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FAQs
Portfolio optimization is a multiple objective problem that uses Mean-Variance Optimization.
This mathematical technique was pioneered by Harry Markowitz in the early 1950's and was published in 1952 by the Journal of Finance.
Implemented using Mean-Variance Optimization, his theory of portfolio allocation to this day is the most successful
applications of quantitative finance. The main aspect of this concept is asset diversification.
If all the assets of a portfolio move together and have similar risk, the portfolio volatility will simply be
equal to the weighted average of the individual asset volatilities. Therefore, the main objective of Portfolio Optimization is the
process of selecting assets that complement one another on the basis of volatility and market movement.
Mean-Variance Optimization to achieve desired asset allocation was used by institutional investor and money managers for many years and recently
became of interest to mainstream investors around the world due to the affordable access to global markets provided by the internet.
The Five Star Portfolio Optimization technique refers to the simple methodology we use to achieve better diversification.
Using the Portfolio Optimization Pitchlet, you can evaluate the One-Day Value At Risk of the optimal portfolio along with total risk,
expected return, Sharpe ratio and Treynor ratio. The model picks the optimal portfolio from the efficient frontier given your specified level
of risk, and a set of constraints on weight and return. The resulting portfolio is then compared to your existing portfolio.
As a rational investor, your main objective is to outperform your existing portfolio in all 5 categories.
For each category in which you outperform your existing portfolio, you will get one star.
The best optimization is achieved when, after several iterations, you get all five stars.
Relative Score is the number between 0 and 100, representing performance of a
portfolio in a given category, as compared to other investors' scores.
The Relative Score Diagram presents your position in a given performance category in contrast
to the average positions of all registered investors.
For example, if your score is in the middle of the bar, you are performing as an average investor in that category.
As your score increase or decreases you move towards either end of the bar.
For the risk bar, your objective is to stay close to the left side; for all other categories your
objective is to move as far to the right as possible.
The score of 0 means that your portfolio either generates negative expected return or performs very poorly.
Please Note that we use a 'naive' approach to determine the relative score of the portfolio. Since most investors use various time horizons, have different tolerance for risk, and hold different number of securities from different industries, you have to be careful when interpreting the relative score of your position. Think of your score as a naive interpretation of where you position stays in relation to smoothed position of other investors. As our investor community grows we will adjust the calculation of the relative score to account for individual time horizons, different tolerance for risk, sector and industry allocations as well as number of securities in your portfolio and types of financial instruments. All Pitchlets in this toolset are written in the context of Modern Portfolio Theory (MPT). The theory suggests that rational investors will use diversification to optimize their portfolios. The goal of this toolset is to suggest rational investors a unique, optimal portfolio that can be constructed with respect to his or her risk preferences and constraints. MPT is a sound method for many investors to establish a disciplined approach to investing. It simply assumes that most investors dislike risk, and will make decisions based solely on maximizing returns for a risk level that is acceptable to them. Macroaxis's Wealth Management Toolset is built on this very simple assumption, giving mainstream investors the tools to reduce exposure to individual asset risk by holding a diversified portfolio.
Diversification is an investment strategy designed to reduce exposure to risk by combining a variety of assets, which are unlikely to all move in the same direction.
The goal of portfolio diversification is to reduce the risk of your entire portfolio.
Volatility is limited by the fact that not all asset classes or industries, or individual companies move
up and down in value at the same time or at the same rate. Portfolio Diversification will reduces your risk
(both the upside and downside) and allows for more consistent performance under a wider range of economic conditions.
Portfolio Value at Risk (VaR) measures how the total value of your portfolio is likely to decrease over the next trading day if no anomalies occur in the market.
VaR depends on the model used to calculate it, as well as user inputs such as Confidence Interval. There are a lot of caveats in interpreting VaR values, and some criticism from the academic community has been recently published. However, when used in conjunction with other performance measures it can be a good indicator of the over health of your position. Portfolio Value at Risk is one of the components of our five star optimization technique.
The Sharpe and Treynor ratios are used to rank the performance of portfolios. They show how well your portfolio compensates you for the risk taken. When you compare two assets or two portfolios with the same expected returns against the same benchmark, the asset with the higher ratio simply gives more return for the same risk and should be preferred to the asset with low ratio. Both Sharpe and Treynor ratios are used in our five star optimization technique.
