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Portfolio Optimization in Optimal Trader

Introduction

Portfolio Optimization is a risk management tool in Optimal Trader based on Modern Portfolio Theory for which Harry Markowitz was awarded the Nobel Price in 1990. This application will help you to optimize your portfolio with regard to the risk of the individual assets, the correlation between the assets and the expected returns of your assets. Portfolio Optimization is a powerful and easy to use risk management feature in Optimal Trader which will help you to allocate assets optimally in your portfolio.

 

Portfolio Optimization in Optimal Trader

The upper left table

In the upper left table you can select which stocks Optimal Trader will include when calculating the efficient frontier. You can edit expected return, standard deviation, minimum allowed weight, maximum allowed weight and weight limit for each stock. If you want to return to the default settings, simply click the "Default"-checkbox.

Columns from left to right:

• Incl. : Select/deselect stocks to include when calculation optimal portfolios
• Equities
• Default : Click this checkbox if you want to return to the default values of the current stock. Values reset are expected returns, standard deviation, min weight, max weight and weight limit.
• Exp. Ret./Y : Expected return per year
• Stand. Dev./Y : Standard deviation per year
• Max Weight : The maximum allowed weight of the current stock in the portfolio expressed in percent
• Min Weight : The minimum allowed weight of the current stock in the portfolio expressed in percent
• Weight Limit : A constraint expressed in percent that limits the allowed weights to be either larger than the Weight Limit value or zero. Weights between zero and the weight limit are not allowed. Because this constraint is non-linear the efficient frontier may not be entirely "smooth" with this setting applied. A lot of computer power is needed to calculate optimal weights with regard to this constraint.
• Optim. Weight : The optimal weights of your stocks expressed in percentage of the total portfolio

You can apply a specific value for all stocks by right-clicking a value and select Apply to whole column. You could for instance select 20% as Max Weight for a stock and select Apply to whole column. This would result in a portfolio where no stock will constitute more than 20% of the total portfolio.

The upper right chart

Here the price movements for all selected stocks normalized to the same starting point are displayed. Keep your mouse above a curve and a tooltip will appear with the name of the corresponding stock.

The lower left table

The lower left table ontains the correlation matrix with correlations between all selected stocks. The correlation lies between -100% and 100%. As you can see the correlation is always 100% when correlating a stock with itself.

The lower right chart

All stocks and the efficient frontier are shown in a risk-return space. Risk increases as you move to the right in the chart and expected returns increase as you move upwards in the chart.

Every colored dot corresponds to a stock in your portfolio placed at its standard deviation and it's averaged return. Keep your mouse above a dot to see the name of the corresponding stock in a tooltip. The same colors are applied to the dots in the lower right chart and the curves in the upper right chart for each stock.

The Efficient Frontier

The curve in the lower right chart is the efficient frontier, which is constituted of all optimal combinations of stocks. The curve begins on the left side with the optimal stock combination with the smallest attainable portfolio risk of all possible stock combinations. That portfolio is selected by default which is why a red solid circle is placed there. You can read the weights of that portfolio in the upper left table.

Click on another part of the curve to move the red solid circle and select another efficient portfolio. The weights in the upper left table will immediately adapt to your change.

The combination far out to the right on the efficient frontier only tries to maximize return without any risk consideration. This portfolio is solely constituted by the stock with the highest averaged return and is of course not a realistic portfolio combination.

 

Better Estimation of Expected Returns

The weak part in traditional Markowitz based portfolio optimization is the estimation of expected returns. Traditionally and theoretically, expected returns are simply estimated by averaging historical daily returns. This obviously is not an optimal solution. You can improve expected returns estimation by letting the expected returns be calculated by the Statistical Classification Indicator.

All objects will be classified to belong to one of 3888 pattern groups. The average
future returns for the corresponding pattern groups is obtained from a large database with over 500000 results, and is used as an estimation of expected return.

This feature is found under the Options button and is named Expected returns: Statistical Classification. To return to traditional expected returns estimation select Expected returns: Default.

 

Integration with Portfolio Scan

You can also let the expected returns be proportional to Portfolio Scan results. Portfolio Scan is a feature in Optimal Trader which helps you to find stocks that meet your investment criteria and helps you to compare stocks. The result of Portfolio Scan is a value for each stock which will be larger the better the stock has performed with regard to your criteria.

Portfolio Optimization will allocate to assets in your portfolio with regard to Portfolio Scan scores of each stock, the risk of each stock and correlation between stocks. Portfolio Optimization combined with Portfolio Scan results is thus a very powerful investment tool!

This feature is found under the Options button and is named Expected returns: Portfolio Analysis. To return to traditional expected returns estimation select Expected returns: Default.

The illustrated guide Mutual Fund Portfolios describes the integration between Portfolio Scan and Portfolio Optimization more thoroughly.

 

Tips

Tip 1

You can limit the weights in the upper left table. You could for instance limit the weights so that a minimum of 10% and a maximum 30% of all assets will be included in your portfolio. In that case a new efficient frontier will be calculated, optimal with regards to these constraints.

A lot of computer power is needed to identify the efficient frontier, but it will only take a couple of seconds in Optimal Trader to calculate it even for large portfolios with many stocks.

Tip 2

You can automatically deselect stocks in you portfolio where the first model (second chart from top, under the top model) is generating a sell signal (if you have run the Best Models and Settings function, the first model will be the best model). This will give you a portfolio consisting only of stocks which at the moment have a buy signal from the best model.

This function is found under the Options button and is named Deselect equities with sell signals from Model 1. The corresponding function also exists for the top model (neural network or Combined Analysis Model).

Do not forget to run Best Models and Settings and afterwards optimize your portfolio before selecting this option.