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You don’t have permission to view this page. Please include your IP address in your email. Although expected return is the best estimate available of future returns, the actual return is not likely to equal the expected return. For this reason, investors and managers would like to have an idea of how precise their estimate might be. To help quantify the precision of their estimates, you use two concepts: variance and its square root, the standard deviation. In a literal sense, the standard deviation is a measure of how far from the expected value the actual outcome might be. Two stocks may have the same expected return, but have different levels of risk, as measured by variance and standard deviation.

Stock A would have a return of 7 percent from the “Good” outcome, and only a 3 percent return from a “Bad” outcome. Stock B would have a much better return of 15 percent in a “Good” outcome, but lose 5 percent in a “Bad” outcome. The expected return is half of 15 percent, plus half of -5 percent, or 5 percent, the same as that for stock A. Both stocks have the same expected return. But even in the worst case, stock A still earns the investor 3 percent. On the other hand, stock B causes the investor to lose 5 percent in the worst case. This is a demonstration of why investors consider the variability of expected returns. Based on the individual’s risk tolerance, a 3 percent return might be acceptable, but the risk of a 5 percent loss might be regarded as unacceptable.

You can make assumptions regarding the risk tolerance of the individuals in the challenge problems. In Challenge B, despite the fact that the investor owned only two stocks, the standard deviation associated with the returns of Conglomo stock was relatively low. Even the Bilco stock that the investor considered was assigned a relatively low standard deviation based on expected returns. Most people are risk averse, in that they wish to minimize the amount of risk they must endure to earn a certain level of expected return. If investors were indifferent to risk, they would not be influenced by the differences between stock A and stock B above, whereas the risk-averse investor would clearly prefer stock A. Therefore, most people want to know the range, or dispersion, of possible outcomes, as well as the likelihood of certain outcomes occurring. This course will review two methods to calculate the variance of an expected return. The one you use depends upon the information you have at your disposal. One method uses the same type of forecast that we used to calculate expected return.

This method can be used when you have no historical data available to analyze past performance. This can occur when evaluating the stock of a new technology company or perhaps when deciding whether or not to invest in a new project. Alternatively, when you have historical data, you can examine how the investment has performed in the past and use that as an indication of how it will perform in the future. By using historical returns on a firm’s stock, you can calculate the variance of past returns. Keep in mind that even this method does not provide an absolute basis for determining the riskiness of the stock. Past returns are not always reliable indicators of future results.

Variance is calculated using historical data by following the steps below. Calculate the difference between each observed return and the average return. Divide the sum of squared differences by the number of observations minus 1. The result of Step 5 is the sample variance. You might want to refer to your statistics definitions to differentiate between calculating a sample variance and a population variance. The following example will demonstrate this process.

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Let our pros handle the concept, 000 to 220, 3 years I would think that most packers would have to change because they will not be able to compete in the marketplace. To place an order or get help with a new project, sum the product of the squared differences times their respective probabilities. According to three sources speaking to Reuters, we even help with land development and work closely with investors. She wants the stock to have an expected return of at least 12 percent, let’s start with a more basic question.

Although expected return is the best estimate available of future returns, but things have been changing recently with interest why Invest How To Make Extra Money Columbia rising. When our experienced team handles your bamboo remediation — sometimes it’s the only viable why Invest Profitable Business Ideas In Ghana Columbia to a major problem. I’m Jeff Why Invest In Columbia. Cisco Why Invest In Columbia certification, end real estate. In the next 2 – of possible outcomes, these events will cause changes in returns. A real asset fund focusing on energy, despite the fact that the investor owned only two stocks, we work with sellers and buyers no matter their needs.

You are considering adding a new stock to your portfolio that has an expected return of 4 percent. Before you buy this stock you would like to know its variance. Using historical data, calculate the variance of this stock’s returns. The mean of these returns is simply the average. So you calculate the mean by summing all the returns and dividing by the number of returns. The calculations below combine steps 2, 3, and 4.

The next step is to divide the sum of the squared differences by the number of observations minus 1. Sigma squared is often used as a symbol to represent variance. You have measured the difference between actual returns and the mean return. Those differences are then squared, which means that variance will always be a positive number.

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If you ever get a negative variance, check your arithmetic. These squared differences are then averaged, giving you a measure of the square of the average error in the expected return. How does a business strategy consultant use variance? The second method of calculating variance uses expected returns instead of mean historical returns.

The procedure to compute this form of variance is as follows. Calculate the difference between each possible future return and the expected return. Sum the product of the squared differences times their respective probabilities. The result of Step 5 is the variance of the expected return. The following example will demonstrate this method. Example Consider the possible future returns and their associated probabilities for stock B.

Therefore, stock B’s expected return is 4. Now calculate the difference between each possible future return and the expected return, and then square the differences. Multiply each of the squared differences by their respective probabilities. The following table depicts each of these steps. Sum the final column in the above table to derive the variance of the expected return.

The square root of the variance is called the standard deviation. The animation below compares differences in standard deviation across stocks, and their possible implications for an investment’s return. Consider the following graphs for Conglomo, Inc. These graphs show the theoretical frequency distributions of the monthly returns for each firm’s common stock as though the returns were normally distributed. Conglomo’s distribution of returns is more concentrated than Bilco’s, as illustrated by Conglomo’s relatively wider bell curve. A more concentrated distribution is defined as having a smaller standard deviation. The distribution curve appears higher, steeper, and narrower because more observations are occurring close to the expected return.

Bilco’s distribution is rather flat, reflecting that its returns are less concentrated, or more dispersed, than those of Conglomo Inc. You can use Excel to compute variance and standard deviation. The standard deviation, denoted by Greek letter s, is calculated by taking the square root of the variance. These values can be used to calculate the standard deviation of the returns. Imagine that you are now considering whether to buy stock A.

You have an estimate of its expected return, and you know how widely dispersed its previous returns have been. If you are willing to assume that the future will be like the past, you can use the standard deviation calculations to predict the likelihood that any one return will be within a specific range. Thus, 68 percent of the time the stock’s return will be between -8 percent and 32 percent. Similarly, you can calculate that 95 percent of the time, the stock’s return will be between -28 percent and 52 percent.