Does a Rebalancing Band Improve Gold’s Downside Protection?
A 2010–2025 monthly case study using semivariance and downside deviation
Abstract
This analysis compares the S&P 500 with portfolios that began with 90 percent stocks and 10 percent gold. Using monthly returns from 2010 through 2025, it tests whether a tolerance-band strategy—rebalancing to 10 percent gold whenever gold moves below 7.5 percent or above 12.5 percent—improved downside protection. The strategy modestly reduced return but reduced downside risk by considerably more, producing the highest return relative to downside risk among the approaches examined.
Key Findings
Annual return fell modestly.
Semivariance fell about 20 percent.
Downside-adjusted return improved.
My previous article, “Does Adding Gold Reduce Portfolio Risk?,” used 16 annual observations to compare the S&P 500 with 90/10 stock-and-gold portfolios that were either rebalanced annually or never rebalanced. It found that gold modestly reduced risk, but that most of the benefit depended on maintaining the intended allocation. The article utilized the semivariance and based the risk/return ratio on downside risk rather than the typical mean return and standard deviation of return measures because a risk measure based on downside price movements is more relevant than one dominated by positive returns.
This post extends the previous analysis by considering a more complex rebalancing procedure and by comparing risk/return ratios with monthly data over the January 2010 to 2025 period. Four strategies are considered.
A portfolio invested entirely in the S&P 500.
A portfolio maintained at 90 percent S&P 500 and 10 percent gold through annual rebalancing.
A portfolio that began with the same 90/10 allocation but was never rebalanced.
A portfolio using the 7.5-to-12.5-percent tolerance band and returning to 90 percent stocks and 10 percent gold whenever either boundary was breached.
The calculations use monthly total returns for SPY as a proxy for the S&P 500 and GLD as the gold investment, with distributions reinvested. Taxes, transaction costs and bid-ask spreads are excluded.
Adding gold created a tradeoff. Returns went down but risk went down by a greater amount. The reduction in risk was largest when reallocation was actively managed.
· The tolerance-band portfolio produced a compound annual return of approximately 13.74 percent, compared with 14.02 percent for the S&P 500. Gold therefore reduced return by about 0.28 percentage point annually, but it reduced downside risk sufficiently to improve return relative to downside risk.
· The S&P 500 had zero-target semivariance of 0.007655 and annualized downside deviation of 8.75 percent; the 90/10 portfolio without rebalancing, 0.006844 and 8.27 percent; the annually rebalanced 90/10 portfolio, 0.006139 and 7.84 percent; and the tolerance-band portfolio, 0.006117 and 7.82 percent.
A higher ratio indicates that the portfolio produced more average return for each unit of downside risk.
This is described as “Sortino-style” rather than a conventional Sortino ratio because the numerator does not subtract a risk-free return or another minimum acceptable return. Zero is used only as the threshold for identifying downside months: returns below zero contribute to downside deviation, while returns at or above zero do not.
The results were:
S&P 500: 1.624.
90/10 portfolio without rebalancing: 1.663.
90/10 portfolio with annual rebalancing: 1.751.
90/10 portfolio with tolerance-band rebalancing: 1.764.
The tolerance-band strategy produced the highest downside-adjusted return, although its advantage over annual rebalancing was small. Its ratio improved not because gold raised raw return, but because downside risk declined proportionately more than return.
The more important result is that both disciplined rebalancing approaches performed substantially better on a downside-adjusted basis than either the S&P 500 alone or the portfolio that was allowed to drift.
The tolerance-band strategy also moderated the most severe monthly loss.
S&P 500: −12.26 percent.
90/10 portfolio without rebalancing: −11.71 percent.
90/10 portfolio with annual rebalancing: −10.91 percent.
90/10 portfolio with tolerance-band rebalancing: −10.86 percent.
Gold did not prevent losses, but it reduced their magnitude. Because semivariance squares negative returns, reducing a particularly large loss has a significant effect on measured downside risk.
Annual rebalancing restores the portfolio to its target allocation on a fixed schedule, whether or not the allocation has changed materially. The tolerance-band rule instead requires a transaction only when gold moves at least 2.5 percentage points away from its 10 percent target.
The rule triggered eight rebalances during the 16-year period, compared with 16 scheduled annual rebalances. It maintained the intended diversification with fewer transactions while producing slightly lower downside risk and a slightly higher return relative to downside risk.
Some Notes:
This is a historical case study rather than proof that every investor should hold 10 percent gold or use these exact boundaries.
The period from 2010 through 2025 was unusually favorable to U.S. equities. Results could differ during an extended period of weak stock returns, high inflation or unusually strong gold performance.
The downside target used to calculate semivariance is a judgment selected by the analyst. This analysis uses a target of zero, so only months with negative returns are treated as downside observations. An analyst could instead choose a target of 3 percent, negative 3 percent, the inflation rate, the Treasury-bill return or the minimum return needed to finance retirement spending. Changing the target would change both the number of months classified as downside periods and the resulting semivariance.
Taxes, which are relevant for brokerage but not retirement accounts and trading costs are excluded.
