The Macroaxis mean-variance optimization framework is designed to model the process of effective portfolio origination that, if properly applied, can lead to significant reduction of systematic risk, while achieving way above-average risk-adjusted returns over long period of time. The Macroaxis optimization engine is based on the assumption that the stock prices may exhibit significant volatility as well as inconsistencies between portfolio historical and projected values; which in-turn, can minimize the benefits and effects of diversification.

Portfolio Suggestion

Portfolio Suggestion is our flagship module. Based on the implementation of Mean-Variance optimization, the module simply attempts to suggest to you (in the context of Modern Portfolio Theory) a better portfolio taking your current portfolio as an input. This technique is not new. Institutional money managers and private financial advisers have been using this technique for many years. But unlike professional money managers, Macroaxis is not a store with a predefined pool of mutual funds (or a selected set of model portfolios) and does not limit the landscape of market possibilities. Plus, our optimization algorithm goes a little further to provide you with more than one educated option to create efficient portfolio based on your unique appetite for risk.
Even though we strongly believe in Efficient-market hypothesis our suggestion algorithm uses the power of mathematics to synthetically manufacture efficient portfolios based on market risk reduction through examining of asset correlation and mean-variance optimization.
The output of the portfolio suggestion module is segregated into two distinct categories, so that it is easier for the investor to select the right option.

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Portfolio Optimization

1. Segregation based on closeness to original portfolio

Suggestion One

Portfolio Optimization

Optimizing your existing positions to adjust to an asset allocation that is optimal for your specified risk appetite. No additional assets are added. This is a classical mean-variance optimization without rebalancing
Suggestion Two

Passive Rebalancing

Removing assets with negative expected returns and replacing them with assets drawn from the market. Then rebalancing it to get an asset allocation that is optimal for your specified risk level.
Suggestion Three

Active Rebalancing

Removing 40 to 60% of assets with poor performance and adding better performing assets from the market. Then rebalancing it to get an asset allocation that is optimal for your specified risk level
Suggestion Four

Total Rebalancing

Replacing all of your existing positions with better performing assets. Then rebalancing your new portfolio to get asset allocation that is optimal for your specified risk level

The greener the suggestion the closer it is to your original portfolio in terms of asset composition and class.

2. Segregation based on performance gain over original portfolio

We provide a very simple four-star optimization methodology. A star is given for every category in which the suggested portfolio outperforms your existing portfolio.

    Next day Value At Risk (VaR) — Value of your portfolio that is likely to decrease over the next trading day
    Expected Return — Weighted-average daily return of all assets in your portfolio
    Total Risk — Standard deviation (volatility) of the portfolio returns
    Sharpe Ratio — Excess return per unit of total risk in your portfolio

Perfect Optimization
Perfect Optimization
Suggested portfolio outperforms the original portfolio in all four categoreis
Good Optimization
Good Optimization
Suggested portfolio outperforms the original portfolio in three out of four categoreis
Weak Optimization
Weak Optimization
Suggested portfolio outperforms the original portfolio in two out of four categoreis
Poor Optimization
Poor Optimization
Suggested portfolio outperforms the original portfolio in one out of four categoreis
No Optimization
No Optimization
Suggested portfolio does not outperform the original portfolio in any of four categoreis

Portfolio Optimization

This toolset is written in the context of Modern Portfolio Theory (MPT). MPT suggests that rational investors will use diversification to optimize their portfolios. The goal of this toolset is to suggest a unique, optimal portfolio that can be constructed with respect to an investor's risk preferences and constraints.

Modern Portfolio Theory (MPT) is a sound method for many investors in establishing a disciplined approach to investing. It simply assumes that most investors dislike risk, and will make decisions based on maximizing returns for a level of risk that is acceptable to them. This toolset is built on this very simple assumption, giving mainstream investors a set of conventional techniques to reduce exposure to individual asset risk by holding a diversified portfolio of assets.

How to Use This Toolset

Using the Wealth Optimization Toolset is easy. As a rational investor, your objective is to build a portfolio where the excess return per unit of total risk is maximized. You can reduce portfolio risk simply by holding securities that are not perfectly correlated. In other words, you can reduce exposure to individual asset risk by holding a diversified portfolio. Diversification will allow for the same portfolio return with reduced risk. Whether you are a risk taker or an extremely conservative investor, this toolset will allow you to construct a portfolio that is optimized against your specific risk preferences and objectives.

