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Pythagoras
Performance
Return for Risk
Dividends
Drawdowns
Volatility
Diversification

Asset Allocation


VBMFX 30.00%GLD 20.00%SPY 50.00%BondBondCommodityCommodityEquityEquity

S&P 500 Index

Performance

Performance Chart

The chart shows the growth of an initial investment of $10,000 in Pythagoras, comparing it to the performance of the S&P 500 index or another benchmark. All prices have been adjusted for splits and dividends. The portfolio is rebalanced Every 3 months.


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The earliest data available for this chart is Nov 18, 2004, corresponding to the inception date of GLD

Returns By Period

As of Apr 2, 2026, the Pythagoras returned 0.18% Year-To-Date and 10.64% of annualized return in the last 10 years.


1D1MYTD6M1Y3Y*5Y*10Y*
Benchmark
S&P 500 Index
0.72%-3.54%-3.95%-2.09%15.95%16.96%10.34%12.24%
Portfolio
Pythagoras
0.73%-3.56%0.18%3.80%19.57%16.97%10.45%10.64%
SPY
State Street SPDR S&P 500 ETF
0.75%-4.28%-3.65%-1.42%18.14%18.48%11.86%14.06%
VBMFX
Vanguard Total Bond Market Index Fund
0.21%-1.63%-0.30%0.35%3.55%3.40%0.08%1.50%
GLD
SPDR Gold Shares
1.75%-10.65%10.47%22.97%52.25%33.69%22.00%14.11%
*Multi-year figures are annualized to reflect compound growth (CAGR)

Monthly Returns

Based on dividend-adjusted daily data since Nov 19, 2004, Pythagoras's average daily return is +0.04%, while the average monthly return is +0.74%. At this rate, your investment would double in approximately 7.8 years.

Historically, 64% of months were positive and 36% were negative. The best month was Apr 2020 with a return of +8.3%, while the worst month was Oct 2008 at -12.3%. The longest winning streak lasted 11 consecutive months, and the longest losing streak was 5 months.

On a daily basis, Pythagoras closed higher 56% of trading days. The best single day was Oct 13, 2008 with a return of +6.0%, while the worst single day was Mar 12, 2020 at -5.5%.


JanFebMarAprMayJunJulAugSepOctNovDecTotal
20263.25%1.92%-5.49%0.73%0.18%
20252.90%0.36%-0.74%0.78%2.86%3.15%0.94%2.37%4.48%2.09%1.37%0.42%22.98%
20240.44%2.31%3.61%-2.14%3.33%2.00%2.38%1.99%2.50%-0.33%2.66%-2.01%17.82%
20235.25%-3.10%4.21%1.14%-0.35%2.74%2.08%-1.25%-4.08%-0.10%6.35%3.64%17.17%
2022-3.62%-0.53%1.21%-5.93%-0.40%-4.81%4.77%-3.48%-6.54%3.26%5.58%-2.59%-13.15%
2021-1.44%-0.33%1.76%3.65%1.95%-0.18%2.09%1.42%-3.26%3.77%-0.45%2.90%12.26%

Benchmark Metrics

Pythagoras has an annualized alpha of 4.37%, beta of 0.48, and R² of 0.81 versus S&P 500 Index. Calculated based on daily prices since November 19, 2004.

  • This portfolio participates in less of S&P 500 Index's moves in both directions, but captures a larger share of gains (59.12%) than losses (48.05%) — typical of diversified or defensive assets.
  • This portfolio generated an annualized alpha of 4.37% versus S&P 500 Index — delivering returns beyond what market exposure alone would predict.
  • Beta of 0.48 indicates this portfolio moves significantly less than S&P 500 Index — a genuinely defensive profile with reduced participation in both market rallies and downturns.

Alpha
4.37%
Beta
0.48
0.81
Upside Capture
59.12%
Downside Capture
48.05%

Expense Ratio

Pythagoras has an expense ratio of 0.17%, which is considered low. Below, you can find the expense ratios of the portfolio's funds side by side and easily compare their relative costs.


Return for Risk

Risk / Return Rank

Pythagoras ranks 78 for risk / return — better than 78% of portfolios on our site. You're getting solid returns for the risk taken. A good sign, especially for investors who want growth without excessive volatility.


Pythagoras Risk / Return Rank: 7878
Overall Rank
Pythagoras Sharpe Ratio Rank: 7979
Sharpe Ratio Rank
Pythagoras Sortino Ratio Rank: 8383
Sortino Ratio Rank
Pythagoras Omega Ratio Rank: 8585
Omega Ratio Rank
Pythagoras Calmar Ratio Rank: 7070
Calmar Ratio Rank
Pythagoras Martin Ratio Rank: 7171
Martin Ratio Rank
The rank (0–100) shows how this investment's returns compare to the risk taken. Higher = better. Based on the past 12 months of data, combining Sharpe, Sortino, and other metrics used by quantitative funds and institutional investors.

