Avoid financial ruin instead of shooting for the stars.

Investors today have access to an unprecedented amount of information about the financial markets. The have instant access to a dizzying array of investment opportunities, and dozens of strategies to choose from. They can take advantage of a wide variety of tools and resources that will enable them to manage their own investments, or they can assemble a team of advisers, portfolio consultants, financial planners, and accountants to do it all for them. And for those who want the best of both worlds, where they can dabble in the markets part time under the guidance and supervision of a professional, they can hire a personal investing coach.

Much of the information investors need to process is quantitative, based on mathematical models of the economy, the capital markets, and their own evolving financial circumstances. They need methods and procedures for sorting, filtering, and analyzing the mountain of raw data and statistics in order to convert it into usable intelligence.

This course examines the analytical, psychological, and behavioral aspects of investing so that you can create an effective investment strategy. Whether you intend to manage your own investments or delegate the management of your wealth to professionals, it is critically important to have an understanding of how the markets work, and who you are as an investor.

Successful investing is a 5-step process.

• Step 1 is to arrive at a reasonable understanding of who you are as an investor.
• Step 2 is to define a set of investment objectives.
• Step 3 is to develop a written investment policy statement
• Step 4 is to implement your plan in the marketplace
• Step 5 is to evaluate your performance and adapt to changing conditions

In step 1 we will guide you through a series of questions about you preferences, beliefs, assumptions, and expectations. We review the evidence that shows how we humans make systematic cognitive mistakes when processing and reacting to information. This step warns that these mistakes negatively impact the outcome of active investment strategies. There is now a rich base of research in the field of Behavioral Finance, which will help you navigate through the many pitfalls and obstacles every investor faces, with a minimum of damage to your nest egg and your ego.

In step 2 we'll explore the many possible investment goals you might have.

In step 3 we'll develop a framework for investing that considers passive strategies (investing in market-tracking index funds) and active strategies (actively seeking to “beat” the market return). This framework will help you determine how active you want to be, given the demands on your time and the returns available from an active investing approach.

In step 4 we describe the steps involved in putting your plan into practice. It covers the mechanisms for trading, monitoring, and evaluating your results.

In step 5 we go over the procedures for monitoring, evaluating, rebalancing, and optimizing your investment portfolio.

You will also learn about the efficient market hypothesis which states that market prices accurately reflect all available information. The goal of this lesson is to examine whether active investing is profitable. The debate is fierce and the issue is far from decided.

Other lessons delve into some key investing concepts, such as the time value of money, the equity risk premium, and mean reversion.

One of the most important concepts of the course is that the quality of each decision you make will depend on its contribution to risk and return in your carefully designed investment portfolio.

The covariance of two securities in our portfolio is the expected value of the product of one variable’s deviation from its mean and the other variable’s deviation from its mean.

If the most likely outcomes are associated with one being above its mean while the other is also above its mean, then the covariance is positive. If the most likely outcomes are associated with one being above its mean while the other is below its mean, then the covariance is negative.

The correlation ranges from 1 to −1, with the sign indicating whether the covariance is positive or negative and the magnitude of the correlation indicating the strength of the relationship. If the correlation is 1 or −1, then they are perfectly positively or negatively correlated, and knowing one tells you exactly what the other is. A correlation of zero says that there is no connection between the two.

Given the variances of two returns and the covariance between those two returns, there is an expression for the variance of a linear combination of random variables. We can use this expression for portfolios because the return on a portfolio is just a weighted average of the returns on the individual securities.

For a two-security portfolio, the variance of the return on the portfolio consists of three main parts. The first is the weight on the first security squared multiplied by the variance of the return on that security. The second is a similar expression but for the second security; it is the weight on the second security squared multiplied by the variance of that security. The third component utilizes the correlation between the two securities: It is 2 times the weight on the first security times the weight on the second security, with all of that multiplied by the covariance. The covariance is equal to the correlation between 1 and 2, times the standard deviation of 1, times the standard deviation of 2.

MPT is a school of thought about how to describe the nature, characteristics, and behavior of a given collection of financial assets.

How you build your portfolio will determine how much, how fast, and how safely your savings will grow.

In this lesson, you will learn how behavioral economists describe various aspects of investor behavior. Very few of us are "natural born" investors. Our brains are hard-wired for survival and reproduction, not maximizing the growth of our investment portfolio. So we tend to encounter internal conflicts of interest when it comes to making investment decisions.

For example, we have a very strong fight-or-flight response to perceived threats to our survival. When the stock market goes through one of it's bouts of volatility, many of us react as if our survival is being threatened. If the market is really rocky, we tend to panic at the worst time and sell our holdings near the bottom.

Therefore, the first question you need to consider is what is your tolerance for financial risk? Because you are experienced as an investor, you have the ability to look at your actual behavior during times of market turmoil. That's exactly what you should do. Don't rely on what you think you would do if the market suddenly dropped, because most investors believe they are much better than they actually are at remaining calm in the face of adversity. Go back and look. It may be an eye-opening experience.

