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grigory [225]
3 years ago
5

Do bonds reduce the overall risk of an investment portfolio? Let x be a random variable representing annual percent return for t

he Vanguard Total Stock Index (all Stocks). Let y be a random variable representing annual return for the Vanguard Balanced Index (60% stock and 40% bond). For the past several years, assume the following data. x: 14 0 39 25 32 27 28 14 14 15 y: 6 2 29 17 26 17 17 2 3 5 Compute the coefficient of variation for each fund. Round your answers to the nearest tenth.
Mathematics
1 answer:
rjkz [21]3 years ago
6 0

Answer:

COV (all stocks) = 0.55

COV (stocks and bonds) = 0.82

Step-by-step explanation:

Coefficient of Variation is used to measure variability.

It is defined as the ration of standard deviation and the mean.

It can be used to compare variability of two population or two samples.

Formula:

\text{Coefficient of Variation} = \displaystyle\frac{\text{Standard Deviation}}{\text{Mean}}

\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}

where x_i are data points, \bar{x} is the mean and n is the number of observations.

Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}

x: 14, 0, 39, 25, 32, 27, 28, 14, 14, 15

Mean = \frac{208}{10} = 20.8

Standard~Deviation = \sqrt{\frac{1169.6}{9} } = 11.39

Coefficient~of~Variation = \frac{11.39}{20.8} = 0.55

y = 6, 2, 29, 17, 26, 17, 17, 2, 3, 5

Mean = \frac{124}{10} = 12.4

Standard~Deviation = \sqrt{\frac{924.4}{9} } = 10.13

Coefficient~of~Variation = \frac{10.13}{12.4} = 0.82%

Since coefficient of variation of x is less compared to y, thus it could be said bonds does not reduce overall risk of an investment portfolio.

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The school store opened on the first day of school with 45 notebooks and 15 pencils. Within two days it sold all of these items.
malfutka [58]

The number of pencils sold on the first day  is 5 pencils.

The number of notebooks sold on the first day  is 10 notebooks.

The number of pencils sold on the second day 10 pencils.

The number of notebooks sold on the second day   35 notebooks.

<u>Step-by-step explanation:</u>

Given data,

  • The total number of notebooks in the store = 45 notebooks.
  • The total number of Pencils in the store = 15 pencils.
  • The number of days that all items were sold = 2 days.

Now, you have to calculate the no.of notebooks and no. of pencils sold each day.

<u>In the first day :</u>

The number of sale of notebooks and pencils are given by,

Twice as many notebooks were sold as pencils.

Let us take, the number of pencils sold on the first day  = x

And,  the number of notebooks sold on the first day  = 2x (Twice as pencils).

<u>In the second day :</u>

The number of sale of notebooks and pencils are given by,

For every 7 notebooks​ sold, 2 pencils were sold.

The number of pencils sold on the second day =   2y

The number of notebooks sold on the second day   = 7y

<u> The equation is framed for number of notebooks sold on each day :</u>

The number of notebooks sold ⇒ 2x + 7y = 45   -------(1)

<u> The equation  is framed for number of pencils sold on each day :</u>

The number of pencils sold: x + 2y = 15  ----------(2)

Solving the equations by multiplying eq(2) by 2 and subtract it from eq(1),

  2x + 7y = 45

-<u> (2x + 4y) = 30</u>

   <u>        3y = 15  </u>

⇒ y = 15/3

⇒ y = 5

The value of y is 5.

Substitute y=5 in eq (2),

⇒ x + 2(5) = 15

⇒ x + 10 = 15

⇒ x = 15 - 10

⇒ x = 5

The value of x is 5.

First day sale,

The number of pencils sold on the first day  = x ⇒ 5 pencils

The number of notebooks sold on the first day  = 2x ⇒ 10 notebooks

Second day sale,

The number of pencils sold on the second day =   2y ⇒ 10 pencils

The number of notebooks sold on the second day   = 7y ⇒ 35 notebooks.

8 0
2 years ago
Drag and drop the constant of proportionality into the box to match the table. If the table is not proportional, drag and drop "
Nikitich [7]

The table is proportional and the constant of proportionality is 1.5

Step-by-step explanation:

Proportional relationships are relationships between two variables

where their ratios are equivalent

  • One variable is always a constant value times the other
  • The relation between the two variables represented graphically by a line passes through the origin point

The table:

→ x  :  0  :  2  :  4  :  6

→ y  :  0  :  3  :  6  :  9

To prove that y ∝ x find the ratio between each value of y with corresponding value of x

∵ \frac{3}{2}=1.5

∵ \frac{6}{4}=1.5

∵ \frac{9}{6}=1.5

∴ \frac{y}{x}=k

∴ k = 1.5

∵ The origin point is in the table

∴ y ∝ x

∴ The table is proportional

The table is proportional and the constant of proportionality is 1.5

Learn more:

You can learn more about proportional in brainly.com/question/10708697

#LearnwithBrainly

4 0
3 years ago
Read 2 more answers
Two angels re supplementary. The larger angle is 48 degrees more than the 10 times the smaller angle. Find the measure of each a
evablogger [386]
Supplementary angles are two angles that add up to 180°.

STEP 1:
find the value of x

x= smaller angle
10x + 48= larger angle

Add the two angles above to equal 180.

x + (10x + 48)= 180
combine like terms

11x + 48= 180
subtract 48 from both sides

11x= 132
divide both sides by 11

x= 12° smaller angle


STEP 2:
find the value of the second angle

=10x + 48
=10(12) + 48
=120 + 48
=168° larger angle


CHECK:
12° + 168°= 180°
180°= 180°


ANSWER: The smaller angle is 12° and the larger angle is 168°.

Hope this helps! :)
8 0
3 years ago
7 POINTS help help help help help help PLZZZZ!!!
pishuonlain [190]
-2 is the answer it’s very easy
8 0
3 years ago
Evaluate (c − b)2 + a2 for a = –5, b = –2, and c = –4.
ExtremeBDS [4]
[(-4)-(-2)]+(-5)2
[(-4)+2]-10
(-2)-10
-12
Hope this helps!
5 0
3 years ago
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