Modern Portfolio Theory

Financial experts have used Modern Portfolio Theory (MPT) for decades to help them determine the best combination of securities to achieve a desired return at a given level of risk.

Nobel laureate Harry Markowitz developed MPT in the early 1950's. For decades, many large institutional investors and brokerage houses have used some form of MPT to help them build and manage their portfolios. Here at Tara Global Co., we are now making this technique available to the everyday investor.

Markowitz found that economic forces such as interest rates, exchange rates, the price of oil, the weather, etc. affect stocks differently. The most common example is that a high price for oil is good for the oil industry but bad for the airline industry. He found that investing in a diversified group of stocks that behave differently to these forces could reduce risk. In other words, risk depends not only on the volatility of each stock but also on how they behave relative to other stocks in the portfolio.

Calculating the portfolio's return is the easy part. For each stock, the return is the gain in price, plus dividends received, per share during the period. For the portfolio as a whole, it is the weighted-average of the individual security returns.

Risk is another matter. For most investors, the risk they take in an investment is the risk that the return will not be the expected return. In other words, it is the deviation from the average return. The MPT model calculates for each stock, a "standard deviation" from the mean, which the model calls "risk". However, for the reasons given above, the risk level of a portfolio as a whole is not a simple average of the risk level of the individual stocks. The "risk" of one stock may offset the "risk" of another. It takes advanced calculus and some sophisticated calculations to determine the risk level of the portfolio, and the MPT model does that for you.

The MPT model plots an Efficient Frontier of the varying combinations of the stocks in your portfolio that provide the "maximum return and lowest risk". For every point along the Efficient Frontier, the MPT model will display the combination of stocks in the portfolio and the number of shares of each that will produce that level of return and risk based not only on past performance but also on Monte Carlo simulations that forecast future performance.

Risk & Return

MPT assumes that stock prices follow a random walk, and hence, hypothesizes that security prices follow geometric Brownian motion. The instantaneous mean and standard deviations of security returns are extrapolated into the immediate future through Monte Carlo simulations. With the power of technology, these calculations are done in real-time. This enables the system to compute the expected return of securities.

Calculating Optimal Portfolios:

The predicted rate of return relative to the riskiness of the individual assets (Ri) is ranked in a descending order. A series of hypothetical scenario portfolios are formed from a portfolio of one best stock, two best stocks, three best stocks, etc. until the process exhausts the entire spectrum of securities under analysis.

The algorithm terminates when an addition of individual securities will no longer contribute positively to the portfolio's expected risk-return profile.

An optimal portfolio will then determine the degree to which each security included in the portfolio makes a positive contribution to the portfolio, resulting in an optimal combination.

The model uses non-linear quadratic programming to solve for optimal portfolio weights. Non-linear programming allows us to solve non-linear objective functions subject to non-linear inequality constraints using Kuhn-Tucker first-order conditions.

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