Building an Optimal Portfolio

The methodology for optimizing your portfolio is extremely easy. First, import or select assets to be included in your portfolio using Stocks, Funds or ETFs browsers. Second, use Portfolio Analyzer to evaluate your holdings individually, and to compare your entire portfolio performance against selected benchmark. Third, use Portfolio Optimizer and Efficient Frontier Pitchlets to optimize your holdings against your risk preferences and constraints. These three steps are repeated until perfect optimization is achieved. If you are lucky, you can obtain perfect optimization on the very first pitch; or it may take you few iterations until desired optimization is achieved.

Achieving Perfect Optimization

We provide a very simple four-star optimization methodology. Your goal is to outperform your existing portfolio in all four categories.

  Value At Risk (VaR)   Next day Value At Risk (VaR) — Value of your portfolio that is likely to decrease over the next trading day
  Expected Return   Expected Return — Weighted-average daily return of all assets in your portfolio
  Total Risk   Total Risk — Standard deviation (volatility ) of the portfolio return
  Sharpe Ratio   Sharpe Ratio — Excess return per unit of total risk in your portfolio


Two simple ways to optimize your portfolio

1. 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.

2. 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)

Note: Depending on your attitude towards risk, you may settle for allocations that are superior to your existing portfolio but are not perfectly optimal. Although this is totally acceptable, we recommend to get at least three out of five stars before deciding to stop your optimization process.

Portfolio Construction

Correlation Inspector

Correlation Inspector finds correlations between the returns of each asset in the specified portfolio against every other asset it contains. It constructs a conventional correlation table with color-coded cells, identifying the highest and lowest values, as well as values that fall within 1, 2, and 3 standard deviations from 0. Use Correlation Inspector

Watchlist Analyzer

Before comparing or considering investments, it is better to perform a risk-adjusted return calculation that will adjust the returns according to how risky the investments are. The riskier they are, the more the returns are lowered before any comparison. Technically risk refers to mean volatility, which measures how returns vary over a given period of time. An investment or a portfolio that grows steadily has low risk, and another investment with a value that jumps up and down unpredictably has high risk. Use Watchlist Analyzer

Portfolio Optimization

Performance Analyzer

Performance Analyzer runs balanced, risk-adjusted comparisons between different assets. It uses two commonly used performance indicators — Sharpe and Treynor. The Treynor Measure takes into account systematic risk whereas the Sharpe Ratio uses volatility. Assets with higher performance ratios should be preferred to assets with lower performance. Use Performance Analyzer

Portfolio Optimizer

Portfolio Optimizer evaluates the One-Day Value At Risk of the optimal portfolio along with total risk, expected return, and several common performance measures. The result is compared to your existing portfolio. The main objective, as a rational investor, is to outperform the existing portfolio in all 5 categories. Use Portfolio Optimizer

Efficient Frontier

This model constructs a basic Markowitz Efficient Frontier that represents variously weighted combinations of the portfolio's assets, yielding the maximum possible expected return at any given level of risk. It identifies the optimal portfolio on the efficient frontier for the desired risk level. Use Efficient Frontier

Portfolio Rebalancing

Rebalancing is simply the process of buying and selling portions of your existing portfolio after an investment strategy or tolerance for risk has changed, or if market conditions have changed. By using the Wealth Optimization Toolset investors can adjust the weight of each asset in the portfolio to satisfy a newly devised asset allocation.

Applied Modern Portfolio Theory (MPT)

The dot-com crash in the beginning of this century and current financial crisis taught many investors an important lesson: diversification matters.

A combination of rapidly increasing stock prices, individual speculation in stocks, accounting gimmicks and manipulations, widely available venture capital, relaxes lending standards, abuse of collaterized mortgage obligations and securities and adoptions of 'Ponzi' and other pyramid schemes by private fund managers created an exuberant environment in which many investors became exceedingly wealthy.

The bursting of the bubble created a completely opposite effect, as many unprepared and uninsured investors lost their fortunes as quickly as they acquired them just a few years earlier. Following the beginning of a rather lengthy recession, many investors are drastically reconsidering their investment habits as well as asset allocation principles and are turning to a more educated approach to diversification and market risk management.

Macroaxis LLC delivers a simple methodology to communicate complex wealth management analytics. Our implementation of Modern Portfolio Theory (MPT) is based on simplicity, speed, accessibility, and enhanced user experience, making technology that was once accessible only to professional money managers available to the entire investing community.