CH13a-PracProbs

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Boston College *

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301

Subject

Statistics

Date

Feb 20, 2024

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xlsx

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4

Uploaded by UltraAtom12145

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1 -- 3 Consider these historical annual returns for the XX ETF. Date Return 12/31/05 26.112% 12/31/06 27.877% 12/31/07 32.161% 12/31/08 21.859% 12/31/09 10.710% 12/31/10 -0.774% 12/31/11 13.838% 12/31/12 -16.013% 12/31/13 9.614% 12/31/14 14.533% 12/31/15 -2.381% 12/31/16 -2.617% 12/31/17 -37.485% 12/31/18 12.250% 12/31/19 31.997% 1 Solution: 0.094 2 Solution: 0.191 3, 4 Consider this normal distribution graph and the information below for the next two que What is the average return? Compute this to three decimal places and do not represent answer as a percent. What is the standard deviation of the returns? Compute this to three decimal places and represent your answer as a percent. (Hint, use sample stdev formula). You have analyzed 30 years of historical, annual returns of a stock. You found the ave to be 5% and the standard deviation of returns to be 15%. You will estimate the stock' annual returns (for better or worse) as normally distributed, based on your historical an
3 Solution: 35% = 5% + 15% + 15% = u + 2*sigma --> 2.1% + 0.2% = 2.3% 4 Solution: -10% = 5% - 15% = u - sigma --> 0.2% + 2.1% + 13.6% = 15.9% 5 Solution: VaR = return X, such that probability of return being X or less is 5%. So, no. FYI, if VaR was defined like this, you could estimate it with the above Norm "VaR = return X, such that probability of return being X or less is 2.3"%. Then the return X would be u - 2sigma or less, or 5%-15%-15%= -25% or l VaR would be -25%. What is the probability that, in any given future year, the stock return will be 35% or be Round your answer to three decimal places.  Do not record your answer as a %. IE: Write 0.532, not 53.2% What is the probability that, in any given future year, the stock return will be -10% or w Round your answer to three decimal places.  Do not record your answer as a %. IE: Write 0.532, not 53.2% Using the information given for problems 3 and 4 above, could you estimate the Value this stock's annual returns?
estions: your d do not erage return 's future nalysis.
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Answer: 35% = 5% + 15% + 15% = 2.1% + 0.2% = 2.3% Answer = -10% = 5 - 15% = 13.6 + 2.1 + 0.2 = 15.9% = 0.159. mal Distribution Diagram: less etter?  worse?  at Risk of