State 1 2 3 Pr(a) 0.2 0.6 0.2 Given the probability distribution above, determine (Calculate) and compare the: 1. Expected return (means) 2. Variance 3. Standard deviation ra 10% 15% 20% Pr(b) 0.25 0.40 0.35 rb 12% 20% 18%
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risk and return
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- Part a State Pr(a) ra Pr(b) rb 1 0.2 10% 0.25 12% 2 0.6 15% 0.40 20% 3 0.2 20% 0.35 18% Given the probability distribution above, determine (Calculate) and compare the: Expected return (means) Variance Standard deviation Part b How important is risk to returns and what are the key elements that must be analyzed in this regard before an investment decision is made? Discuss in no more than 200 words.Security A has the following probability distribution of returns:Scenario Probability Return1] 0.1 15%2] 0.8 25%3] 0.1 35%What is the variance for Security A?A 0.002B 0.020C 0.200D 0.3001. Calculate the Expected Return and Risk measured in terms of standard deviation and Variance relating to the following information of a Investment avenue: Return in Percentage: -15-10-5+5+10+15 Probability:.10.15.20.20.25.10
- EXAMPLE• Consider the following information:State Probability ABC, Inc. ReturnBoom .25 0.15Normal .50 0.08Slowdown .15 0.04Recession .10 -0.03• What is the expected return?• What is the variance?• What is the standard deviation?If correlation coefficient between an individual security and market is 0.64, the total risk of the security that is standard deviation is 30 %, unsystematic risk of the security in variance term is a. 531.36 b. 900 c. 640 d. 360Coefficient of Variation A standardized measure of the risk per unit of return. Coefficient of Variation = Standard deviation () Expected return (ř) Coefficient of Variation FLI (11.80%/ 14.55%) 81.10% WEB (16.52%/22.00%) 75.10
- What is the variance of the following returns? State probability return Boom .2 .75 normal .55 .25 recession .15 -.1 depression .1 -.5 a. .0413 b. .01239 c. .1944 d. .2601 e. .3519Given Portfolio 1 Expected Return= 0.15 Portfolio variance = 0.001 Standard Deviation = 0.0316 and Portfolio 2 Expected Return= 0.173 Portfolio variance = 0.001011 Standard Deviation = 0.03179 Compare these results.Consider the following information: State Probability ABC, Inc. Return Boom .25 0.15 Normal .50 0.08 Slowdown :15 0.04 Recession .10 -0.03 What is the expected return? What is the variance? What is the standard deviation?
- 10.7 Calculating Returns and Variability Using the following returns, calculate the arithmetic average returns, the variances, and the standard deviations for X and Y: Returns Year X Y 1 12% 14% 2 24 29 3 -27 -33 4 14 17 5 19 37Use the following information: Stock A B Good state 10% 14% Bad state 2% -2% Assume there is 60% probability that the good state occurs and 40% chance the bad state occurs. What is the standard deviation of stock A? (Please use 5 decimal places, this should be written in percentage, so an answer of 23.143% should be written as .23143)Year Returns X Y 1 11% 18% 2 25 26 3 11 10 4 −18 −23 5 10 17 Using the returns shown above, calculate the arithmetic average returns, the variances, and the standard deviations for X and Y. (Do not round intermediate calculations. Enter your average return and standard deviation answers as a percent rounded to 2 decimal places, e.g., 32.16, and round the variance answers to 5 decimal places, e.g., .16161.) X Y Average returns % % Variances Standard deviations % %