Buy the Dip – The Math Behind Contributing in a Fluctuating Market

Buy the Dip – The Math Behind Contributing in a Fluctuating Market

Is it time to sell? Is it time to buy? These are great questions that tend to come up more when market volatility is at it’s highest. So what’s the right answer? We’ll make the argument that one of the soundest investment strategies when the markets are volatile or even going down is to just keep buying. But why? And does that actually work?

Market Context: Early 2026

Global equity markets have experienced notable volatility since late 2024. Geopolitical uncertainty — particularly surrounding Iran and broader Middle East tensions — has weighed on investor sentiment. U.S. technology stocks, which led market gains for much of the prior decade, posted significant drawdowns in 2025 as rising interest rates compressed valuations on high-multiple growth companies. The S&P 500 has seen intra-year swings well above its historical average.

For investors in accumulation mode — meaning those making regular contributions to a 401(k), 403(b), or similar account — this environment has a specific and often overlooked mathematical effect. This post explains that effect.

How Dollar Cost Averaging Works

Dollar cost averaging (DCA) is the result of investing a fixed dollar amount at regular intervals, regardless of price. Because the contribution amount is fixed, the number of shares purchased varies inversely with price: lower prices produce more shares per dollar contributed; higher prices produce fewer.

The arithmetic consequence is that the average cost per share paid over time is always lower than the simple average of the prices observed — a property known as the AM-GM inequality (the arithmetic mean of prices exceeds the harmonic mean, which is what DCA produces). The greater the dispersion in prices — i.e., the more volatility — the wider that gap becomes.

In practical terms: a period of depressed prices followed by recovery does not merely return an account to where it was. It generates a larger share balance than a steady upward path to the same endpoint, because more shares were accumulated at lower cost during the trough.

Illustrated Example: $100/Month Over 12 Months

The following compares two hypothetical scenarios. In both, an investor contributes $100 per month for 12 months ($1,200 total). In both, the share price at month 12 is $21.00. The only variable is the price path.

Scenario A — Steady Appreciation: Price rises smoothly from $10.00 to $21.00 over 12 months, gaining roughly $1/month.

Scenario B — Volatile Path, Same Endpoint: Price starts at $10.00, declines to a trough of $6.50 by month 4, then recovers and finishes at $21.00.

Month Steady Price Steady Shares Volatile Price Volatile Shares Extra Shares
Month 1 $10.00 10.000 $10.00 10.000 +0.000
Month 2 $11.00 9.091 $8.50 11.765 +2.674
Month 3 $12.00 8.333 $7.00 14.286 +5.952
Month 4 $13.00 7.692 $6.50 15.385 +7.692
Month 5 $14.00 7.143 $8.00 12.500 +5.357
Month 6 $15.00 6.667 $10.00 10.000 +3.333
Month 7 $16.00 6.250 $12.00 8.333 +2.083
Month 8 $17.00 5.882 $14.50 6.897 +1.014
Month 9 $18.00 5.556 $17.00 5.882 +0.327
Month 10 $19.00 5.263 $19.00 5.263 +0.000
Month 11 $20.00 5.000 $20.50 4.878 -0.122
Month 12 $21.00 4.762 $21.00 4.762 +0.000

Summary — $100/Month

  Scenario A (Steady) Scenario B (Volatile)
Total Contributed $1,200.00 $1,200.00
Total Shares Accumulated 81.64 109.95
Final Share Price $21.00 $21.00
Ending Portfolio Value $1,714.42 $2,308.96
Gain on Contributions $514.42 $1,108.96

Same $1,200 contributed. Same $21.00 ending price. Scenario B produces 28.31 additional shares and an ending value of $2,308.96 vs. $1,714.42 — a difference of $594.54 on a $1,200 investment, driven entirely by the price path.

Scaled to a Typical 401(k): $3,500/Month

Applying the same two scenarios at a contribution rate of $3,500 per month — representative of combined employee and employer contributions for many households — scales the effect proportionally.

Total contributed over 12 months: $42,000

  Scenario A (Steady) Scenario B (Volatile)
Total Contributed $42,000.00 $42,000.00
Total Shares Accumulated 2,857.37 3,848.26
Final Share Price $21.00 $21.00
Ending Portfolio Value $60,004.70 $80,813.53
Gain on Contributions $18,004.70 $38,813.53

At this contribution level, the volatile path produces an ending value of $80,813.53 versus $60,004.70 in the steady scenario — a difference of $20,808.83 on $42,000 contributed, with identical beginning prices, ending prices, and total dollars invested.

