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Optimal Mutual Fund Portfolios
A Guide

Introduction

In some retirement accounts, variable life insurance policies, or other programs you can switch mutual funds with no transaction fees and without reporting gains/losses on your tax return. This is an ideal opportunity to invest your capital in an optimal portfolio - minimizing risk and maximizing profits. Simply reallocate your portfolio once every week or month and your investments are always adapted to the current market behaviour.

Following the steps described below steps will give you an optimal portfolio. This optimal portfolio will consider the following factors:

• Correlation between different securities in your portfolio – don’t put all eggs in one basket.
• The risk for every security. Risk, in this model, is the "jumpiness" of the price (the daily standard deviation of return), not the risk of large losses.
• Expected returns will partly be estimated using a statistical classification, an advanced in-house developed statistical system estimating expected returns based on current price patterns.
• Expected returns will also reflect the current trends: the short term trend, the medium term trend and the long term trend.
• Sell signals from the best models with their best settings – funds with sell signals from the best model will be de-selected from your optimal portfolio.
• Your trading horizon, that is how often you are reallocating your portfolio (every day, every week or every month)
• Your preferred risk-level – selected by clicking in the efficient frontier.

 

Walk through these steps to produce an optimal portfolio

These guidelines are for a typical user, reallocating the portfolio once every week.

Prepare Data

1. Download all mutual funds of interest from your fund manager. This includes equity funds, bond funds and hedge funds. You can try to include funds with a standard deviation close to zero such as money market funds, but beware that they can introduce numerical problems in the optimization algorithm.

2. Walk through all funds with the up- and down-key on your keyboard and delete funds with a First Date earlier than two years back– they have a too short price history for analysis and will impact calculation of the portfolio which is based on the global time period - the available period shared among all funds in the portfolio. 3. Walk through all funds and check the Last Date. If a fund is updated later than other funds, the last date will be earlier than for other funds. When comparing funds with each other, only overlapping time regions are considered. For that reason you might consider removing funds if their last date is earlier than for other funds, otherwise analysis today is for one day back in time.

In the right part of the window

4. Walk through all funds and check if the charts look alright. Sometimes the price history is erroneous, resulting in either large jumps in the charts or portions of missing data. This can be because of uncorrected adjustments for dividends or splits.

Before

Erroneous charts will distort analysis, so you must either fix the price history (under Options/Split Adjustment or export the chart history to Excel, edit the data in Excel and import the data back) or remove the fund.

After

 

Adjust Settings

5. Click Options and set the Trading Horizon to one week if it isn't already selected. When you are letting Optimal Trader search for the best settings and models, it will look at the current price pattern and estimate performance for all models and all settings one week ahead from a database with similar price patterns. Trading signals from a certain model with certain settings for these similar cases in the database have resulted in a large number of returns one week ahead. The average of these returns for these similar cases is used as a basis to determine which model and which settings are the best for the current case. Also, when estimating returns with the Statistical Classification Indicator, expected returns are made for one week ahead.

Options Dialog

6. Check that the Delay is set to one day if you are trading Mutual Funds. If you are trading a fund today, your order will probably be carried out tonight with the price of today. But the basis of your decision has been the price history up until yesterday, so you will have a delay of one day when trading mutual funds.

7. Under Best Models and Settings, click Select settings with highest absolute returns. When comparing different funds with each other you are not interested in returns compared to a buy-and-hold strategy. You will want to compare returns with other funds and this is the setting that is right for that.

8. Select Apply to All Equities and click OK.

 

Select And Optimize Models

9. Click Best Models and Settings and select Best Models, Best Settings and Best Optimization Period. Select Apply to all Equities and click OK. This will automatically select the best models and the best settings for the current price behaviour for all your funds based on statistical historical results for other equities which have similar price behaviour. The choices made will also reflect that your trading horizon is one week and that the delay before a buy/sell-order is carried out is one day.

