Measuring Claims - Class Example

1. Over the past 3 years an investment returned 0.18, -0.11, and 0.08. What is the variance of returns?

Calculate the standard deviation of the following returns.  Year       Return 1             0.25 2             0.16 3             0.01 4             0.07 5             -0.11

Suppose the average return on Asset A is 6.6 percent and the standard deviation is 8.6 percent and the average return and standard deviation on Asset B are 3.8 percent and 3.2 percent, respectively. Further assume that the returns are normally distributed. Use the NORMDIST function in Excel® to answer the following questions.    a. What is the probability that in any given year, the return on Asset A will be greater than 11 percent? Less than 0 percent? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) b. What is the probability that in any given year, the return on Asset B will be greater than 11 percent? Less than 0 percent? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) c-1. In a particular year, the return on Asset A was −4.25 percent. How likely is it that such a low return will recur at some point in the future? (Do…

uppose the average return on Asset A is 7.1 percent and the standard deviation is 8.3 percent, and the average return and standard deviation on Asset B are 4.2 percent and 3.6 percent, respectively. Further assume that the returns are normally distributed. Use the NORMDIST function in Excel® to answer the following questions.   a. What is the probability that in any given year, the return on Asset A will be greater than 12 percent? Less than 0 percent? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) b. What is the probability that in any given year, the return on Asset B will be greater than 12 percent? Less than 0 percent? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) c-1. In a particular year, the return on Asset A was −4.38 percent. How likely is it that such a low return will recur at some point in the future? (Do not round…

The probability distributions of expected returns for the assets are shown in the following table: Asset A Prob Return 0.2 -5% 0.4 10% 0.4 15% a) Calculate the expected return for asset A. b) Calculate the standard deviation for asset A.

Which one of the following is defined as the average compound return earned per year over a multiyear period?   Multiple Choice   A Geometric average return B Variance of returns C Standard deviation of returns D Arithmetic average return E.  Normal distribution of returns

Assuming that the rates of return associated with a given asset investment are normally distributed; that the expected​ return, r​, is 18.7​%; and that the coefficient of​ variation, CV​, is 1.88​, answer the following​ questions:   a. Find the standard deviation of​ returns, sigma Subscript rσr. b. Calculate the range of expected return outcomes associated with the following probabilities of​ occurrence: (1)​ 68%, (2)​ 95%, (3)​ 99%.

Normal probability distribution    Assuming that the rates of return associated with a given asset investment are normally​ distributed; that the expected​ return, r​, is 10.4​%; and that the coefficient of​ variation, CV​, is 1.01​, answer the following​ questions:   a.  Find the standard deviation of​ returns, σr. b.  Calculate the range of expected return outcomes associated with the following probabilities of​ occurrence: (1)​ 68%, (2)​ 95%, (3)​ 99%.

Use the data shown in the following table: K a. Compute the average return for each of the assets from 1929 to 1940 (the Great Depression). b. Compute the variance and standard deviation for each of the assets from 1929 to 1940. c. Which asset was the riskiest during the Great Depression? How does that fit with your intuition? Note: For all your answers type decimal equivalents. Data table Year 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 S&P 500 -0.08906 -0.25256 - 0.43861 -0.08854 0.52880 -0.02341 0.47221 0.32796 -0.35258 0.33204 -0.00914 - 0.10078 Small Stocks - 0.43081 -0.44698 -0.54676 -0.00471 2.16138 0.57195 0.69112 0.70023 - 0.56131 0.08928 0.04327 -0.28063 Corp. Bonds 0.04320 0.06343 -0.02380 0.12199 0.05255 0.09728 0.06860 0.06219 0.02546 0.04357 0.04247 0.04512 World Portfolio -0.07692 -0.22574 -0.39305 0.03030 0.66449 0.02552 0.22782 0.19283 -0.16950 0.05614 -0.01441 0.03528 Treasury Bills 0.04471 0.02266 0.01153 0.00882 0.00516 0.00265 0.00171 0.00173…

Over a particular period, an asset had an average return of 5.8 percent and a standard deviation of 8.9 percent.   What range of returns would you expect to see 68 percent of the time for this asset?

