Multi-Asset MVO Portfolio Optimizer with Backtesting
Multi-Asset Mean-Variance Optimization
Multi-Asset MVO Portfolio Optimizer
ETFs: SPY, IWM, EFA, VWO, GLD, TLT, HYG, EMB, CEMB, IYR | Data through 2026-03-06 | 10 assets
This model uses mean-variance optimization (MVO), a framework developed by Harry Markowitz (1952) and extended by Robert Merton. It finds the portfolio allocation that maximizes return for a given level of risk, or minimizes risk for a given return target. Two optimized portfolios are computed: a long only portfolio (no weight constraints) and a constrained portfolio with a maximum allocation of 25% per asset. Note that MVO is a return seeking model and may not be suitable for all investors, such as pension funds or insurance companies. For more details, view documentation.
This is an asset allocation model. It determines how much weight to assign to each asset class, not which individual stocks to pick. If you're interested in stock selection, .
The model uses historical returns to estimate expected returns and covariances, so it will naturally concentrate in assets that had high past returns with low covariance. If you believe future returns will differ from the past or have your own capital market expectations, .
A default set of 10 asset classes is pre-selected, but there is a wider list of 31 to choose from. You can check how removing or adding assets will impact the Sharpe ratio in both portfolios before applying. Be careful not to select asset classes that overlap in their underlying holdings, a warning will appear if you do. To see how overlap groups were determined, .
If you have specific constraints or already hold a portfolio with certain assets, you can define the minimum and maximum allocation for each selected asset class in the interactive constraint simulator. .
Asset Class Overlap Analysis
Research based assessment of which ETFs in the 31 asset universe have significant holdings overlap or redundant factor exposure.
1. US Large Cap Cluster: SPY, QQQ, VIG
• QQQ top holdings (AAPL, MSFT, NVDA, AMZN, META, GOOGL) represent ~30% of SPY
• VIG (Dividend Growth) is heavily weighted to large cap US stocks that overlap SPY
• Selecting all three concentrates ~60 70% of combined exposure in the same mega caps
2. Developed ex US Broad vs Country: EFA, EWJ, VGK, EWL
• EFA (iShares MSCI EAFE) already contains Japan (~20%), Europe (~60%), Australia
• EWJ, VGK, EWL are each subsets of EFA
• Selecting EFA + country ETFs double counts those regions
3. Europe Sub Overlap: VGK, EWL
• VGK tracks FTSE Developed Europe, which includes Switzerland at ~15% weight
• EWL is pure Swiss equities. Selecting both means ~15% of VGK duplicates EWL
4. EM Broad vs Country: VWO, FXI, INDA, EWZ, EWY, EWT, EWW
• VWO contains: China ~30%, India ~20%, Brazil ~5%, Taiwan ~18%, S. Korea ~12%, Mexico ~2%
• Each country ETF is a subset of VWO. Useful for tilting, not adding alongside
5. World Index vs Everything: ACWI, SPY, EFA, VWO
• ACWI = ~60% US + ~28% Dev ex US + ~12% EM
• It already contains SPY, EFA, and VWO. Best used as standalone global allocation
6. Precious Metals / Commodities: GLD, SLV, DBC
• GLD and SLV both driven by real interest rates, USD, and safe haven demand (~0.85 correlation)
• DBC (Commodities) includes ~10% precious metals allocation, overlapping with GLD
• Silver has higher industrial use (~50%) vs gold (~10%)
7. US Corporate Bonds: HYG, LQD
• HYG = high yield (junk) bonds, LQD = investment grade corporate bonds
• Both are US corporate credit; ~0.75 0.85 correlation depending on regime
8. Energy / Commodities: DBC, XLE
• DBC is ~55% energy (crude oil, natural gas); XLE tracks US energy companies
• Both heavily driven by oil prices. Selecting both concentrates energy exposure
9. Hedge Fund Strategies: QAI, MNA
• QAI = multi strategy hedge fund replication; MNA = merger arbitrage
• Merger arb is one component of the multi strategy approach QAI tracks
1.860▲ +0.844 vs SPY
Long-Only Max Sharpe | Ret 27.91% Vol 13.08%
1.747▲ +0.731 vs SPY
Constrained Max Sharpe | Ret 16.91% Vol 7.62%
0.891▼ -0.125 vs SPY
Long-Only Min Variance | SPY Sharpe: 1.016
1.140▲ +0.607 vs SPY
Long-Only Max Sharpe | Ret 19.34% Vol 13.70%
0.752▲ +0.219 vs SPY
Constrained Max Sharpe | Ret 10.27% Vol 8.71%
-0.191▼ -0.724 vs SPY
Long-Only Min Variance | SPY Sharpe: 0.533
0.792▲ +0.258 vs SPY
Long-Only Max Sharpe | Ret 13.77% Vol 12.18%
0.576▲ +0.041 vs SPY
Constrained Max Sharpe | Ret 9.11% Vol 8.64%
0.071▼ -0.463 vs SPY
Long-Only Min Variance | SPY Sharpe: 0.534
Asset Statistics
Click to select/deselect asset classes. Green = included in model. Minimum 3 assets.