The best model will be at the second chart from the top, under the Top Model. Best Models and Settings always puts the best model there. If you look at a Report after you have performed Best Models and Settings you can see that the model with the highest expected returns will be at the second chart from the top. We will later use the result from the best model in the Portfolio Optimization tool, by automatically removing funds with a sell signal from the best model in our optimal portfolio.

10. Click Optimize and select Optimize all equities to optimize your funds with the models and settings chosen in the last step. Optimize active models for all equities.

 

Adjust Portfolio Optimization Settings

11. Start the Portfolio Optimization tool by clicking Portfolio Optimization. If the Portfolio Optimization tool detects that two funds are strongly correlated with each other, that is if their price movements are more than 99% similar, a warning is displayed about this fund pair. You should remove one of these funds, preferably the one with the shortest price history.

Warning

12. Now we want to de-select funds which have a sell-signal from the best model for the next week. Click Options and select Deselect Equities with sell signals from Model 1. This excludes funds which have a sell-signal from the best model from the Best Models and Settings - function.

13. Click in the grid under the Max Weight-column and set a max-weight to 25%. Click Enter. Click that cell again, right-click on it and select Apply to Whole Column. This will limit the maximum weight of an equity to a maximum of 25% of your portfolio. This is an important step to make because we can never calculate an optimal portfolio, we can only estimate an optimal portfolio. It is too risky to estimate an optimal portfolio with no limits.

 

Adjust Settings for Expected Returns

14a. Now, click Options and select Expected Returns: Portfolio Scan. Other systems simply use average historical results as their Expected Returns, but we will use a more powerful approach by letting the expected returns be calculated with the help of various Portfolio Scan factors. The default settings in Portfolio Scan are ok – they are partly based on different current trends, but most importantly they are also based on expected returns results from a statistical classification of every fund. The current price pattern of the stock is analyzed and classified to belong to one of 3888 pattern-groups. The classification is based on several properties such as volatility, trend strength and fractal dimension. A large database with 500000 results is used to give an estimation of future returns based on the current pattern group. The values are based on average results for stocks in the database which exhibited the same pattern.

14b. Select 1 Week as Horizon under Expected Returns/Day (Statistical Classification) 14c. Select 13 days for the period of the Short Term Trend, 40 days for the period of the Medium Term Trend and 100 days for the period of the Long Term Trend. 14d. Apply the weights for each factor as follows: 11% weight to the Short Term Trend, 15% weight to the Medium Term Trend, 19 % to the Long Term Trend, and 55 % to the Expected Returns/Day (Statistical Classification). Why are we emphasizing the Long Term Trend more than the Short Term Trend? We are not! Trends over longer time periods are often weaker than trends over shorter time periods (when scaled to %/day), which is why we are giving less weight to shorter trends. The trend for the last three days may well be 2%/day while the trend for the last 200 days usually is less than 0.2%/day. 14e. Click No Normalization. This is important as the expected returns would be scaled otherwise, distorting results in Portfolio Optimization.

14f. Click Save Settings to save these settings for future usage.

15. Click Start Scan and after that click Select. The results of the entire Portfolio Scan operation is that we now have replaced the default expected returns in Portfolio Optimization with expected returns made up of: 16% of the short term trend, 16% of the medium term trend, 16% of the long term trend and 52% of the expected returns from the statistical classification model.

 

Select Risk Level And Read Out Optimal Portfolio

16. Now you can select your preferred risk-level by clicking the Efficient Frontier in the lower right chart and the optimal portfolio for that risk-level is displayed in the upper left grid under the Optim. Weight-column. Clicking at the left-most position on the Efficient Frontier will give you an optimal portfolio with the least possible risk, and the right-most position will give you a portfolio with the highest possible expected returns, at the cost of increased risk.

 

Next Week

Next week, click Update All after starting Optimal Trader and perform step 9 to 16 again to read out the new optimal portfolio.