Suppose the returns on an asset are normally distributed. The historical average annual return for the asset was 5.2 percent and the standard deviation was 10.6 percent.   a. What is the probability that your return on this asset will be less than –9.7 percent in a given year? Use the NORMDIST function in Excel® to answer this question.  b. What range of returns would you expect to see 95 percent of the time?  c. What range of returns would you expect to see 99 percent of the time?

Compute the expected return, variance, and standard deviation of the following assets. Show the solutions   Probability Return of Assets   Asset A Asset B Asset C 25% .030 .030 -.030 25% .050 .180 .280 25% .100 .080 -.180 25% .280 -.050 -0.180 Expected Return       Variance       Standard Deviation

a risk manager gathers the following sample data to analyze annual returns for an asset: 12%, 25% and -1%. he wants to compute the best unbiased estimator of the true population mean and standard deviation. the manager's estimate of the standard deviation for this asset should be closest to a. 0.0111 b. 0.0113 c. 0.1054 d. 0.1204.

calculate the following M-squared measureT-squared measure, andAppraisal ratio (information ratio) Fund  Average return Standard Deviation Beta coefficient Unsystematic Risk A 0.240 0.220 0.800 0.017 B 0.200 0.170 0.900 0.450 C 0.290 0.380 1.200 0.074 D 0.260 0.290 1.100 0.026 E 0.180 0.400 0.900 0.121 F 0.320 0.460 1.100 0.153 G 0.250 0.190 0.700 0.120 Market 0.220 0.180 1.000 0.000 Risk free return 0.050   0.000   Out of the performance measures you calculated in part a., which one would you use undereach of the following circumstances:i. You want to select one of the funds as your risky portfolio.ii. You want to select one of the funds to be mixed with the rest of your portfolio,currently composed solely of holdings in the market-index fund.iii. You want to select one of the funds to form an actively managed stock portfolio

ndard deviation of the following annual returns:

calculate the following Sharpe Ratio (SP) Treynor Measure Jensen Measure  M2 measure T2 measure Information Ratio (appraisal ratio) Fund  Average return Standard Deviation Beta coefficient Unsystematic Risk A 0.240 0.220 0.800 0.017 B 0.200 0.170 0.900 0.450 C 0.290 0.380 1.200 0.074 D 0.260 0.290 1.100 0.026 E 0.180 0.400 0.900 0.121 F 0.320 0.460 1.100 0.153 G 0.250 0.190 0.700 0.120 Market 0.220 0.180 1.000 0.000 Risk free return 0.050   0.000

An asset has an average return of 11.33 percent and a standard deviation of 24.18 percent. What is the most you should expect to lose in any given year with a probability of 2.5 percent? −37.03% −61.21% −24.94% −12.85% −59.69%

es Suppose the returns on an asset are normally distributed. The historical average annual return for the asset was 5.7 percent and the standard deviation was 18.3 percent. a. What is the probability that your return on this asset will be less than -4.1 percent in a given year? Use the NORMDIST function in Excel® to answer this question. (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) b. What range of returns would you expect to see 95 percent of the time? (Enter your answers for the range from lowest to highest. A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) c. What range of returns would you expect to see 99 percent of the time? (Enter your answers for the range from lowest to highest. A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter…

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. .3519

Show your work (use of formula, etc.) in solving the problem.    Provide your answer/solution in the answer space provided below. Answer the question: Given the following historical returns, calculate the average return and the standard deviation: Year Return 1 14% 2 10% 3 15% 4 11%

Suppose the returns on an asset are normally distributed. The historical average annual return for the asset was 5.2 percent and the standard deviation was 10.6 percent. a. What is the probability that your return on this asset will be less than -9.7 percent in a given year? Use the NORMDIST function in Excel® to answer this question. Note: Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16. b. What range of returns would you expect to see 95 percent of the time? Note: Enter your answers for the range from lowest to highest. A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16. c. What range of returns would you expect to see 99 percent of the time? Note: Enter your answers for the range from lowest to highest. A negative answer should be indicated by a minus sign. Do not round intermediate calculations and…

Find expect value and variance of A and B which

Assume that you have obtained the following information for Asset A:   Rate of Return Probability 5.5% 25% 7.25% 55% 11% 20%   Compute the expected rate of return for Asset A, using the information provided in thechart above   Assume that the standard deviation of the expected returns for Asset A is 1.87%.  With  information and the expected rate of return that you calculated for Asset A in Part A of this  problem, compute the co-efficient of variation for Asset A.