Portfolio Optimization

Over the last 30 years portfolio optimization including different implementations of Modern Portfolio Theory (MPT) became a trusted methodology for many professional money managers and financial advisors to establish a disciplined approach to building wealth for their clients. With the advancement in technology and availability of computing power to perform very intensive mathematical calculations, the paradigm of mean-variance optimization can now be brought to new generation of investors significantly reducing the cost of delivery of advanced financial analytics.
As an investor, your ultimate goal is to build wealth. Optimizing your investment portfolio is an essential element in this goal. However, portfolio optimization doesn't happen overnight. It is a process that takes both time and strategic planning. Investing will always carry a degree of risk. However, portfolio optimization helps to lessen this risk by setting you up to make sound investment decisions. These strategic investment decisions will allow you to create an efficient investment portfolio over time.

What is Portfolio Optimization?

The objective of portfolio optimization is to build an investment portfolio that yields the maximum possible return while also reducing the total amount of risk involved. Implementing portfolio optimization strategies will leave you with a balanced portfolio where your investment capital is spread across various asset classes. Investors call this an efficient portfolio, but what does an efficient portfolio really look like?
An efficient investment portfolio is based on the concept of diversification. Ultimately, diversification across classes is a risk-mitigation strategy. To plan for systemic risk, an efficient portfolio will include a wide variety of asset types and classes. Ideally, investors spread their asset classes over Stocks, Bonds, Debt instruments,Funds,Commodities, ETFs, Cash, and Cryptocurrency.
Having a diversified investment portfolio that consists of these various types of asset classes helps to create an optimized investment portfolio. Investing in diversified asset classes helps your portfolio continue to perform as the market at large fluctuates. For example, when the stock market is performing well, commodities and bonds tend to perform poorly. Conversely, when stock prices fall, commodities and bonds rise in value. This is why having a diversified investment portfolio is so important for yielding high returns, while also safeguarding your portfolio against investment risk. However, having a diversified investment portfolio is just the beginning when it comes to portfolio optimization. You must also put time and research into building diversification within each asset class. Of the various asset classes, your stock portfolio will require the most diversification when it comes to optimization. So, how do you optimize your portfolio?

Creating an Optimized Portfolio

Generally speaking, portfolio optimization refers to a statistical approach to making optimal investment decisions across different financial instruments. When it comes to building your stock portfolio, you never want to put all your eggs into one basket. The stock market is volatile, as you can never be certain of what the market will do at any given moment. This is why you must diversify your stock holdings by owning stocks from a variety of different sectors or industries.
Implementing sector diversification when investing in stocks lowers your overall risk and equips your portfolio and generate smooth returns over time. This approach typically involves rebalancing portfolios to achieve the most efficient mix of instruments based on a trade-off between risk and expected return. So, what are the various stock market sectors that you should invest in? The Global Industry Classification Standard or GICS is the primary financial industry standard for defining sector classifications. The GICS breaks the stock market down into 11 sectors, 24 industry groups, 68 industries, and 157 sub-industries. The Macroaxis wealth optimization framework is designed to model the process of effective portfolio origination that, if properly applied, can lead to a significant reduction of systematic risk while achieving way above-average risk-adjusted returns over a long period. The classical approach to portfolio optimization is known as Modern Portfolio Theory (MPT). It involves categorizing the investment universe based on risk (standard deviation) and return, and then choosing the mix of investments that achieves the desired risk-versus-return tradeoff. Portfolio optimization can also be thought of as a risk-management strategy as every type of equity has a distinct return and risk characteristics as well as different systemic risks, which describes how they respond to the market at large. Macroaxis enables investors to optimize portfolios that have a mix of equities (such as stocks, funds, or ETFs) and cryptocurrencies (such as Bitcoin, Ethereum or Monero)

Stocks Shares of ownership issued by a publicly traded corporation. These shares are usually traded on stock exchanges and conform to government regulations which are meant to protect investors from fraudulent practices
Funds Financial instruments that are backed up by a pool of investments in different types of securities such as stocks, bonds, money market instruments, and mutual funds. Most funds use strategies that allow investors to pool money together with other investors to purchase a collection of instruments with different characteristics
ETFs Financial instruments that are similar to funds in their composition but differ in a way their prices are adjusted. Unlike funds, ETFs are traded on the exchanges throughout the day just like stocks
Cryptos An internet-based asset that uses blockchain technology and cryptographical functions to conduct financial transactions. The main difference between cryptocurrency and traditional equity instruments or currencies is that cryptocurrencies use decentralized control and are independent of central banking systems.

Self-guided Investors optimize their portfolios to maintain a risk-return balance that meets their personal investing preferences and liquidity needs. To do this, they must regularly rebalance their portfolios to make sure they are not deviating from their practices; and this is where Macroaxis personalized approach to portfolio optimization adds values and an unprecedented amount of functionalities. Below are two modules that can be used to quickly build and backtest optimal portfolios as well as many supplemental tools that can help investors to improve risk-adjusted returns on their portfolios instantly.

