returns count as downside risk. Downside deviation is the square root of semivariance and expresses that risk in more familiar percentage-return terms.
Semivariance does not replace standard deviation. It answers a different question. Standard deviation asks how variable returns were in either direction. Zero-target semivariance asks how often, and by how much, returns fell below zero.
The Results
Return: The S&P 500 produced the highest compound annual return from 2010 through 2025: 14.02 percent, compared with 13.66 percent for the annually rebalanced 90/10 portfolio and 13.62 percent for the portfolio that was never rebalanced. A $10,000 investment grew to approximately $81,563 in the S&P 500, $77,605 in the rebalanced portfolio, and $77,100 in the unrebalanced portfolio.
Risk: Annual rebalancing produced the clearest reduction in both conventional and downside risk. Standard deviation declined from 13.89 percent for the S&P 500 to 12.94 percent for the rebalanced portfolio and 13.18 percent for the unrebalanced portfolio. Zero-target semivariance fell by approximately 18 percent with annual rebalancing but only 6 percent without it. Downside deviation declined from 4.69 percent for the S&P 500 to 4.25 percent with annual rebalancing and 4.54 percent without rebalancing. In the worst year, the S&P 500 lost 18.18 percent, compared with losses of 16.44 percent for the rebalanced portfolio and 17.62 percent for the unrebalanced portfolio.
Return relative to risk: Arithmetic average annual return divided by standard deviation was 1.07 for the S&P 500, 1.11 for the annually rebalanced portfolio, and 1.09 for the unrebalanced portfolio. Using average annual return divided by zero-target downside deviation—a Sortino-style measure—the ratios were 3.17, 3.39, and 3.17, respectively. Gold therefore improved risk-adjusted performance when the 10 percent allocation was maintained but produced almost no improvement in downside-adjusted performance when the portfolio was allowed to drift.
Why Rebalancing Mattered
The unrebalanced portfolio did not remain a 90/10 portfolio. Stocks substantially outperformed gold during much of the period, causing gold to become a progressively smaller share of the portfolio.
By the beginning of 2025, gold represented only about 3.5 percent of the unrebalanced portfolio. Gold’s strong performance during 2025 raised its share to approximately 4.8 percent by year-end, but that remained far below the original 10 percent allocation.
The portfolio therefore had much less gold available to cushion stock-market losses than an investor might assume from its original allocation. An investor who chooses a 10 percent gold allocation for diversification cannot establish the allocation once and expect its protective role to remain unchanged.
Rebalancing periodically sells some of the asset that has performed better and purchases more of the asset that has performed worse. That can feel uncomfortable, but it is precisely what preserves the intended allocation and its diversification benefits.
What Semivariance Adds
The standard-deviation results suggest that adding gold modestly reduced volatility. The semivariance results tell a somewhat stronger story: maintaining the gold allocation reduced downside risk by considerably more than it reduced overall volatility.
Standard deviation fell by about 7 percent when the portfolio was rebalanced annually. Zero-target semivariance fell by approximately 18 percent.
This distinction matters because reducing downside losses is one of the principal reasons investors hold gold. Treating unusually large positive returns as a form of risk can obscure the value of an asset whose intended purpose is protection against adverse outcomes.
The number of negative years did not change. All three portfolios lost money in 2018 and 2022. Gold did not prevent those losses, but annual rebalancing reduced their severity.
Because semivariance squares each shortfall below zero, reducing a large loss can materially reduce measured downside risk even when the number of losing years remains unchanged. Semivariance therefore captures both the occurrence and magnitude of negative returns, not merely their frequency.
Important Qualifications
This is an illustration rather than a definitive finding about gold. Sixteen annual observations provide a relatively small sample, and only two years had negative S&P 500 returns. The semivariance estimates therefore depend heavily on what happened in 2018 and 2022.
A more rigorous analysis would use monthly returns, producing roughly 192 observations over the same period. It could also compare different downside targets, such as the Treasury-bill return, inflation, or the minimum return needed to finance retirement spending.
The period also strongly favored U.S. equities. The S&P 500 produced exceptional returns, causing any allocation to gold to reduce total wealth. A different starting date could produce different results.
Finally, semivariance is not the only measure of downside risk. Expected shortfall, maximum drawdown, and recovery time provide additional information about severe losses and the experience of remaining below a previous portfolio peak.
Conclusion
Adding 10 percent gold modestly reduced returns but also reduced portfolio risk. The improvement was more apparent when risk was measured by semivariance rather than standard deviation because gold’s principal benefit was reducing negative outcomes rather than eliminating fluctuations in both directions.
That benefit largely disappeared when the portfolio was not rebalanced. The broader lesson is therefore not simply that every investor should own 10 percent gold. It is that diversification must be maintained rather than merely initiated—and that conventional volatility may not fully measure the value of an asset whose purpose is to moderate losses.
Appendix: How to Reproduce the Calculations
The calculations can be reproduced in a spreadsheet with one row for each calendar year from 2010 through 2025.
Step 1: Enter the Annual Returns
Create the following columns:
Column A: Year
Column B: S&P 500 total return
Column C: Gold total return
Column D: Annually rebalanced portfolio return
Enter the years 2010 through 2025 in cells A2 through A17.
Enter returns as decimals. A 10 percent return is entered as 0.10, while an 18 percent loss is entered as -0.18.
For example, the 2022 entries are:
S&P 500: −18.18 percent, entered as -0.1818
Gold: −0.77 percent, entered as -0.0077
Step 2: Calculate the Annually Rebalanced Portfolio
For each year, multiply the S&P 500 return by 90 percent and the gold return by 10 percent.
