GBA Workbench – Sharpe Portfolio

This algorithm solves for the optimal portfolio weights to maximise the Sharpe ratio of the portfolio.

The Sharpe ratio characterizes how well the return of an asset compensates the investor for the risk taken.

As per Investopedia:

“It was developed by Nobel laureate William F. Sharpe. The Sharpe ratio is the average return earned in excess of the risk-free rate per unit of volatility or total risk. Subtracting the risk-free rate from the mean return, the performance associated with risk-taking activities can be isolated. One intuition of this calculation is that a portfolio engaging in “zero risk” investment, such as the purchase of U.S. Treasury bills (for which the expected return is the risk-free rate), has a Sharpe ratio of exactly zero. Generally, the greater the value of the Sharpe ratio, the more attractive the risk-adjusted return.

Investopedia

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

  • “Risk Free Rate”
  • “Lower Bounds” (the minum weighting for each instrument at each re-allocation date; an often used default is 0.00)
  • “Upper Bounds” (the maximum weighting for each instrument at each re-allocation date; an often used default is 1.00)
  • “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 following parameters were used:

  • Bounds (0,1)
  • Lookback 3 months
  • Re-allocation Monthly

The portfolio:

30 US listed ETF country funds and bond mutual funds.

sharpe

Stat                 Sharpe Portfolio    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         497.37%             403.96%
Daily Sharpe         0.86                0.50
CAGR                 9.11%               8.21%
Max Drawdown         -23.84%             -55.25%

MTD                  1.58%               3.38%
3m                   -0.11%              6.69%
6m                   2.70%               10.17%
YTD                  7.88%               13.50%
1Y                   8.16%               15.74%
3Y (ann.)            1.73%               9.99%
5Y (ann.)            4.94%               15.28%
10Y (ann.)           7.27%               7.06%
Since Incep. (ann.)  9.11%               8.21%

Daily Sharpe         0.86                0.50
Daily Mean (ann.)    9.32%               9.79%
Daily Vol (ann.)     10.89%              19.47%
Daily Skew           -0.34               -0.05
Daily Kurt           9.58                7.81
Best Day             6.12%               11.58%
Worst Day            -7.74%              -9.03%

Monthly Sharpe       0.82                0.59
Monthly Mean (ann.)  9.40%               9.03%
Monthly Vol (ann.)   11.50%              15.28%
Monthly Skew         0.34                -0.61
Monthly Kurt         4.19                0.97
Best Month           17.36%              10.93%
Worst Month          -10.99%             -16.79%

Yearly Sharpe        1.00                0.51
Yearly Mean          9.32%               9.46%
Yearly Vol           9.30%               18.52%
Yearly Skew          0.38                -0.94
Yearly Kurt          0.12                0.74
Best Year            30.41%              33.36%
Worst Year           -6.47%              -37.00%

Avg. Drawdown        -1.59%              -2.28%
Avg. Drawdown Days   27.88               34.86
Avg. Up Month        2.43%               3.39%
Avg. Down Month      -2.28%              -3.73%
Win Year %           85.00%              80.00%
Win 12m %            83.47%              76.27%
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