Although both Sharpe and Treynor ratios are used to rank the performance of portfolios, they have a very subtle difference. Unlike Sharpe, the Treynor Ratio relates excess return to the systematic (or market) risk [beta]. The choice of a benchmark to calculate beta is very important when using Treynor Ratio.
Although no consensus exists among investors on the exact amount of securities to hold in a well diversified portfolio, the general rule of thumb for most investors is to hold between 12 and 15 stocks. Recent research suggests, however, that many investors taking advantage of the low transaction costs afforded by today's online brokers may best optimize their portfolios by holding closer to 20 stocks.
We have tested the PitchletTM Toolset on Windows 2000, Windows XP, and Windows Vista. Please refer to the Requirements section for more information.
Analytics from the Wealth Management PitchletTM Toolset was tested and can be successfully executed and presented in Mozilla Firefox and Internet Explorer 6.0 (and up). Pitchlets may not be fully compatible with a few of older browsers still in use, including 4.x versions of Internet Explorer (and lower), 4.x versions of Netscape (and lower), 7.x versions of Opera (and lower), the CompuServe browser (run IE separately),and the AOL browser. In all cases, we recommend people using any of the browsers listed above upgrade to the latest version of Internet Explorer and/or Mozilla Firefox. According to our latest tests, the best performance and user experience is realized with the latest version of Mozilla Firefox.
At this time you can import portfolio from a Microsoft Excel Worksheet using the format displayed below.
Only valid symbols and their quantities are imported. To import portfolio from an .xls file, simply go to the
'My Portfolio' page and click on the 'Import' button.
Yes, you can export your existing portfolio to Excel. The export example is shown below.
Your existing assets and their quantities are exported along with weight and current market value.
To export your portfolio to .xls file simply go to the
'My Portfolio' page and click on the 'Export' button.
The goal of portfolio theory is to optimally allocate your investments between different assets.
Macroaxis Wealth Management Toolset is a easy to use set of modules that will allow you to make this
allocation by optimizing the trade-off between your risk and return constrains. Using our
Portfolio Optimizer or
Efficient Frontier
as well as available market browsers you can quickly optimize your portfolio against you personal risk and return preference.
The easiest way to determine if your portfolio is optimal is to pitch
Portfolio Optimizer
several times replacing your current portfolio with resulted optimal portfolio after each iteration.
You should stop this process when all relative scores of your portfolio are identical
(or almost identical) to relative scores of the optimal portfolio.
Another way to determine if your portfolio is optimal is to Pitch Efficient Frontier several times replacing your current portfolio with resulted optimal portfolio after each iteration. You should stop this process when risk and return characteristics of both portfolios are the same (i.e. current and optimal portfolios simply overlap each other on the risk/return graph) 
The performance of the individual will have to be compared against the overall performance of
the market as indicated by various indices such as the S&P or NASDAQ. This way a relative
comparison of performance can be developed.
Lets now learn to compute the 'Total Yield'. For example if the portfolio value of Mr. X is $ 2,00,000 at the beginning of this month. During the month he added $ 8,000 to the fund. During this month he also received a dividend income of $ 1,000. Assuming the value of the portfolio at the end of this month is $ 2,20,000. The total yield will be = ((220000 – (2,00,000 + 9000)) / ( 2,00,000 + (1/2 * 9000)) ) *100 = 5.38% per month
Beta indicates the proportion of the yield of a portfolio to the yield of the entire market
(as indicated by some index). If there is an increase in the yield of the market, the
yield of the individual portfolio may also go up. If the index goes up by 1.5% and the yield
of your portfolio goes up by 0.9%, the beta is 0.9/1.5 i.e 0.6. in other words, beta indicates
that for every 1 % increase in the market yield, the yield of the portfolio goes up by 0.6%.
High beta shares do move higher than the market when the market rises and the yield of the
fund declines more than the yield of the market when the market falls.
You can be indifferent to market swings if you know your stocks well. Or you can put your portfolio into neutral
or bias for the upside if you're bullish or a little for the downside if you're bearish.
