Overview
Portfolio Optimizer (Portopt) uses Modern Portfolio Theory (MPT) to optimize your investment portfolio. MPT is a mathematical theory, invented by Harry Markowitz, that earned him the Nobel prize in economics. MPT is often used in the financial industry to plan for optimal diversifications of portfolios.
Portopt allows for two investment strategies: In the first strategy it maximizes the expected return of the portfolio, and, according to a chosen risk penalty, simultaneously minimizes the total risk (low penalty means high risk, high penalty means low risk). In the second strategy, it minimizes the total risk for a given expected return. For each strategy, Portopt calculates the optimal percentage of investment for each asset in the portfolio.
In an optimal portfolio, according to MPT, assets should not be selected individually by looking just at their expected return and risk. Rather, MPT considers the correlation between stocks. Hence, it tries to avoid investing in stocks that have similar trends (that are in the same market, for example), in order to choose the best diversification for the given risk willingness.
In order to measure the expected return, risk, and correlations of stocks, Portopt uses monthly closing quotes over a historical period of time. Portopt allows for different periods to adjust for shorter or longer investment horizons (long periods are for long-term investments, short periods for shorter investments).
FAQ
How do I delete a stock on the iPad version?
Swipe with one finger over the stock in the list. A delete button pops
up besides the stock. Tap it to delete the stock. This is standard
iOS behaviour for deleting list items.
Are the expected returns and risks that are computed by Portopt guaranteed for my portfolio?
No. Portopt uses MPT, which is a mathematical theory that looks at historical data. It computes an optimal diversification based on the past. The results using MPT may be reasonable when looking at the past, but MPT is not able to predict the future.
I read that some studies showed that MPT does not really model the market?
True. Nevertheless, it is still widely used in the financial industry, especially for long term planning. It is one of many tools available to investors.
Where can I find a good introduction to MPT?
This Wikipedia page provides a good start.
Why does Portopt recommend to invest more into stock A than stock B, even though stock B has a higher expected return than stock B?
MPT minimizes the overall risk of a portfolio through diversification. Although stock B may have a higher expected return (and possibly a smaller risk) than stock A, the overall risk of the portfolio would be higher if more is invested in B than A. One reason could be that stock B is in the same market than other stocks of your portfolio. In statistical terms, MPT minimizes the covariance of the portfolio.
Why does Portopt recommend to invest in a stock with negative expected return?
Again, MPT minimizes the overall risk of the portfolio. The stock in question may have a favorable risk correlation with the other stocks in your portfolio.
Why does adding a stock via Google Finance result in different statistics than adding the same stock with Yahoo Finance?
We cannot guarantee for the accuracy of the historical stock data from either source. It seems to be a known issue (see this
link).
Can I mix stocks with data from Yahoo Finance and stocks with data from Google Finance in the same portfolio?
Version 1.0.1 on Android allowed this. Since this can result in
duplications, we disabled this feature in later versions. Portopt now
clears the portfolio if the data source is changed.
How many stocks can I add to the portfolio?
The number of stocks in Portopt is limited by the memory of your device. On modern smartphones, portfolios with 50 and more entries are no problem.
What is the solution precision?
To solve the MPT model, Portopt uses a numerical algorithm that repetitively solves a set of mathematical equations. At each iteration, the result of these equations gets closer and closer to the actual real solution of the MPT. Once the algorithm is within the solution precision, it stops and returns the result. Therefore, high precision means very close to the real solution.
Why would I want to reduce the precision?
The larger a portfolio becomes, the harder it is to solve the MPT model. Reducing the precision can reduce the solving time significantly. Also, in some rare cases it is just not possible for the algorithm to approximate a solution for the given precision. Reducing the precision in these cases can sometimes solve the issue.
Why would I want to change the penalty parameter?
High risk penalties allow for more conservative portfolios. However, since the penalty slider changes the risk penalty on a logarithmic scale, it may be harder to use it accurately with high values.