Current Sharpe Ratios
New Sharpe Ratios (3Y)
Asset
Ticker
Ann. Return (%)
Ann. Vol (%)
Sharpe
VaR 95%
CVaR 95%
Skewness
Kurtosis
Max DD (%)
US Large Cap
SPY
18.87
15.05
1.016
1.42
2.13
0.635
19.448
-19.21
US Small Cap
IWM
11.20
21.21
0.359
1.99
2.86
0.153
3.186
-28.23
Dev. ex-US Equity
EFA
14.84
14.49
0.776
1.39
1.99
-0.092
9.626
-14.33
EM Equities
VWO
13.60
15.39
0.650
1.50
2.14
-0.095
4.786
-18.07
Gold
GLD
34.60
19.11
1.623
1.58
2.76
-1.205
11.647
-14.49
US Long Bonds
TLT
-0.79
14.56
-0.301
1.55
2.06
-0.098
0.673
-23.07
High Yield Bonds
HYG
8.14
5.45
0.836
0.49
0.72
0.489
6.265
-4.59
EM Govt Bonds
EMB
9.22
7.44
0.756
0.72
1.04
0.018
2.291
-8.04
EM Corporate Bonds
CEMB
6.90
4.35
0.761
0.41
0.62
-0.422
4.069
-3.88
Real Estate
IYR
7.44
17.23
0.223
1.81
2.55
-0.120
2.577
-17.87
Asset
Ticker
Ann. Return (%)
Ann. Vol (%)
Sharpe
VaR 95%
CVaR 95%
Skewness
Kurtosis
Max DD (%)
US Large Cap
SPY
12.75
16.95
0.533
1.66
2.49
0.141
8.377
-26.22
US Small Cap
IWM
3.99
22.64
0.012
2.28
3.12
0.027
1.648
-35.07
Dev. ex-US Equity
EFA
8.72
16.07
0.311
1.57
2.22
0.075
5.106
-30.94
EM Equities
VWO
4.47
17.11
0.044
1.69
2.36
0.163
3.895
-34.62
Gold
GLD
22.10
17.31
1.062
1.58
2.48
-0.959
10.553
-21.48
US Long Bonds
TLT
-5.74
15.91
-0.595
1.69
2.18
-0.012
0.449
-45.60
High Yield Bonds
HYG
3.81
7.47
0.012
0.72
1.11
-0.025
6.333
-16.25
EM Govt Bonds
EMB
2.63
9.73
-0.112
1.00
1.43
0.272
4.212
-29.43
EM Corporate Bonds
CEMB
2.14
5.63
-0.280
0.56
0.85
-0.276
7.193
-20.76
Real Estate
IYR
5.20
18.69
0.079
2.05
2.73
-0.050
2.537
-36.67
Asset
Ticker
Ann. Return (%)
Ann. Vol (%)
Sharpe
VaR 95%
CVaR 95%
Skewness
Kurtosis
Max DD (%)
US Large Cap
SPY
13.70
17.91
0.534
1.68
2.80
-0.616
15.677
-35.75
US Small Cap
IWM
9.75
23.05
0.244
2.10
3.39
-0.726
9.092
-44.63
Dev. ex-US Equity
EFA
8.42
17.20
0.249
1.54
2.56
-1.186
16.966
-37.01
EM Equities
VWO
7.79
19.20
0.191
1.83
2.82
-0.929
11.464
-40.27
Gold
GLD
13.83
15.67
0.619
1.51
2.28
-0.716
9.370
-23.89
US Long Bonds
TLT
-0.95
14.91
-0.341
1.48
2.07
0.020
5.080
-51.11
High Yield Bonds
HYG
4.95
8.31
0.098
0.68
1.22
-0.109
26.605
-22.54
EM Govt Bonds
EMB
3.46
9.99
-0.067
0.85
1.50
-2.645
42.662
-29.43
EM Corporate Bonds
CEMB
3.95
6.44
-0.028
0.52
0.95
-1.943
35.171
-21.22
Real Estate
IYR
5.76
20.45
0.080
1.84
3.07
-1.490
24.449
-45.03
Portfolio Summary
Portfolio
Return (%)
Volatility (%)
Sharpe
VaR 95%
CVaR 95%
US Large Cap
US Small Cap
Dev. ex-US Equity
EM Equities
Gold
US Long Bonds
High Yield Bonds
EM Govt Bonds
EM Corporate Bonds
Real Estate
Long-Only Max Sharpe
27.91
13.08
1.860
1.13
1.87
42.5%
0.0%
0.0%
0.0%
57.5%
0.0%
0.0%
0.0%
0.0%
0.0%
Long-Only Min Var
7.56
4.46
0.891
0.41
0.61
0.0%
0.0%
0.0%
0.0%
0.6%
0.0%
40.4%
0.0%
59.0%
0.0%
Constrained 25% Max Sharpe
16.91
7.62
1.747
0.64
1.07
22.7%
0.0%
0.0%
0.0%
25.0%
0.0%
