The Sharpe Ratio is simply the slope of the line that connects a portfolio and the Risk Free Rate. The line with the highest Sharpe Ratio is the one that connects Optimal Portfolio and the Risk Free Rate. The mathematical formula for the Sharpe Ratio is:

[ (Return – Risk Free Rate) / Standard Deviation ]

Basically, it is the return for taking risk divide by the risk taken. Logically, if we want to maximize the return / risk ratio, we maximize the Sharpe Ratio.

Given a risk free rate (T-Bill rate), we can construct portfolios by combining the risk free asset and any portfolios on the Efficient Frontier. All the possible combinations are represented by a line connecting the risk free rate and the risky portfolio on the frontier. However, there is only one such line that offers the highest return given a risk. This is the line tangent to the Efficient Frontier. The risky portfolio that lies both on the line and the frontier is called the Optimal Portfolio. Therefore, we can find the Optimal Portfolio by finding the line that has the highest slope, which is the Sharpe Ratio.

In 1952, Harry Markowitz published his doctoral thesis that laid the foundation of what is now known as the Modern Portfolio Theory. His paper has changed the investment industry ever since. And Markowitz received a Nobel Price in 1990 for his researches.

The MPT defines risk as the standard deviation of expected returns. Basically, it means the stability of the returns. If a stock has suddenly increased 200% in the past two weeks, it is a RISKY stock because its return is not stable despite the fact that it went up. Basically, you can translate low risk as consistency.

MPT further assumes that for every rational investor, the goal is to achieve the highest return with the highest consistency (lowest risk). And thus, it is totally possible to construct an optimal portfolio that has the highest return/risk ratio. We all know that diversification reduces risk. The MPT provides the way to find the portfolio that provides the best risk-reducing benefit while sacrificing as little return as possible. This induces the concept of Efficient Frontier.

Does it ever surprise you why there are so many investment books in Barns and Nobles? Have you ever wonder why those investment experts in CNBC bother to wake up so early in the morning talking about their analysis? After all, if they are making a killing in the market, shouldn’t they be sleeping in some vacation resort in the Caribbean’s?

The only reasonable solution I can think of is: They are not beating the market; they are just saying they do so they can make money off their books or analysis reports. As a result, most of the stock picking methods and analysis are based on “experience” and lack of a solid theoretical foundation.

After taking some investment class and studying Six Sigma quality management, I am experimenting on treating the stock picking process as a process. The continuous improvement of the outcome of this process needs a theoretical basis to spawn innovative ideas. In the investment industry, the dominant theoretical foundation is the Modern Portfolio Theory (MPT).

Based on the Modern Portfolio Theory, I will start with the Markowitz analysis process and improve upon it. The results I post are portfolios selected using back-tested variants of this analysis, their expected annual return average about 20% for Large Cap Portfolio and 30% for Small Cap Portfolio.

I wish anyone who uses my posts can send me feedbacks through comments so I can use them to improve the analysis model.

To understand and use the results I post, you need to know the basic of Modern Portfolio Theory.