Portfolio optimization is a multiple objective problem that uses Mean-Variance Optimization. This mathematical technique was pioneered by Harry Markowitz in the early 1950s 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.

What is Macroaxis Five Star Portfolio Optimization technique? Top

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.

Instant Portfolio Optimization

What is the Relative Score and how is it used in Portfolio Optimization? Top

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.

Total Portfolio Optimization

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.

What is Modern Portfolio Theory (MPT)? Top

All Modules 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 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.

What is Portfolio Diversification? Top

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.

Portfolio Optimization with correlation analysis

Why Portfolio Diversification is important? Top

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.

What is portfolio Value at Risk (VaR)? Top

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.

Portfolio Optimization with Value At Risk(VAR)

Is VaR by itself a good performance measure? Top

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.

What are Sharpe and Treynor ratios and how are they used? Top

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.

What is the difference between Sharpe and Treynor ratios? Top

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.

Why is my portfolio limited to only 20 assets? Top

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 online brokers may best optimize their portfolios by holding closer to 20 stocks.

Is my browser compatible with the Macroaxis? Top

To take advantage of the newest Macroaxis features, you'll need to use one of the following fully supported browsers:
Firefox 2.0+ (Download at www.mozilla.org) We recommend Firefox 3.5 for the best & fastest experience.
Internet Explorer 7.0+ (Download at www.microsoft.com)

We don't test the following browsers, but believe they will work:
Google Chrome (Download at www.google.com)
Safari 3.0+ (Download at www.apple.com)
Opera 9.5+ (Download at www.opera.com)

Can I import portfolio from external sources? Top

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.

Can I export my portfolio to Microsoft Excel? Top

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.

How macroaxis can help me to optimize my portfolio? Top

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.

Portfolio Optimization

How do I know my portfolio is optimal? Top

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 run 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)

Expected portfolio value with portfolio optimization

Expected portfolio value with portfolio optimization

How can I measure my Portfolio Performance? Top

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

Portfolio Performance with Portfolio Optimization

Portfolio Performance with Portfolio Optimization

What is Portfolio Beta? Top

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.

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.

How can I use Beta to achieve Portfolio Diversification and Portfolio Optimization? Top

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.

How to build a portfolio? Top

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.

What are Market Browsers? Top

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

Can I have stocks, funds and etf in same portfolio? Top

Yes, you can combine stocks, funds, and ETFs into a single portfolio. Alternatively, you can construct different portfolio for every type of equity.

Why is my account is limited to only 8 analytics run per day? Top

Portfolio analytics takes huge amount of computing resources. Since we are a small company we cannot afford to have hundreds of server in our cluster, we have restricted analytics uses 8 times a day.

We would love to offer unlimted analytics useage to our users, in fact initially we had the no limits on this. Due to popularity of Macroaxis offering we are not in position to continue offering unlimted use of our analytics. We are working to increase our computing power and soon we'll remove all the usage restrictions.

References

Modern 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 Resources

Robust Portfolio Optimization and Management by Frank J. Fabozzi, Petter N. Kolm, Dessislava Pachamanova, Sergio M. Focardi
Portfolio 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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