Key Points

The advantage is mathematically derived, not speculative. The outcome above is a direct result of fixed-dollar investing mechanics, not a forecast or assumption about future market direction.

The effect scales with contribution frequency and volatility. The more frequently contributions are made and the wider the price swings, the more pronounced the DCA advantage relative to a smooth price path to the same endpoint.

The endpoint price is the critical variable. DCA produces a favorable share accumulation during a trough, but the value of those shares is only realized at the price prevailing when they are eventually sold. The analysis above assumes full recovery to the starting growth trajectory — the actual outcome depends on the price at the time of distribution.

The current environment fits the setup precisely. Elevated volatility, sector-level drawdowns in tech, and macro uncertainty have created the kind of price dispersion in which fixed-dollar contributions accumulate shares at below-average prices. If markets recover to prior trajectories — as they have following every prior drawdown cycle on record — the share accumulation advantage converts directly to portfolio value.

BONUS: A Note on Oil Prices

Oil prices are elevated in 2026, driven by Iran-related supply risk and the partial closure of the Strait of Hormuz to commercial tanker traffic. WTI crude has traded in the $85–$95/barrel range in recent months, and some headlines have characterized this as historically extreme. The data tell a more nuanced story.

Oil was above $85/barrel for nearly five consecutive years — from 2010 through most of 2014. During that same period, the Dow Jones Industrial Average delivered cumulative price gains of approximately 80%. High oil prices and strong equity returns coexisted for half a decade.

Year WTI Oil Avg ($/bbl) DJIA Return Note
2008 $99.60 -31.9% Financial crisis — oil peaks, market crashes
2009 $61.70 +22.7% Post-crisis recovery begins
2010 $79.50 +14.1% Recovery continues
2011 $95.10 +8.1% Arab Spring supply concerns; oil above $85
2012 $94.10 +7.3% Oil sustained above $85
2013 $97.90 +26.5% Oil above $85; DJIA +26.5%
2014 $93.20 +7.5% Oil above $85 most of year; OPEC flood begins Dec
2015 $48.80 +0.2% Oil collapses on OPEC supply surge
2016 $43.30 +13.4% Oil near lows; equities rebound
2017 $50.90 +25.1%  
2018 $64.90 -5.6% Rate hike concerns; equity pullback
2019 $57.00 +22.3%  
2020 $41.50 +7.2% COVID demand collapse
2021 $68.10 +18.7% Re-opening demand surge
2022 $94.30 -8.8% Russia-Ukraine; energy spike; rate hikes
2023 $77.60 +13.7%  
2024 $76.90 +12.5%  

As the table shows, WTI averaged above $85/barrel in 2011, 2012, 2013, and 2014 — and averaged above $90 in 2011 and 2013. The DJIA returned +26.5% in 2013 alone, while oil averaged $97.90/barrel. The correlation between high oil prices and poor equity returns is not consistent historically. The 2015–2016 oil collapse, often cited as a relief for consumers, coincided with near-zero equity returns in 2015 and a flat market environment.

Current WTI prices in the $85–$95 range are elevated relative to the low-inflation era of 2015–2020, when oil averaged $40–$60/barrel. However, they are not elevated relative to the 2010–2014 period, during which the economy expanded and equities performed strongly. The geopolitical risk premium embedded in today’s price reflects a specific, identifiable supply-side concern — not a broad demand destruction signal.

 

The Bottom Line

Investing works. Investors do not. We are primed to make the wrong decision at the wrong time for the wrong reasons when our heart starts talking louder than our head does about market conditions. Listen to your head – the numbers tend to work out in your favor. Always feel free to reach out with questions to us and let us know how we can help you out and serve you well thorugh this time.

 

 

Disclosure: Examples are hypothetical and for illustrative purposes only. They do not represent the performance of any specific investment. Oil and DJIA data sourced from EIA, InflationData.com, and Yahoo Finance/DIA. All investing involves risk, including possible loss of principal. Past performance is not indicative of future results. Dollar cost averaging does not guarantee a profit or protect against loss in declining markets.