Mathematics, 21.03.2020 09:59, keilyn80

"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 14.7% (i. e. an average gain of 14.7%) with a standard deviation of 33%. 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.

a.) What percent of years does this portfolio lose money, i. e. have a return less than 0%

b.) What is the cutoff for the highest 15% of annual returns with this portfolio"

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answered: 12233445566

a) In 32.82% this portfolio lose money, i.e. have a return less than 0%

b) The cutoff for the highest 15% of annual returns with this portfolio is an annual return of 48.86%.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 0.147 \sigma = 0.33$

a.) What percent of years does this portfolio lose money, i.e. have a return less than 0%

This is the pvalue of Z when X = 0. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{0 - 0.147}{0.33}$

Z = -0.445

Z = -0.445 has a pvalue of 0.3282

In 32.82% this portfolio lose money, i.e. have a return less than 0%

b.) What is the cutoff for the highest 15% of annual returns with this portfolio"

This is X when Z has a pvalue of 1-0.15 = 0.85. So it is X when Z = 1.035.

$Z = \frac{X - \mu}{\sigma}$

$1.035 = \frac{X - 0.147}{0.33}$

X - 0.147 = 0.33*1.035

X = 0.4886

The cutoff for the highest 15% of annual returns with this portfolio is an annual return of 48.86%.

answered: Guest

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.