backtestStrategy non-sensical example under backtest investment strategies help center page

on the otherwise amazing page:

https://uk.mathworks.com/help/finance/backtest-investment-strategies.html

there are 5 strategies defined, among which a Max_Sharpe_Ratio, based on a function maxSharpeRatioFcn, defined as:

function new_weights = maxSharpeRatioFcn(current_weights, pricesTT)
% Mean-variance portfolio allocation

nAssets = size(pricesTT, 2);
assetReturns = tick2ret(pricesTT);
% Max 25% into a single asset (including cash)
p = Portfolio('NumAssets',nAssets,...
    'LowerBound',0,'UpperBound',0.1,...
    'LowerBudget',1,'UpperBudget',1);
p = estimateAssetMoments(p, assetReturns{:,:});
new_weights = estimateMaxSharpeRatio(p);

end

Great! except, when the backtestEngine gets a runBacktest, the max_sharpe one produces:

• the lowest sharpe
• lowest total return
• highest volatility
• highest turnover
• max drawdown
• highest buy/sell cost

summaryByStrategies=9×5 table
                       Equal_Weighted    Max_Sharpe_Ratio    Inverse_Variance    Markowitz_Optimization    Robust_Optimization
                       ______________    ________________    ________________    ______________________    ___________________

    TotalReturn             0.18745            0.14991            0.15906                 0.17404                 0.15655     
    SharpeRatio             0.12559           0.092456            0.12179                 0.10339                 0.11442     
    Volatility            0.0063474          0.0070186          0.0055626               0.0072466               0.0058447     
    AverageTurnover      0.00087623          0.0065762          0.0028666               0.0058268               0.0025172     
    MaxTurnover            0.031251              0.239            0.09114                 0.21873                0.073746     
    AverageReturn        0.00083462         0.00068672          0.0007152              0.00078682              0.00070651     
    MaxDrawdown            0.072392           0.084768           0.054344                0.085544                0.064904     
    AverageBuyCost         0.047298             0.3449            0.15228                  0.3155                  0.1328     
    AverageSellCost        0.047298             0.3449            0.22842                  0.3155                  0.1328     

to note, one of the 5 strategies is the equal_weighted.

So, the question is: how (on earth), a strategy "designed" to produce a "max" sharpe, gets the lowest possible performance across the 5 of them ... mathematically it doesn't make sense ...

Answer 1

[Alejandra Pena-Ordieres]

The backtest engine utilizes past data to estimate the mean and covariance matrix needed to find the maximum Sharpe ratio portfolio. Then, the maximum Sharpe ratio portfolio obtained from the past data is invested in future unseen data. However, as the old financial disclaimer goes, past performance is not a reliable indicator of future results. The example that you're referring to is one great example of the past performance disclaimer.

[Alejandra Pena-Ordieres]

This is mentioned in the Examine Backtest Results:

"When analzying these results, remember that the backtest engine computes the weights using past data. At the moment the weights are computed (with the past data), the portfolio weights obtained from the Max_Sharpe_Ratio strategy are the ones that achieve the maximum Sharpe ratio. After those weights are computed, they are invested in future unseen data. Consequently, in this summary, the Max_Sharpe_Ratio results are the lowest SharpeRatio with lowest returns. This example demonstrates that past performance is no guarantee of future results and a strategy that has performed well in the past may not perform well in the future."