If the S&P 500 return is in cell B2 and the gold return is in C2, enter the following formula in D2:
=0.9*B2+0.1*C2
Copy the formula down through D17.
This calculation assumes that the portfolio is restored to 90 percent stocks and 10 percent gold at the beginning of every year.
Step 3: Calculate the Portfolio Without Rebalancing
Create six additional columns:
Column E: Beginning S&P 500 value
Column F: Beginning gold value
Column G: Ending S&P 500 value
Column H: Ending gold value
Column I: Beginning total portfolio value
Column J: Unrebalanced portfolio return
Enter the initial investments:
In E2, enter 9000.
In F2, enter 1000.
Calculate the ending values for 2010:
In G2, enter =E2*(1+B2).
In H2, enter =F2*(1+C2).
Calculate the beginning total portfolio value:
In I2, enter =E2+F2.
Calculate the portfolio’s return for the year:
In J2, enter =(G2+H2)/I2-1.
The ending values for one year become the beginning values for the next year:
In E3, enter =G2.
In F3, enter =H2.
Then calculate the next year’s ending values:
In G3, enter =E3*(1+B3).
In H3, enter =F3*(1+C3).
In I3, enter =E3+F3.
In J3, enter =(G3+H3)/I3-1.
Copy the formulas down through 2025.
Do not restore this portfolio to its original 90/10 allocation. Its weights change automatically as the two investments produce different returns.
Step 4: Calculate Ending Values and Compound Annual Returns
For the S&P 500 portfolio, the ending value is:
=10000*PRODUCT(1+B2:B17)
For the annually rebalanced portfolio, the ending value is:
=10000*PRODUCT(1+D2:D17)
For the unrebalanced portfolio, the ending value is:
=G17+H17
The compound annual growth rate, or CAGR, is:
=(Ending value/10000)^(1/16)-1
The resulting compound annual returns were:
S&P 500: 14.02 percent
Annually rebalanced portfolio: 13.66 percent
Unrebalanced portfolio: 13.62 percent
The corresponding ending values were approximately:
S&P 500: $81,563
Annually rebalanced portfolio: $77,605
Unrebalanced portfolio: $77,100
Step 5: Calculate Standard Deviation
Standard deviation measures the variability of all annual returns, whether positive or negative.
For the S&P 500, use:
=STDEV.S(B2:B17)
For the annually rebalanced portfolio, use:
=STDEV.S(D2:D17)
For the unrebalanced portfolio, use:
=STDEV.S(J2:J17)
The results were:
S&P 500: 13.89 percent
Annually rebalanced portfolio: 12.94 percent
Unrebalanced portfolio: 13.18 percent
The lower figures for the diversified portfolios indicate that adding gold reduced overall volatility.
Step 6: Calculate Zero-Target Semivariance
Semivariance measures only returns below a selected target. The target in this analysis is zero, so positive years contribute nothing to downside risk.
Create three more columns:
Column K: S&P 500 squared downside return
Column L: Rebalanced portfolio squared downside return
Column M: Unrebalanced portfolio squared downside return
For the S&P 500, enter in K2:
=MIN(B2,0)^2
For the rebalanced portfolio, enter in L2:
=MIN(D2,0)^2
For the unrebalanced portfolio, enter in M2:
=MIN(J2,0)^2
Copy all three formulas down through row 17.
Calculate the average of each column:
S&P 500 semivariance: =AVERAGE(K2:K17)
Rebalanced portfolio semivariance: =AVERAGE(L2:L17)
Unrebalanced portfolio semivariance: =AVERAGE(M2:M17)
Positive years remain in the calculation as zeros.
The resulting semivariances were:
S&P 500: 0.002196
Annually rebalanced portfolio: 0.001805
Unrebalanced portfolio: 0.002066
The rebalanced portfolio’s semivariance was approximately 18 percent below that of the S&P 500.
Step 7: Convert Semivariance to Downside Deviation
Because semivariance is expressed in squared-return units, its square root is easier to interpret.
Use:
=SQRT(semivariance)
The resulting downside deviations were:
S&P 500: 4.69 percent
Annually rebalanced portfolio: 4.25 percent
Unrebalanced portfolio: 4.54 percent
Downside deviation expresses below-target risk in percentage-return terms, just as standard deviation expresses overall volatility in percentage-return terms.
Step 8: Compare Return With Risk
First calculate the arithmetic average annual return for each portfolio:
S&P 500: =AVERAGE(B2:B17)
Annually rebalanced portfolio: =AVERAGE(D2:D17)
Unrebalanced portfolio: =AVERAGE(J2:J17)
The conventional return-to-volatility measure is:
Arithmetic average annual return ÷ standard deviation
The resulting ratios were:
S&P 500: 1.07
Annually rebalanced portfolio: 1.11
Unrebalanced portfolio: 1.09
This measure is the inverse of the coefficient of variation when average return is positive. It also resembles a Sharpe ratio with a zero risk-free rate, although no risk-free return was subtracted in this analysis.
The downside measure is:
Arithmetic average annual return ÷ downside deviation
The resulting zero-target Sortino-style ratios were:
S&P 500: 3.17
Annually rebalanced portfolio: 3.39
Unrebalanced portfolio: 3.17
The calculations show that adding gold modestly improved return relative to overall volatility. Its benefit was more apparent when risk was defined as downside loss—but only when rebalancing maintained the intended gold allocation.