Efficient Frontier

What is the Macroaxis Efficient Frontier?

The Macroaxis Efficient Frontier is an implementation of Modern Portfolio Theory (MPT) and Capital Asset Pricing Model (CAPM). We are not trying to determine a unique Market Portfolio, but rather our investor landscape contains portfolios that our community holds and analyzes on the basis of risk and return. The best performing portfolios (in green) are shaping up the efficient frontier. Eventually the frontier line will become a solid line that will be similar to what the actual theory assumes -- any asset is infinitely divisible. The risk of a portfolio comprises systematic risk, also known as undiversifiable risk, and unsystematic risk which is also known as idiosyncratic risk or diversifiable risk. Systematic risk refers to the risk common to all securities. Unsystematic risk is the risk associated with individual assets. Unsystematic risk can be diversified away to smaller levels by including a greater number of assets in the portfolio (specific risks "average out"). The same is not possible for systematic risk within one market. Depending on the market, a portfolio of approximately 30-40 securities in developed markets such as the UK or US will render the portfolio sufficiently diversified to limit exposure to systemic risk only. In developing markets a larger number is required, due to the higher asset volatilities. A rational investor should not take on any diversifiable risk, as only non-diversifiable risks are rewarded within the scope of this model. Therefore, the required return on an asset, that is, the return that compensates for risk taken, must be linked to its riskiness in a portfolio context - i.e. its contribution to overall portfolio riskiness - as opposed to its "stand alone riskiness." In the CAPM context, portfolio risk is represented by higher variance i.e. less predictability. In other words the beta of the portfolio is the defining factor in rewarding the systematic exposure taken by an investor.

Basically, for a given amount of risk, the portfolio lying on the efficient frontier represents the combination offering the best possible return. Mathematically the Efficient Frontier is the intersection of the set of portfolios with Minimum Variance (MVS) and the set of portfolios with Maximum Return.

How do I benefit from the Efficient Frontier?

Our Wealth Management Collaboration Platform is a set of comprehensive modules that, although written in the context of Modern Portfolio Theory, can be utilized by both experts and novice investors. We are proud to be one of the first companies to give investors the ability to create optimal portfolios at virtually no cost. Regardless of your background, budget, or investment philosophy, you will find our platform and community useful in building optimal portfolios for yourself or your clients. Simply create your portfolio and run one of our optimization modules; than see your portfolio on investor landscape, hopefully on the efficient frontier. This is educated diversification - no gimmicks, just math.

Portfolio Suggestion with Efficient Frontier

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.

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 carefully selected from the market. 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 Suggested portfolio outperforms the original portfolio in all four categoreis

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

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