Markowitz Experiment — The Efficient Portfolio of Early 2020 | What If You Had Held It
What if you bought what the efficient frontier pointed to? — Theory vs. reality
The efficient frontier is drawn from past returns. So if you had bought the most efficient weighting of the past, would it have stayed efficient? At the end of 2019 we drew the frontier for 14 candidate assets from the previous five years (60 monthly returns), put $10,000 into the maximum-Sharpe portfolio on it, and held it to the end of September 2026. Those six years and nine months include both the 2020 COVID crash and the 2022 rate shock.
The candidates were chosen only by rules that could be checked at the end of 2019: the five largest US companies by market value (Apple, Microsoft, Alphabet, Amazon, Meta), three top small-cap holdings of the Russell 2000 ETF (IWM) (Generac, Arrowhead, Haemonetics), and six asset-class ETFs (SPY, EFA, EEM, AGG, GLD, ARKK). The frontier and the max-Sharpe portfolio are both computed within these 14 assets.
1. The frontier’s answer was half bonds
The maximum-Sharpe portfolio on the end-2019 frontier was not what you might expect. Instead of piling into the previous five years’ winners, it put 52.0% in AGG, a broad US bond ETF, and 10.8% in gold (GLD). Stocks, led by Microsoft, Amazon and Haemonetics, added up to only 37.1%.
The Impregnable Fortress.난공불락의 요새
Solid defense and diversification build a formation that holds firm against any risk.
Correlation map of the 14 assets
Two numbers explain it. Over the previous five years AGG had the lowest volatility of the 14 assets, 3.2% a year, and a correlation of −0.19 with the S&P 500 (SPY), so it tended to move slightly the other way. Put an asset that barely moves and holds up when stocks fall at the base, add equities on top, and the computed risk shrinks a lot. That gave the portfolio an expected Sharpe ratio of 1.87, more than twice the S&P 500’s 0.85 over the same window. The risk-free rate (three-month T-bills) was 1.50% at the time. As the card above shows, DIVA classifies it as ‘The Impregnable Fortress’ (LED): low risk, efficient and diversified.
The correlation map above makes the choice obvious. Stocks and stock ETFs mostly moved together (SPY–EFA 0.85). Of the 91 pairs among the 14 assets, the five with the lowest correlation all paired bonds (AGG) or gold (GLD) with stocks, and all were negative (MSFT·GLD −0.30, GOOGL·GLD −0.26, MSFT·AGG −0.19, SPY·AGG −0.19, SPY·GLD −0.17). The frontier built its base on those pairs.
What the max-Sharpe portfolio held
| Holding | Weight | 2015–19 return (μ) | Vol (σ) | |
|---|---|---|---|---|
AGG ETF | 52.0% | 3.0% | 3.2% | |
MSFT Large cap | 16.4% | 29.1% | 21.5% | |
GLD ETF | 10.8% | 5.5% | 13.9% | |
AMZN Large cap | 10.1% | 40.1% | 28.6% | |
HAE Small cap | 7.5% | 26.7% | 29.2% | |
ARWR Small cap | 2.5% | 88.3% | 92.1% | |
AAPL Large cap | 0.5% | 24.9% | 26.4% |
2. If you had simply held it
$10,000 put in at the end of 2019 was worth $17,813 at the end of September 2026 (+78.1%). The same money in the S&P 500 became $26,059 (+160.6%), and an equal split across the 14 assets became $25,198 (+152.0%). The minimum-variance portfolio at the left end of the same frontier (AGG 89.7%) reached only $11,943 (+19.4%).