Another question has to do with decision bias. Investing is making a series of buy and sell decisions over time. When you make a decision, are you aware of your natural biases and assumptions? We all have them. There's no escaping decision bias. A skilled investor may have the same biases and assumptions as an unskilled investor, but the difference is that the skilled investor knows she has them, and therefore is able to take them into account when she makes decisions. An unskilled investor who is not aware of (or wont admit to having) biases and assumptions will make the same misjudgments and errors repeatedly, because he is unaware of the biases that are at work.

Other examples of self awareness include susceptibility to suggestion, weakness in math or probability skills, a preference for certain companies, industries, or countries (home bias), and there are many others. Think of it this way. A perfectly rational and unbiased investor would have complete command of his emotions and intellect, and would use them with full efficiency. This investor would be very close to Star Trek's Mr. Spock. But he doesn't exist in the real world. So in order to improve as an investor, all you need to do is find your weaknesses and learn to make allowances for the fact that you have them when you are considering an investment decision.

Generally speaking, the expected return on a portfolio is the weighted average of expected returns on the individual securities, where the weights used in the average are the portfolio weights for each individual security.

Let's use a simple example of a $10,000 portfolio with only two holdings. Holding 1 is currently worth $6,000 and is expected to earn a return of 12% over the next 12 months. Holding 2 is worth $4,000 and is expected to earn 8%. The expected return on the portfolio is calculated by taking $6,000 x 12%, plus $4,000 x 8%, which gets us to 10.4%.  With this framework, we can systematically vary the weights between the two securities and see how the expected return and variation of the portfolio vary. This is how we manage investment risk.

Variance Effects

But the variance of our portfolio return is more complicated than it seems on the surface because we need to know how the return on one security is related to the return on the other. For example, consider the case in which when Holding 1 has a big positive return, then Holding 2 typically has a big negative return (and vice versa).  Therefore, both of these securities have high variances alone.

If we have a portfolio with a 50-50 split between the two securities, we can calculate the expected return and the variance of the portfolio. In this case, the expected return on the portfolio return will clearly be close to zero. What about the variance in this case? When the first security has a positive return, then the typically negative return of the other pulls the portfolio return down to zero. Similarly, when the first security has a negative return, then the typically positive return on the other pulls the portfolio return up to zero.

In this case, the variance of the portfolio return is low because regardless of what happens to either individual security, the portfolio return is close to its mean return of zero. This implies that the portfolio return has a small variance. Thus, even though both of the individual securities have high variance on their own, the portfolio variance is small.

Now let's consider the case in which when one security has a big positive return, so does the other usually, and when the first security has a big negative return, so does the other. Taken alone, they both have only large positive and negative returns and, as a result, have large individual variances.

In this case, the return on a 50-50 portfolio will either be big positive (when both are big positive) or big negative (when both are big negative). Because we don’t know ahead of time which will occur, the average return for the portfolio will be close to zero (the average of a big positive and a big negative). But the variance will be large because the realized returns on the portfolio will either be big positive or big negative.

Note that in both cases, the individual securities had large variance. However, in the first case, the variance of the portfolio return was small, whereas for the second case, the variance of the portfolio variance was large. This relationship can be captured using the concepts and formulas for correlation and covariance.

Hersh Shefrin and Meir Statman, two pioneers in the field of Behavioral Portfolio Theory, wrote a paper on the subject that explains how it works.

Consider these two questions.

1. How much would you be willing to pay to get rid of a risk that you face now?

2. How much would you need to get paid to take on a new risk you don’t have now? The answer to these two questions tells us something about your aversion to investment risk. In other words, it helps us to measure your risk tolerance.

How do investment advisers determine risk preferences for people in the market? The answer is that they don’t. Rather, they typically just assume some degree of risk aversion and leave it at that. But you can do better. By thinking about these two questions, you can at least learn something about your true risk tolerance. And that knowledge will come in very handy as you navigate through a world that's loaded with risk - some that you can't avoid, and some that you can.

But there is evidence to suggest that people care about much more than just the expected value and variance of an investment. If we assume that only rates of return and the variance of returns matter, then we will have missed some important features of investors’ risk preferences. If we only consider mean and variance to build our portfolio, then our thought process may signal that something is not important when in fact it is. That means that when we use a model to tell us what risk is and what return we should get for that risk, it may be misleading.

Investors are much more sensitive to losses than gains in their portfolios. They feel the pain of a loss about twice as much as the pleasure of a gain. It's important to keep this in mind the next time you open your brokerage statement and see that your portfolio has lost  5% or 10% of its value since you last looked at it. Some investors can't tolerate more than a 10% loss in value, even though they understand that the market fluctuates from month to month. This lopsided aversion to temporary declines in portfolio value can cause some investors to make the mistake of panic selling. Just being mindful of the human tendency to over-react to temporary losses can help you avoid this costly mistake.