CHAPTER 22 estimating risk and return on assets 1. WHAT IS RISK? Risk is the variability of an asset’s future returns. When only one return is possible‚ there is no risk. When more than one return is possible‚ the asset is risky. The greater the variability‚ the greater the risk. 2. RISK – RETURN RELATIONSHIP Investment risk is related to the probability of actually earning less than the expected return – the greater the chance of low or negative returns‚ the riskier the investment
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called as standard normal. Normal distribution problems and solutions – Formulas: X < μ = 0.5 – Z X > μ = 0.5 + Z X = μ = 0.5 where‚ μ = mean σ = standard deviation X = normal random variable Normal Distribution Problems and Solutions – Example Problems: Example 1: If X is a normal random variable with mean and standard deviation calculate the probability of P(X<50). When mean μ = 41 and standard deviation = 6.5 Solution: Given Mean μ = 41 Standard deviation σ = 6.5 Using
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of 25% (Anderson‚ Sweeney‚ & Williams‚ 2012). The measure of variability is expressed through an element of dispersion across a population sample. Variability is measured through the calculation of range‚ interquartile range‚ variance‚ standard deviation‚ and coefficient of variation. The range is not commonly used as it is influenced significantly by outliers; however‚ it is measured by the subtracting the smallest value by the largest value. Interquartile range represents the difference
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following measures of variation for the data set. Show your work. A table has been provided to help you calculate the standard deviations. In the table round values in the last two columns to four decimal places. Report the standard deviation statistics to four decimal places. Range: _____0.6________ Standard Deviation of this data: ___.1648__________ Estimated Standard Deviation for all pieces produced: ______.1721_______ X x-µ (x-µ)2 3.8 -.2667 .0711 3.9 -.1667 .0277 3.9 -.1667 .0277 4.0 -.0667
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and variability (standard deviation) of Reynolds‚ Hasbro‚ and Vanguard Index 500 Trust during the past 5 years. Which one appears to be riskiest? S&P 500 REYNOLDS HASBRO Mean 0.57% 1.87% 1.18% Variance 0.13% 0.88% 0.66% Standard Deviation 3.60% 9.37% 8.12% - Conclusion: Reynolds appears to be riskiest. - Explanation: Given the fact that risk reflects the uncertainty of future return on a given asset or a portfolio of assets‚ standard deviation is thus used as
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higher standard deviation and the higher variance. If we compare both stocks‚ Reynolds is riskier than Hasbro in this case. The higher variance indicates higher chance that the actual return on Reynolds will deviate from the expected return. S&P 500 REYNOLDS HASBRO Mean/Average 0.574333 1.874833 1.183833 Variance 12.972333 87.730541 65.866763 Standard Deviation 3.601713 9.366458 8.115834 Answer 2. At individual stock level‚ Reynolds fluctuates more than Hasboro as it has higher Standard Deviation
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variance (or standard deviation) of real estate returns and the correlation between real estate returns and returns for each of the other asset classes. (Note that the correlation between real estate returns and returns for cash is most likely zero.) 3. (a) Answer (a) is valid because it provides the definition of the minimum variance portfolio. 4. The parameters of the opportunity set are: E(rS) = 20%‚ E(rB) = 12%‚ σS = 30%‚ σB = 15%‚ ρ = 0.10 From the standard deviations and the correlation
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a multi-meter was used to measure the resistance in a pack of ten resistors. Each member measured the resistors twice to allow for more precise statistical analysis. After all measurements were recorded‚ statistical analysis such as mean‚ standard deviation‚ and true mean range with 90%‚ 95%‚ and 99% confidence intervals were used to obtain the results. Once calculations were made‚ it was determined that there was error in this laboratory due to the environment and to human error‚ however all
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service clients. However‚ TDS is organized into 100 different geographically regions. The average sales for a region is $1‚000‚000‚ with a standard deviation of $100‚000. The manager of each geographical region has the autonomy to establish a compensation plan. The average annual compensation for an insurance agent is $60‚000‚ with a standard deviation of $12‚000. Assume that TDS has hired you as a consultant. Your services are desired to help TDS make two critical decisions. The first decision
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of fast foods are students’ favorite? 2.0 Gender Figure 1 Gender Frequency Percent Male 22 48 Female 28 52 Total 50 100 Mean 25 Median 25 Mode #N/A Standard deviation 4.24 Standard Deviation= =4.24 Figure 1 shows the gender of sample at SEGI students. There are 22 male students and 28 female students in this sample. 3.0 Age Figure 2 Age Male Female Frequency
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