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Portfolio Theory



Introduction

Generally speaking, the purpose of a portfolio of differing securities is in order to reduce non-systematic risk through the application of diversification. MVS employs the following mathematical approach to portfolio selection: The Matrix Equations and Valuation Metrics generate a cumulative distribution function as exhibited in the "companies section." This is essentially a differential equation relating three different terms, market price, time, and probability. The function is solved for the "holding period," which reduces the CDF to a probability function for market price at this future value. A matrix containing all available securities for the portfolio is solved for each security using an iterative root finding program. This generates an ideal ratio with the highest predicted return while inducing the lowest anticipated risk. A graphical representation of this process is depicted below:



Graphical Interpretation

The various securities in the portfolio are evaluated for increase in mean value and standard deviation. Those securities with high risk and high reward are balanced out by those with lower risk and more stable earnings. Graphing the relative proportions of each security results in a number of ideal proportions (based on error estimate/confidence interval). The highest "peak" is the ideal proportion and results in the highest value for alpha over a specified time-frame. This is how risk is mitigated while optimizing earnings. This is an "open-ended" fund, where the proportions of securities in each portfolio are rapidly changing and being updated as the market changes. Results from The Macro Project are used to predict future macroeconomic trends. The ratio of securities with high values for beta and volatility are increased in proportion during a period of undervaluation and vice versa.

Applications to Long Term Investing Strategy

MVS rarely invests in securities that are trading at exorbitant price to earnings multiples, unless it is the result of an isolated "off" quarter, and therefore, transient. Although it is possible for a security to trade at a high earnings multiple for an extended period of time (e.g. Netflix), the growth in share price will usually be greater with securities trading at more reasonable P/E ratios. In other words, although a company's earnings may eventually catch up with the share price, it is often at the expense of having capital allocated in a security with a higher value for alpha.

At MVS, we tend to champion a "buy and hold" philosophy, and tend to use these market events as entry (or exit) points as opposed to instances to exercise options. The reason is simple, regardless of the claims of any fund manager; there is no way to predict future events absolutely. However, the chance that an oversold or overbought security will approach its fundamental value increases in probability as time progresses. Simply stated: by holding onto an investment for a longer period of time, the effect of stochastic fluctuations in the market are reduced, and gradually the positive effects of inserting at the correct time will increase. By exercising this logic frequently, the "random walk" phenomenon will be reduced and averaged out.





Reducing Non-Systematic Risk

Generally speaking, a portfolio consisting of at least 20 different securities is considered to possess the minimum amount of diversification needed to protect against catastrophic losses. This is because the standard deviation of each security with respect to that of the portfolio is significantly reduced. Several of the managed portfolios at MVS have higher than normal risk (including non-systematic risk) from a technical and theoretical standpoint. The securities that make up these portfolios have strong fundamental indicators that reduce this overall risk, and, although this increases the standard deviation of the portfolio as well as the non-systematic risk, since systematic risk is arguably lower, the performance of the portfolio is expected to be greater. In other words, standard deviation of performance is predicted to be skewed in the positive direction due to the fundamentals of the individual securities.



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