Value over six years and nine months
How the four portfolios did
| Portfolio | Value | Total return | CAGR | Max drawdown |
|---|---|---|---|---|
Max Sharpe (end-2019) | $17,813 | +78.1% | 8.9% | −21.1% |
S&P 500 (SPY) | $26,059 | +160.6% | 15.3% | −23.9% |
Equal weight, 14 assets | $25,198 | +152.0% | 14.7% | −42.1% |
Min variance (end-2019) | $11,943 | +19.4% | 2.7% | −16.0% |
The max-Sharpe portfolio compounded at 8.9% a year, clearly ahead of three-month T-bills (2.84% a year on average over the holding period). The gap to the S&P 500 was still large. With only about a third in stocks, it fell far behind in the strong equity years of 2021 (max Sharpe +5.5%, S&P 500 +28.7%) and 2024 (+12.8% vs +24.9%). Yet it did not cut risk much either: its maximum drawdown was −21.1%, close to the S&P 500’s −23.9%. Where that drawdown came from is the heart of this experiment.
The figures above reflect US-dollar returns only. The won weakened 16.8% against the dollar, from 1,156.35 at the end of 2019 to 1,350.50 at the end of September 2026. For a Korean investor who converted ₩10 million, the max-Sharpe portfolio would be worth ₩20.80 million and the S&P 500 ₩30.43 million. The ranking does not change. Taxes, trading fees and FX costs are not included. DIVA’s Markowitz analysis does not model currency moves, so for a won-based investor the exchange rate is one more variable that changes the outcome.
3. It worked once, then it broke
Setting the holding period’s two sell-offs side by side makes the portfolio’s character clear.
Q1 2020 vs 2022
| Portfolio / asset | Q1 2020 (COVID) | 2022 (rate shock) |
|---|---|---|
Max Sharpe (end-2019) | +0.2% | −20.1% |
S&P 500 (SPY) | −19.4% | −18.2% |
AGG (US bonds) | +3.1% | −13.0% |
GLD (gold) | +3.6% | −0.8% |
MSFT (Microsoft) | +0.3% | −28.0% |
In Q1 2020, while the S&P 500 fell −19.4%, the max-Sharpe portfolio held flat at +0.2%. Bonds (AGG +3.1%) and gold (GLD +3.6%) rose and offset the equity losses, exactly as the frontier had computed. For the full year it returned +22.5%, ahead of the S&P 500 (+18.3%).
2022 was the opposite. As rates rose fast, bond prices and stock prices fell together. AGG returned −13.0% and Microsoft −28.0%, and the max-Sharpe portfolio fell −20.1%, more than the S&P 500 (−18.2%). The cushion had started moving with stocks. The correlation between AGG and the S&P 500 rose from −0.19 in 2015–2019, when the frontier was drawn, to 0.23 in 2020–2021 and 0.64 in 2022–2026. AGG’s own volatility also rose, from 3.2% to 5.9% a year.
The two sell-offs had different causes. 2020 was a growth scare in which investors sold stocks and ran to safe assets; 2022 was an inflation and rate shock that dragged bonds and stocks down together. The previous five years contained only the first kind, so the frontier treated bonds as a reliable cushion.
4. Volatility held up; returns did not
The frontier’s ‘expected’ figures simply carry the past five years’ average returns, volatilities and correlations into the future. Here are the end-2019 expectations next to the actual figures for the following six years and nine months.
End-2019 expectations vs what happened
| Portfolio | Return (μ) exp. → actual | Vol (σ) exp. → actual | Sharpe exp. → actual |
|---|---|---|---|
Max Sharpe (end-2019) | 15.3% → 9.3% | 7.4% → 12.5% | 1.87 → 0.52 |
S&P 500 (SPY) | 11.7% → 15.7% | 11.9% → 16.9% | 0.85 → 0.76 |
Equal weight, 14 assets | 23.4% → 15.7% | 15.2% → 19.8% | 1.44 → 0.65 |
Min variance (end-2019) | 4.0% → 2.9% | 2.9% → 6.6% | 0.88 → 0.00 |
The max-Sharpe portfolio expected 15.3% a year and earned 9.3%, while its volatility rose from 7.4% to 12.5%. The expected Sharpe of 1.87 became 0.52 because both sides missed. The S&P 500, by contrast, beat its expectation (11.7%) with 15.7%. Return forecasts did not miss in one direction; they missed both ways.