25.0%
2.3%
25.0%
0.0%
Constrained 25% Min Var
10.85
6.18
1.173
0.57
0.85
6.8%
0.0%
0.0%
3.2%
9.0%
6.0%
25.0%
25.0%
25.0%
0.0%
Portfolio
Return (%)
Volatility (%)
Sharpe
VaR 95%
CVaR 95%
US Large Cap
US Small Cap
Dev. ex-US Equity
EM Equities
Gold
US Long Bonds
High Yield Bonds
EM Govt Bonds
EM Corporate Bonds
Real Estate
Long-Only Max Sharpe
19.34
13.70
1.140
1.29
1.94
29.5%
0.0%
0.0%
0.0%
70.5%
0.0%
0.0%
0.0%
0.0%
0.0%
Long-Only Min Var
2.65
5.60
-0.191
0.54
0.84
0.0%
0.0%
0.0%
0.0%
1.8%
0.0%
9.3%
0.0%
88.9%
0.0%
Constrained 25% Max Sharpe
10.27
8.71
0.752
0.89
1.25
25.0%
0.0%
1.1%
0.0%
25.0%
0.0%
24.9%
0.0%
24.1%
0.0%
Constrained 25% Min Var
5.13
7.45
0.189
0.75
1.03
2.1%
0.0%
0.0%
2.3%
13.6%
7.0%
25.0%
25.0%
25.0%
0.0%
Portfolio
Return (%)
Volatility (%)
Sharpe
VaR 95%
CVaR 95%
US Large Cap
US Small Cap
Dev. ex-US Equity
EM Equities
Gold
US Long Bonds
High Yield Bonds
EM Govt Bonds
EM Corporate Bonds
Real Estate
Long-Only Max Sharpe
13.77
12.18
0.792
1.13
1.80
42.5%
0.0%
0.0%
0.0%
57.5%
0.0%
0.0%
0.0%
0.0%
0.0%
Long-Only Min Var
4.57
6.15
0.071
0.53
0.89
0.0%
0.0%
0.0%
0.0%
6.3%
4.5%
21.8%
0.0%
67.4%
0.0%
Constrained 25% Max Sharpe
9.11
8.64
0.576
0.76
1.28
25.0%
0.0%
0.0%
0.0%
25.0%
0.0%
25.0%
0.0%
25.0%
0.0%
Constrained 25% Min Var
5.03
7.15
0.125
0.68
1.04
3.9%
0.0%
0.0%
0.0%
13.9%
17.3%
25.0%
14.9%
25.0%
0.0%
1. Efficient Frontier
Max Sharpe ★ and Min Variance ◆ markers. Capital Market Line from Rf through tangency portfolio.
1b. Cumulative Returns
2. Long-Only vs Constrained 25% — Allocation Comparison
3. Correlation Matrix
4. Allocation vs Target Return
Stacked area: how allocation shifts as target return rises. Red dashed = Max Sharpe.
5. Interactive Constraint Simulator
Set min/max allocation per asset for the Long-Only portfolio.
Click Optimize to see the custom-constrained Max Sharpe portfolio.
The right panel shows the Sharpe ratio and how it compares to the unconstrained baseline.
6. Strategy Backtest
Walk forward backtest with 3 year rolling lookback (long only, unconstrained).
On the last trading day of every month (or every two months for bimonthly), the MVO model is re-optimized using the trailing 3 calendar years of data
to find the optimal weights, and the portfolio is rebalanced to these new weights. Most of the time, the asset classes
remain the same and the rebalancing simply adjusts the allocation percentages back to the new optimum.
Between rebalances, weights drift naturally as prices move.
Period: 2019-03-14 to 2026-03-06. Hover over lines for current weights; hover over dots for turnover at each rebalance.
Default: 10 bps (0.10%). Covers bid ask spread and slippage for liquid ETFs.
7. Portfolio Composition Analysis
Why the optimizer selected this allocation, and which assets are close to being included.
