A Sample Portfolio Optimization Program in Excel PRELIMINARY USER INSTRUCTIONS

Transcription

1 A Sample Portfolio Optimization Program in Excel PRELIMINARY USER INSTRUCTIONS Copyright 2006 By Robert C. Smithson, Anava Capital Management LLC And Anava Corporation This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License, version 2, as published by the Free Software Foundation. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program; if not, write to the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA USA. The author can be contacted at: Anava Capital Management LLC

2 WARNING This is a preliminary and very incomplete set of instructions for the use of the accompanying spreadsheet. It is intended only to give users the basic instructions for the use of the spreadsheet and the accompanying macros. At this time there is very little explanation of the reasons the calculations are done as they are, and extreme caution should be used in using any results from the spreadsheet. A more complete version of this manual will be made available at the class taught by the author on November 15, Those users who are able to understand and write Microsoft VBA for Excel will find the source code is unprotected, and for the most part commented. This is not commercial quality code, and problems may be found. The code and spreadsheet are being posted at this time to provide students with the opportunity to gain some familiarity with the code before the class. IT IS STRONGLY SUGGESTED THAT YOU SAVE A COPY OF THE ORIGINAL SPREADSHEET BEFORE YOU TRY USING OR MODIFYING IT. IT IS NOT PROTECTED TO COMMERCIAL STANDARDS.

3 Instructions The Input worksheet: Normally, the only unprotected parts of this sheet are the gray cells. The most important values are the Ticker and Sector columns. The Sector columns are not necessary to run an optimization by ticker, but are used to create a data table that can allow optimization by sector. If the sectors are used, the input values must be sorted by sector. The program takes a maximum of 99 securities. It takes about ten minutes on a 2.5 GHz Pentium 4 to analyze 25 securities, and the time increases rapidly above that. I've run a maximum of about 80, which took about an hour. The security symbols can be typed in, or generated directly from SI Pro. Just use the SI Pro View Editor to create a view that shows nothing but the ticker in the first column and the sector in the second, run your screen, sort the results by sector (very important for sector analysis), and export the view to a spreadsheet. Copy the results to the ticker and sector fields above. Remember that the data comes from Yahoo finance, and that the Yahoo symbols are not always the same as those in SI Pro. The program will ignore and flag bad symbols when downloads are run. It will also ignore and flag symbols for which data is not available for the entire time period requested. You have to enter the current annualized treasury rate most closely corresponding to your expected holding period, the start and end dates (both should be market days at present) of the sample data, and the sampling period (daily, weekly, or monthly). You can also specify a minimum and maximum percentage of the portfolio that any one security can have. This cannot be set security-by-security at present. The values

4 apply to all the securities in the input column. It's probably best to start with these set at a minimum of 0% and a maximum of 100%. Once you're used to the program you can play with other settings. Remember that if you specify other values, you must be sure that a solution is possible. You can't build a portfolio of ten stocks with a minimum of 50% of the portfolio in each stock, but you can with two stocks. The last parameter specifies how many random guesses the program checks as possible starting points for the gradient ascent optimization process. The larger the value, the longer the process takes, but the better the chance that the absolute optimum will be found. Empirically, 1000 works well for 100 or fewer input securities. A zero value will cause the program to compute a number, but the computed value generally takes longer to run, and doesn't seem to improve accuracy, so I usually just leave it at There are three buttons that run the various routines. "Download" downloads the data requested from Yahoo finance. You can use the default "Data" worksheet, but if you are planning on doing a lot of analysis, don't fall into the habit of just using the Data sheet and re-downloading the data every time you need it. This is unfair to other Yahoo users and could conceivably get you blocked from the website. Instead just add a new worksheet for each dataset of interest. (The example has four added for this purpose - TestData, 3MnData and 3YrData.) Then download to those spreadsheets so each dataset is downloaded only once and can be saved and re-used. "Compute Sector Values" produces an equal-dollar-weighted portfolio for each sector represented in the input stocks. At present, this only works if the tickers are SORTED BY SECTOR. The default output sheet is "Sectors." This doesn't download anything, so you can do it as often as you want. "Optimize Portfolio" runs the optimization for a selected definition of optimize. The Sharpe ratio is one of the most commonly used, but not necessarily the best, measure of portfolio performance. It maximizes (mean portfolio return - risk free return for the same period) / (portfolio standard deviation). Other possible selections are minimum standard deviation, minimum down standard deviation, best performance for a given standard deviation, and lowest standard deviation for a given performance. The output is on the "Results" sheet:

5 There's only one gray square on this sheet. You can enter the total amount to be invested in the optimized portfolio. The results are: Top left: The mean return over the sample period (in the case above 1 day), standard deviation, and Sharpe ratio of the optimized portfolio for the input data. Bottom left: The green dots on the chart represent each of the random portfolios, the best of which is used as the starting point for the gradient ascent optimization. They are plotted with the mean return on the vertical axis, and the standard deviation (risk) on the horizontal axis. Points high and to the left are good. Those low and to the right are bad. The magenta point represents the optimized portfolio. It is usually found a little outside the area covered by the random guesses. That s because of the additional optimization produced by the gradient ascent technique. Top right: This is what you really want. It gives the dollar percentage in each stock in the optimized portfolio. It also gives the actual dollar value in each stock, given the available funds for investment in the gray block. Notice that in the example case, the optimum portfolio has only six stocks instead of the original twelve. This is usually the case in optimizations using data with unpredictable variations in time. Some securities just adds noise. In investing that means risk. THE EXAMPLE DATA AND RESULTS: The example used here ran a modified O Shaughnessy Value screen on the SI Pro data dated 6/30/2006. It was assumed that the investor had holdings consisting of the results

6 of the same screen run three months earlier, on 3/31/2006. A trial new portfolio was constructed that consists of the previous holdings plus any new companies that appeared in the screen done on 6/30/2006. The assumption is that the investor will add any new companies to his existing holdings and re-optimize. Existing holdings are bought or sold only as required to meet the weights produced by the new optimization. All of this analysis could have been done on June 30 of this year. The combined portfolio was optimized using daily data from 3/30/2006 to 6/30/2006, and also using monthly data from 6/2003 through 6/2006. The performance of the optimized portfolios was then tested for short-term performance (over four months 6/30/2006 to 10/31/2006). Several portfolios were constructed from the results of the optimization screen and backtested as just described. The first two are shown below. They are an equal-dollarweighted portfolio containing the candidate stocks on June 30, 2006, and the same portfolio optimized based on the previous 3 months performance only: Notice that in the above case, the portfolio optimized for best performance over the previous three months actually under-performed the equal dollar performance over the next four months. This is a good example of the adage, What goes up must come down. In seems that the best performing portfolio over a given 3-month period can be a poor performer immediately afterwards. The next two portfolios use the 3-year optimization alone, and the both the 3-year and 3- month optimizations equally weighted:

7 As can be seen, the three-year optimization substantially outperformed the equal-dollar weighting. Evidently long-term past performance is more valid when extrapolated into the future than is short-term performance, at least for this screen. Equally weighting the short-term and long-term screens produced intermediate results, as might be expected. Now we might be tempted on seeing these results to say that if the recent performance of the stocks is such a poor predictor of future short-term performance, maybe it s anticorrelated. Maybe bad performance in the last three months is a good predictor of good performance in the next four. Let s try it with a portfolio that uses the product of the weights based on previous three-year performance and one minus the weights based on previous three-month performance: This is the best result yet % over four months isn t half bad. Can we trust it? Not really. This example shows one of the subtle biases in back testing. The tests of the long-term and short-term weights alone, and of the combined weights were reasonably unbiased, because when I did this test I didn t know what the results would be. Even so, we ve only looked at one time period, and just because the long-term weights were better over that period doesn t mean they will be better over all such periods. Maybe the combined would work better on average over many such periods.

8 The negative use of the short-term weights, however, is biased by the fact that I did it only AFTER I saw the results of the other tests. In short, I tuned the technique to work well over the period on which I tested it. It s always possible to find a method that does a good job of predicting future performance when you know what the future will be. But such good performance has to be strongly discounted until it has been proven by testing over periods when the future performance is not known. Even then, market conditions, laws, and psychology can and will change, and screens and optimization methods that once worked well will stop working. Welcome back to the Investing 101 class.