Asset by asset, the gap is starker. Ranking the 14 assets by volatility in 2015–2019 and again in 2020–2026 gives almost the same order (rank correlation 0.94). The return rankings only half carried over (rank correlation 0.43). Arrowhead, which had the highest average return over the previous five years, returned +3.2% afterwards, and Haemonetics, held by the max-Sharpe portfolio, −8.4%. Alphabet, the large cap with the lowest past return and left out, returned +418.7%, and gold, near the bottom, +166.5%. Assets that swung a lot kept swinging a lot, but assets that rose a lot did not keep rising.
5. Seen from today’s frontier
We redrew the frontier for the same 14 assets using January 2020 to September 2026 data. The dot is the portfolio kept at its end-2019 weights. The point that sat on the curve six years and nine months earlier now sits below it, meaning other weightings would have earned more for the same volatility.
The Impregnable Fortress.난공불락의 요새
Solid defense and diversification build a formation that holds firm against any risk.
The DIVA classification at the top of the card stays ‘The Impregnable Fortress’ (LED). Its efficiency test compares the portfolio not with the raw historical averages but with a frontier corrected for estimation error, so it can differ from the sample curve in the chart. The portfolio’s basic character, low risk and diversified, did not change.
Re-optimizing on today’s data gives a max-Sharpe portfolio of GLD 45.3% · AAPL 23.3% · GOOGL 15.4% · META 5.7% · MSFT 5.6% · HAE 3.5% · GNRC 1.2%. The asset at the base switched from bonds to gold, with nothing at all in AGG, and Apple and Alphabet lead the equity side. Of course, these weights were also chosen knowing the last six years and nine months, so there is no guarantee they are the answer going forward.
Wrapping up: the frontier is a map of the past
The takeaway is not that the efficient frontier is useless. The diversification it computed really did work in the 2020 COVID crash, and which assets swing the most (volatility) barely changed six years and nine months later. What failed were two assumptions: that past average returns carry into the future, and that the relationships between assets (correlations) stay put. The max-Sharpe portfolio is the point that leans hardest on both, so it was shaken the most in 2022, when they gave way.
A point on the frontier is not ‘what will be optimal’ but ‘what was optimal over the window you measured’.
So when reading a DIVA Markowitz result, it is worth looking at the structure of risk before the expected-return figure: which low correlations your portfolio’s low volatility comes from, and whether those correlations would hold in a 2020-style shock and in a 2022-style one. Redrawing the frontier over a different window also shows how much your weights depend on one particular stretch of data.
① This is one starting point (end-2019) and one holding period (six years and nine months). A different starting point could give a different result. Starting the same way at the end of 2021, for example, runs straight into the 2022 drop and leaves the max-Sharpe portfolio worse off.
② Expected returns, volatilities and correlations are sample estimates from monthly returns, the same method as DIVA’s frontier chart. No short selling, weights sum to 1, and weights below 0.1% were set to zero.
③ The portfolio was held without rebalancing, so its weights drifted. The dot in section 5 assumes the end-2019 weights were kept every month, so it does not match section 2’s value exactly.
④ The small caps were taken from IWM’s top holdings, skipping names listed for less than five years (Novocure, Lumentum, Teladoc) and one with an announced takeover (The Medicines Company). They do not represent small caps as a whole, and a different rule could change the optimal weights.
⑤ Taxes, trading fees and FX costs are not included.
This piece is for education and information only and does not recommend buying or selling any security.
Sources: yfinance adjusted prices (month-end, dividends reinvested) · risk-free rate ^IRX (3-month T-bill) · USD/KRW KRW=X · IWM holdings from SEC EDGAR N-PORT (2019-12-31) · model: DIVA Quantizer Markowitz (site calculation as is). Analysis window January 2015–September 2026.
This article was written with the help of AI.