One way to do that is to have a mix of stocks that have certain betas in your portfolio.
When investors are bullish on the market, they like to have high beta stocks in their
portfolios because if they're right, then their stocks go up faster than the market in general,
and their performance is better than the market. If investors are bearish on the market, then
they use the low beta or negative beta stocks because their portfolios will go down less than
the market and their performance will be better than the general market. And if they want to be neutral,
they can then make sure that they have stocks with a beta of 1 or develop a portfolio that
has stocks with betas greater than 1 and less than 1 so that they have the whole portfolio
with an average beta of 1.
A beta for a stock is derived from historical data. This means it has no predictive value for the future, but it does show that if the stock continues to have the same price patterns relative to the market in general as it has in the past, you've got a way of knowing how your portfolio will perform in relation to the market. And with a portfolio with an average beta of 1, you can create your own index fund since you'll move more or less in tandem with the market.
To build a well performing portfolio you’ll need to know the fundamentals of the markets and basic investing concepts.
There are number of financial equity instruments that can be used to assemble your portfolio quickly.
The basic assets that can be added to you portfolio are stocks, funds, and ETFs.
By selecting companies or funds of different sizes, various industries and sectors of
the economy, as well as different parts of the world, you minimize the chance of
underperformance of you portfolio in any one area.
Macroaxis Market Browsers are basic equity browsers that allow you to quickly examine a structured
view of publicly traded stocks, funds, and ETFs.
Securities are grouped into sectors and industries,
allowing you to examine and compare various fundamental,
statistical, and forward-looking indicators using a point-and-click interface.
With Market Browsers you can quickly build a portfolio of traded equities and evaluate their effectiveness and risk tradeoff using on-demand analytics or quickly generate efficient frontier and optimize your fund portfolio using portfolio optimization model
Yes, you can combine stocks, funds, and ETFs into a single portfolio.
Alternatively, you can construct different portfolio for every type of equity.
ReferencesModern Portfolio Theory From Wikipedia, the free encyclopedia Learn About Modern Portfolio Theory (MPT)Markowitz, Harry M. (1952). Portfolio Selection, Journal of Finance, 7 (1) Sharpe, William F. (1964). Capital asset prices: A theory of market equilibrium under conditions of risk, Journal of Finance, 19(3) Lintner, J. (1965). The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets, The Review of Economics and Statistics, 47 (1), 13-39 Burmeister E and Wall KD., The arbitrage pricing theory and macroeconomic factor measures, The Financial Review, 21:1-20, 1986 Chen, N.F, and Ingersoll, E., Exact pricing in linear factor models with finitely many assets: A note, Journal of Finance June 1983 Fama, E. and French, K. (1992). The Cross-Section of Expected Stock Returns, Journal of Finance, June 1992, 427-466 Black, F., Jensen, M., and Scholes, M. The Capital Asset Pricing Model: Some Empirical Tests, in M. Jensen ed., Studies in the Theory of Capital Markets. (1972) French, C. W. (2003). "The Treynor Capital Asset Pricing Model", Journal of Investment Management, 1 (2), 60-72 Lintner, J. (1965). The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets, Review of Economics and Statistics, 47 (1), 13-37 Markowitz, Harry M. (1999). The early history of portfolio theory: 1600-1960, Financial Analysts Journal, 55 (4) Tobin, James (1958). Liquidity preference as behavior towards risk, The Review of Economic Studies, 25 Treynor, J. L. (1961). "Market Value, Time, and Risk." Unpublished manuscript. Treynor, J. L. (1962). "Toward a Theory of Market Value of Risky Assets." Unpublished manuscript. Other ResourcesRobust Portfolio Optimization and Management by Frank J. Fabozzi, Petter N. Kolm, Dessislava Pachamanova, Sergio M. FocardiPortfolio Optimization and Performance Analysis by Jean-Luc Prigent Option Pricing and Portfolio Optimization by Ralf Korn, Elke Korn Portfolio optimizations in incomplete financial markets by Walter Schachermayer Bond Portfolio Optimization by Michael Puhle An MCDM approach to portfolio optimization by M. Ehrgott, K. Klamroth, C. Schwehm |
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