1. Portfolio Optimization Module

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 elementary assumption, giving mainstream investors a set of conventional techniques to reduce exposure to individual asset risk by holding a diversified portfolio of assets. The first step in this process is to build the interrelation between the risk and return of multiple portfolios constructed from assets taken from your current portfolio. After the set of possible portfolios on the frontier is determined, the 'best-fit' portfolio for your utility function is selected. At Macroaxis, this process goes through the following five steps:
1. Construction of the covariance and correlation matrixes
2. Estimation of the expected return
3. Evaluation of historical volatility
4. Building of the efficient frontier
5. Picking one portfolio from the frontier for your specified risk level

How to Use Portfolio Optimization 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 only 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.
As you will experience, the methodology for optimizing your portfolio is very strightforward. First, originate your portfolio by syncing it with your existing brockerage account, importing it manually, or creating from scratch. 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 modules 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 run; or it may take you a few iterations until the desired optimization is achieved.

Achieving Perfect Optimization

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

   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
   Dividend Income — Total potential dividend of the entire portfolio
Even portfolis that may looks like performing very well during good market conditions could be optimized for both risk minimization as well as return maximization. For example, the 10-position portfolio below was optimized without adding or removing any assets. As a result, the portfolio's expected return was increased and risk (volatility of returns) was significantly decreased, resulting in an efficient portfolio that reflects current investment objectives to minimize risk and enhance returns.

Three additional ways to optimize your portfolio quickly

1. The easiest way to determine if your portfolio is optimal is to run 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 execute Efficient Frontier multiple 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)

3. Yet, the quikest way to optimize your portfolio is simply execute Portfolio Quick Fix module which using artificient intelegence alter your current asset allocation to atchive optimization without altering your investing style, asset selection habits, and return expectations.

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 acceptable, we recommend getting at least three out of five stars before deciding to stop your optimization process.

2. Portfolio Suggestion Module

Portfolio Suggestion is our flagship module and a second of our power-tools in the optimization process. Based on the implementation of Mean-Variance optimization, the module attempts to suggest a better portfolio taking your current holdings 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 further to provide you with more than one educated option to create an efficient portfolio based on your unique appetite for risk. Portfolio Suggestion is the extension of the Portfolio Optimization module that enables the evaluation of the efficient frontier for several investing strategies from the very conservative with no equity replacement to the very open, which may include complete rebalancing of your existing holdings. The process goes through the following seven steps:
1. Construction of the covariance and correlation matrixes
2. Estimation of the expected returns
3. Evaluation of historical volatility
4. Building of the efficient frontier
5. Running simulations to find an alternative mix if model portfolio
6. Generating output for all specified optimization strategies
7. Picking one portfolio from the frontier for your specified risk level, strategy, and preferred model.
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:

A. Segregation based on closeness to original portfolio

Typically, active investors follow their investing guidelines, asset selection processes, and risk/return preferences and adjust portfolios as they age or change their investment outlook. The default implementation of the Macroaxis Portfolio Optimization module always respects the positions of the original portfolio, and it will try to find the best possible mix of investors' assets to get them as close to their goal as possible. For example, the optimized portfolio below has an over 100% increase in risk-adjusted return over the original portfolio without adding any new assets or removing any of the current holdings. Investors utilizing Portfolio Suggestion Module will have to select at least one of 4 provided strategies to find the optimal portfolio. If all four strategies are selected, the output of the optimization model will provide results for each of the strategies. This way, an investor can always compare and select the portfolio that most suitable to his or her current investing preferences.

Basic Optimization

By using this options the investor will be optimizing existing positions to adjust to an asset allocation that is optimal for a specified risk appetite. No additional assets will be added. This is a classical mean-variance optimization without rebalancing.

Passive Rebalancing

With this option the optimization algorithm will be 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.

Active Rebalancing

If you select this option we will be 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.

Total Rebalancing

This option will enable the actual replacement 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. This option will trigger our artificient intelegence (AI) altorithm to work with your investing habits.

B. Segregation based on performance gain over original portfolio

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

Supplemental Tools To Portfolio Optimization

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.

Volatility Inspector

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.

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.

Quick 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.

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.

Portfolio Rebalancer

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.


Both, The dot-com crash at the beginning of this century as well as the financial crises of 2008 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, relaxed lending standards, abuse of collateralized 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 an 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.

Even though we strongly believe in Efficient-market hypothesis, our suggestion algorithm uses mathematics to synthetically manufacture efficient portfolios based on market risk reduction by examining asset correlation and mean-variance optimization. The Macroaxis optimization engine is based on the assumption that the stock prices may exhibit significant volatility as well as inconsistencies between historical and projected values, which in turn can minimize the benefits and the effects of diversification.
To solve the issue, Macroaxis delivers a simple methodology to execute and 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.