Return / Risk — by metrics


PortfolioBenchmarkDifference

Sharpe ratio

Return per unit of total volatility

1.72

0.92

+0.80

Sortino ratio

Return per unit of downside risk

2.47

1.41

+1.05

Omega ratio

Gain probability vs. loss probability

1.38

1.21

+0.16

Calmar ratio

Return relative to maximum drawdown

2.47

1.41

+1.05

Martin ratio

Return relative to average drawdown

10.30

6.61

+3.68


How much return does each position deliver for the risk it carries? Higher values mean better reward for the risk taken.

Risk / Return RankSharpe ratioSortino ratioOmega ratioCalmar ratioMartin ratio
SPY
State Street SPDR S&P 500 ETF
590.961.491.231.537.27
VBMFX
Vanguard Total Bond Market Index Fund
440.901.301.161.624.56
GLD
SPDR Gold Shares
851.892.311.352.709.90

Sharpe Ratio

The Sharpe ratio helps investors understand how much return they're getting for the level of risk taken. A higher Sharpe ratio indicates better risk-adjusted performance, meaning more reward for each unit of risk.

Pythagoras Sharpe ratios as of Apr 2, 2026 (values are recalculated daily):

  • 1-Year: 1.72
  • 5-Year: 1.03
  • 10-Year: 1.09
  • All Time: 0.88

These values reflect how efficiently the investment has delivered returns relative to its volatility over different time periods. All figures are annualized and based on daily total returns (including price changes and dividends).

Compared to the broad market, where average Sharpe ratios range from 1.00 to 1.70, this portfolio's current Sharpe ratio is in the top 25%. This signifies superior risk-adjusted performance, meaning the portfolio is delivering strong returns for the level of risk taken compared to most others.

The chart below shows the rolling Sharpe ratio of Pythagoras compared to the selected benchmark. This view highlights how the investment's risk-adjusted performance has changed over time.


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Dividends

Dividend yield

Pythagoras provided a 1.61% dividend yield over the last twelve months.


TTM20252024202320222021202020192018201720162015
Portfolio1.61%1.66%1.67%1.60%1.57%1.12%1.45%1.66%1.76%1.64%1.74%1.85%
SPY
State Street SPDR S&P 500 ETF
1.13%1.07%1.21%1.40%1.65%1.20%1.52%1.75%2.04%1.80%2.03%2.06%
VBMFX
Vanguard Total Bond Market Index Fund
3.50%3.76%3.57%2.99%2.49%1.72%2.31%2.63%2.47%2.45%2.43%2.71%
GLD
SPDR Gold Shares
0.00%0.00%0.00%0.00%0.00%0.00%0.00%0.00%0.00%0.00%0.00%0.00%

Drawdowns

Drawdowns Chart

The Drawdowns chart displays portfolio losses from any high point along the way. Drawdowns are calculated considering price movements and all distributions paid, if any.


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Worst Drawdowns

The table below displays the maximum drawdowns of the Pythagoras. A maximum drawdown is a measure of risk, indicating the largest reduction in portfolio value due to a series of losing trades.

The maximum drawdown for the Pythagoras was 29.01%, occurring on Nov 20, 2008. Recovery took 329 trading sessions.

The current Pythagoras drawdown is 5.40%.


Depth

Start

To Bottom

Bottom

To Recover

End

Total

-29.01%May 20, 2008130Nov 20, 2008329Mar 16, 2010459
-18.74%Dec 28, 2021202Oct 14, 2022292Dec 13, 2023494
-18.22%Feb 20, 202022Mar 20, 202053Jun 5, 202075
-8.96%Jan 29, 2018229Dec 24, 201836Feb 15, 2019265
-8.9%Feb 20, 202534Apr 8, 202523May 12, 202557

Volatility

Volatility Chart

The chart below shows the rolling one-month volatility.


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Diversification

Diversification Metrics


Number of Effective Assets

The portfolio contains 3 assets, with an effective number of assets of 2.63, reflecting the diversification based on asset allocation. This number of effective assets suggests a highly concentrated portfolio, where a few assets dominate the allocation, potentially increasing the portfolio's risk due to lack of diversification.

Asset Correlations Table

The table below displays the correlation coefficients between the individual components of the portfolio, the entire portfolio, and the chosen benchmark.

BenchmarkVBMFXGLDSPYPortfolio
Benchmark1.00-0.180.060.990.87
VBMFX-0.181.000.22-0.180.05
GLD0.060.221.000.060.45
SPY0.99-0.180.061.000.87
Portfolio0.870.050.450.871.00
The correlation results are calculated based on daily price changes starting from Nov 19, 2004