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Safari File Edit View History Bookmarks Develop Window Help G O *83%. Sun Feb 25 21:25:07 Q webwork.carroll.edu WeBWork: MA207 Dill: Sect2-13NormalDistr : 6 Please Help Me With This Stats Probelm! Chegg.com MAA Logged in as copowell. Log Out C MATHEMATICAL ASSOCIATION OF AMERICA WeBWork webwork / ma207_dill / sect2-13normaldistr/6 MAIN MENU Courses Homework Sets 4 56 Sect2-13NormalDistr: Problem 6 Sect2- 13NormalDistr Problem Previous Problem List Next 0 6 User Settings (1 point) Grades FINISHED photos College The Capital Asset Pricing Model is a financial model that assumes returns on a portfolio are normally distributed. Suppose a portfolio has an average annual return of 12.7% (ie, an average gain of 12.7%) with a standard deviation of 29.9%. A return of 0% means the value of the portfolio doesn't change, a negative return means that the portfolio loses money, and a positive return means that the portfolio gains money. Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 Problem 7 Problem 8 Problem 9 Problem 10 Problem 1 Problem 12 (a) In what percent of years does this portfolio lose money? Untitled Export comp 2 (b) what is the cutoff for the highest 15% of annual returns with this portfolio? Microbiology Note: You can earn partial credit on this problem Psych Preview My Answers Submit Answers You have attempted this problem 0 times. You have 10 attempts remaining. Psychosocial Anatomy Email inetriuntor 25

Explanation / Answer

Solution:

The percent of years does the portfolio lose money. That is, find the probability P(X < 0)

Let X be the random variable defined by returns on a portfolio follows normal distribution with mean 12.7% and standard deviation () 29.9%.

The probability P(X < 0) is,
P(X < 0) = P(X - 12.7/29.9 < 0 - 12.7/29.9)
= P(z < -12.7/29.9)
= P(z < -0.42)
From the “standard normal table”, the value of z area to the left of the curve for z = -0.42 is 0.3372.
That is,
P(X < 0) = P(Z < -0.42)
= 0.3372

(b) The cutoff for the highest 15% of annual returns with this portfolio is obtained below:
P(X > x) = 0.15
1-P(X x) = 0.15
P(X x) = 0.85

From the “standard Normal table”, the area covered for value of 0.85 is obtained at z = 1.04.
The cutoff for the highest 15% of annual returns with this portfolio is,
z = X - /
1.04 = X - 12.7/29.9
1.04 * 29.9 = X - 12.7
31.09 = X - 12.7
X = 12.7 + 31.09
= 43.79

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