A 10 percent gold allocation modestly reduced return but reduced downside risk by considerably more. The 7.5-to-12.5-percent tolerance band preserved that protection with only eight rebalances and produced the highest return relative to downside risk among the strategies examined.
Appendix: How to Reproduce the Calculations
The analysis can be reproduced in Excel, Google Sheets or a similar spreadsheet. Use 192 monthly observations from January 2010 through December 2025. Assume that the first observation is in row 2 and the last is in row 193.
1. Enter the Data
Create these columns:
• Column A: Month.
• Column B: SPY monthly total return.
• Column C: GLD monthly total return.
Enter returns as decimals: 4 percent as 0.04 and a 4 percent loss as −0.04. Returns should include reinvested distributions.
For the S&P 500-only portfolio, create Column D and enter:
=B2
Copy the formula through row 193.
2. Construct the Tolerance-Band Portfolio
Create these columns:
• E: Beginning SPY value.
• F: Beginning gold value.
• G: Ending SPY value before rebalancing.
• H: Ending gold value before rebalancing.
• I: Ending total portfolio value.
• J: Monthly portfolio return.
• K: Gold weight before rebalancing.
• L: Rebalancing indicator.
• M: Beginning SPY value for the next month.
• N: Beginning gold value for the next month.
Assume an initial $10,000 portfolio. Enter 9000 in E2 and 1000 in F2.
For the first month, enter:
G2: =E2*(1+B2)
H2: =F2*(1+C2)
I2: =G2+H2
J2: =I2/(E2+F2)-1
K2: =H2/I2
Column K measures gold’s end-of-month portfolio weight before any transaction. In L2, enter:
=IF(OR(K2<0.075,K2>0.125),1,0)
A value of 1 means that gold moved outside the 7.5-to-12.5-percent band. A value of 0 means no rebalancing is required. A weight exactly equal to either boundary does not trigger a transaction.
For the following month’s beginning values, enter:
M2: =IF(L2=1,0.9*I2,G2)
N2: =IF(L2=1,0.1*I2,H2)
When the boundary is breached, these formulas restore the portfolio to 90 percent SPY and 10 percent gold. Otherwise, the ending values carry forward unchanged.
In row 3, set E3 equal to M2 and F3 equal to N2. Repeat the same formulas for Columns G through N and copy them through row 193. Count the rebalances with:
=SUM(L2:L193)
The rule produced eight rebalances during 2010–2025.
3. Construct the Other 90/10 Portfolios
For annual rebalancing, copy the tolerance-band columns and replace the indicator with:
=IF(MONTH(A2)=12,1,0)
This restores the portfolio to 90/10 at the end of each December.
For the unrebalanced portfolio, copy the columns again but always carry each asset’s ending value directly into the next month. The portfolio starts at 90/10, but its weights are never restored.
4. Calculate Semivariance and Downside Deviation
For each portfolio, create a column of squared downside returns. For the S&P 500, enter:
=MIN(D2,0)^2
For the tolerance-band portfolio, use:
=MIN(J2,0)^2
Use the corresponding return column for the other portfolios. Positive monthly returns receive a zero; negative monthly returns are squared. Zero is the analyst-selected target, not a required feature of semivariance. For another monthly target, T, use =MIN(Return-T,0)^2; a 3 percent annual target must first be converted to its monthly equivalent.
Annualized zero-target semivariance is:
=12*AVERAGE(DownsideRange)
The results were 0.007655 for the S&P 500, 0.006844 for the unrebalanced portfolio, 0.006139 for annual rebalancing and 0.006117 for tolerance-band rebalancing.
Downside deviation is:
=SQRT(AnnualizedSemivariance)
The corresponding results were 8.75 percent, 8.27 percent, 7.84 percent and 7.82 percent.
To calculate the percentage reduction in semivariance relative to the S&P 500, use:
=1-(PortfolioSemivariance/SP500Semivariance)
For the tolerance-band portfolio, the reduction was approximately 20.1 percent.
5. Calculate Returns and the Downside-Adjusted Ratio
Ending portfolio value is:
=10000*PRODUCT(1+MonthlyReturnRange)
Compound annual return is:
=(EndingValue/10000)^(1/16)-1
The S&P 500 returned approximately 14.02 percent annually, compared with 13.74 percent for the tolerance-band portfolio.
For the Sortino-style ratio, first calculate annualized arithmetic average return:
=12*AVERAGE(MonthlyReturnRange)
Then divide by downside deviation:
=AnnualizedAverageReturn/DownsideDeviation
The ratios were 1.624 for the S&P 500, 1.663 for the unrebalanced portfolio, 1.751 for annual rebalancing and 1.764 for tolerance-band rebalancing. The measure is described as Sortino-style because no risk-free or minimum acceptable return is subtracted from the numerator.
6. Calculate the Worst Month and Check the Work
The worst monthly return is:
=MIN(MonthlyReturnRange)
The results were −12.26 percent, −11.71 percent, −10.91 percent and −10.86 percent, respectively.
Finally, confirm that all portfolios use identical dates, rebalancing affects the following month’s allocation, rebalancing does not itself create a return, semivariance is annualized before taking its square root, and compound return is not confused with the arithmetic average used in the ratio.