TOPIC 42: MEASURES OF INVESTMENT RISK

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1 Coef cient of determination (R2) A The coef cient of determination is often referred to as R2 It gives the variation in one variable explained by another and is an important statistic in investments B R2 is systematic risk; 1 R2 is unsystematic risk C R2 is calculated by squaring the correlation coef cient (r) D The beta coef cient reports the volatility of some return relative to the market The strength of the relationship is indicated by R2 If R2 equals 015, an investor can assume that beta has little meaning because the variation in the return is caused by something other than the

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140 - Investment Planning movement in the market (unsystematic risk) If R2 equals 095, the variation in the market explains 95 percent of the variation in the return (systematic risk where beta is a good measure of risk) 2 Covariance A Covariance is a measure of the degree to which two variables move together over time A positive covariance indicates that variables move in the same direction, and a negative covariance indicates that they move in opposite directions Larger numbers indicate a stronger relationship, and smaller numbers indicate a weaker relationship B Covariance is an absolute number and can be dif cult to interpret It is often converted into the correlation coef cient, which is easier than covariance to interpret C The covariance between securities 1 and 2 is cov1,2 = (r1,2)( 1)( 2) 3 Correlation coef cient (r) A It is a measure of the relationship of returns between two stocks (1) A correlation coef cient of +1 means that returns always move together in the same direction They are perfectly positively correlated (2) A correlation coef cient of 1 means that returns always move in exactly the opposite directions They are perfectly negatively correlated (3) A correlation coef cient of zero means that there is no relationship between two stocks returns They are uncorrelated B There is an inverse relationship between correlation and diversi cation The lower the correlation, the greater the diversi cation Risk is erased when returns are perfectly negatively correlated C If the correlation coef cient between securities is less than 1, then the risk of a portfolio will always be less than the simple weighted average of the individual risks of the stocks in the portfolio D The correlation coef cient between securities 1 and 2 is r1,2 = (cov1,2)/ 1 2 4 Variance A Variance is the standard measure of total risk B It measures the dispersion of returns around the expected return The larger the dispersion, the more risk involved with an individual security C Variance is an absolute number and can be dif cult to interpret It is often converted into standard deviation, which is easier than variance to interpret The square root of variance is standard deviation 5 Semivariance measures downside risk, which is the dispersion of returns occurring below a speci ed target return such as zero or the T-bill rate 6 Standard deviation ( ) A Standard deviation is a measure of variability of returns of an asset as compared with its mean or expected value It measures total risk B There is a direct relationship between standard deviation ( , sigma) and risk The larger the dispersion around a mean value, the greater the risk and the larger the standard deviation for a security

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Topic 42: Measures of Investment Risk - 141 C Observations will tend to cluster around the expected mean, and the bell-shaped curve is often used to represent the dispersion The standard deviation is a measure of this dispersion or variability (1) Approximately 68 percent of outcomes fall within 1 of the mean (2) Approximately 95 percent of outcomes fall within 2 of the mean (3) Approximately 99 percent of outcomes fall within 3 of the mean D Example: Assume the standard deviation for stock A is 103 If stock A has an average return of 15 percent, then 68 percent of all returns fall within 1397 and 1603 percent E Standard deviation is an absolute measure of dispersion That is, it can be in uenced by the magnitude of the original numbers If stock A and stock B had different returns, a comparison of standard deviations may not indicate that B is more diverse Other measures of risk are useful complements to standard deviation F Steps to calculating historical standard deviation (1) For each observation, take the difference between the individual observation and the average return (2) Square the difference (3) Sum the squared differences (4) For sample , divide this sum by one less than the number of observations For population , divide this sum by the total number of observations (for the CFP Examination, assume sample unless stated differently) (5) Take the square root G Calculation example: Great Properties, Inc, has an average return of 12 percent and the following individual returns for the corresponding time periods listed in the following table What is the standard deviation for Great Properties, Inc Difference Squared 2704 1024 13924 004 1024 18680

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Year Actual Return Average Return 1 12% 68% 2 10 68 3 5 68 4 7 68 5 10 68 Sum of squared differences = The standard deviation is [18680 (5 1)]1/2 = 683%

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