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Essential Concepts
Time Value of Money
Evaluating Cash Flows
Risk and Return
Expected Return
Variance and Standard Deviation

PreMBA Analytical Methods
Risk and Return: Introduction

Why, as an investor, do you receive only a 3 percent return on your deposits in an insured savings account, and at times a double-digit return on money invested in technology-based mutual funds? How do these two investments differ other than the returns they provide? The technology-based mutual fund is much riskier than the insured savings account. Perhaps the most fundamental relationship in finance is the tradeoff between risk and return. On the one hand, if this tradeoff did not exist and the market viewed all investments as having equal risk, no one would invest in the low-return insured savings account if they could invest in the high-return mutual fund. On the other hand, if investors were not compensated for taking risks, no one would be willing to invest in the technology-based mutual fund.

As an investor, a financial manager, an entrepreneur, or a person in any other position that requires making investment decisions, the relation between risk and return raises three basic questions:

  • How do I estimate the percentage return that I will receive on an investment?
  • How much risk does an asset add to a portfolio?
  • What can I do to eliminate some of that risk?

Expected Return

The expected return is the market's, or an investor's, best guess as to the return on an asset. Any technique can be used to arrive at the guess. This section will review two common techniques. One uses a simple average of historical returns. Another technique uses the returns from possible outcomes and the probabilities of those outcomes to arrive at an expected return.

Variance and Standard Deviation

Risk is the possibility that actual returns might differ, or vary, from expected returns. In fact, actual returns will likely differ from expected returns. It is important for decision-makers to estimate the magnitude and likelihood of the difference between actual and estimated returns. After all, there is a big difference if your predictions result in an error of only $100 versus an error of $1 million.

By using the concepts of variance and standard deviation, investors can judge not only how wrong their estimates might be, but also estimate the likelihood, or probability, of favorable or unfavorable outcomes. With the tools of expected return and standard deviation, financial decision-makers are better able to evaluate alternative investments based on risk-return tradeoffs, and their own risk preferences.


The Diversification topic answers the third question regarding what one can do to minimize risk of a group, or portfolio, of investments. By selecting investments that perform differently under the same market conditions, one can create a portfolio that has less risk for the same level of expected return. The concepts of covariance and correlation are used to measure how the returns on assets relate to each other and the market in general and how they can be used to reduce the overall risk to the investor.

Once you answer these basic questions, you may then consider more advanced question: If it is possible to diversify away some risks by holding a portfolio of assets, for what risks should investors receive compensation? Should investors who don't diversify be rewarded with higher returns? The answers to these questions rest in understanding different types of risk such as "market" or "non-diversifiable risk" versus "firm-specific" or "diversifiable" risk. The concept of beta, or how an asset moves relative to the market, helps investors quantify the level of diversifiable risk.

Using "Risk and Return" concepts, you should be able to

  • compute the expected return of an individual security
  • compute the expected return of a portfolio of securities
  • compute a confidence interval around an expected return using standard deviation
  • compute the variance and standard deviation of an individual security
  • compute the variance and standard deviation of a portfolio
  • compute beta, a measure of market risk

With a solid understanding of these finance basics, you will be well prepared to venture into more advanced aspects of financial theory and practice.

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