GBA Workbench – Minimum Variance Portfolio

This algorithm performs a standard mean-variance optimization over a group of instruments in a portfolio. The algorithm optimises the portfolio weightings to achieve a portfolio with minimum variance or volatility.

The algorithm is based on Modern Portfolio Theory.

As per Investopedia:

“Modern Portfolio Theory (MPT), a hypothesis put forth by Harry Markowitz in his paper “Portfolio Selection,” (published in 1952 by the Journal of Finance) is an investment theory based on the idea that risk-averse investors can construct portfolios to optimize or maximize expected return based on a given level of market risk, emphasizing that risk is an inherent part of higher reward. It is one of the most important and influential economic theories dealing with finance and investment.

Also called “portfolio theory” or “portfolio management theory,” MPT suggests that it is possible to construct an “efficient frontier” of optimal portfolios, offering the maximum possible expected return for a given level of risk. It suggests that it is not enough to look at the expected risk and return of one particular stock. By investing in more than one stock, an investor can reap the benefits of diversification, particularly a reduction in the riskiness of the portfolio. MPT quantifies the benefits of diversification, also known as not putting all of your eggs in one basket.”


The user can set the following parameters specific to this algo:

  • “Bounds” (the minum and maximum weighting for each instrument at each re-allocation date)
  • “Lookback” (the lookback period for which portfolio returns and volatility will be calculated, in months)
  • “Re-allocation Period” (the period at the beginning of which the portfolio will be re-weighted)

In the back test below:

  • The lookback is 3 months
  • Upper and lower bounds for weightings are (0.0, 1.0)
  • Re-allocation is monthly
  • The portfolio consists of 30 US listed ETF country funds and bond mutual funds


Stat                 Minimum Variance    S&P
-------------------  ------------------  ----------
Start                1996-06-20          1996-06-20
End                  2016-12-20          2016-12-20
Risk-free rate       0.00%               0.00%

Total Return         498.11%             403.96%
Daily Sharpe         1.02                0.50
CAGR                 9.12%               8.21%
Max Drawdown         -15.31%             -55.25%

MTD                  2.09%               3.38%
3m                   0.96%               6.69%
6m                   3.31%               10.17%
YTD                  4.06%               13.50%
1Y                   4.35%               15.74%
3Y (ann.)            3.45%               9.99%
5Y (ann.)            4.16%               15.28%
10Y (ann.)           5.81%               7.06%
Since Incep. (ann.)  9.12%               8.21%

Daily Sharpe         1.02                0.50
Daily Mean (ann.)    9.14%               9.79%
Daily Vol (ann.)     8.95%               19.47%
Daily Skew           -0.59               -0.05
Daily Kurt           10.69               7.81
Best Day             4.09%               11.58%
Worst Day            -6.53%              -9.03%

Monthly Sharpe       1.05                0.59
Monthly Mean (ann.)  9.13%               9.03%
Monthly Vol (ann.)   8.66%               15.28%
Monthly Skew         0.26                -0.61
Monthly Kurt         3.77                0.97
Best Month           13.14%              10.93%
Worst Month          -9.26%              -16.79%

Yearly Sharpe        1.28                0.51
Yearly Mean          9.10%               9.46%
Yearly Vol           7.10%               18.52%
Yearly Skew          0.85                -0.94
Yearly Kurt          0.76                0.74
Best Year            26.49%              33.36%
Worst Year           -1.23%              -37.00%

Avg. Drawdown        -1.31%              -2.28%
Avg. Drawdown Days   24.32               34.86
Avg. Up Month        1.99%               3.39%
Avg. Down Month      -1.57%              -3.73%
Win Year %           90.00%              80.00%
Win 12m %            88.56%              76.27%




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