Question

Calculate the **variance** of the following
returns.

Year Return

1 0.06

2 -0.05

3 -0.16

4 0.28

5 0.08

Enter the answer with 4 decimals, e.g. 0.1234.

Answer #1

Variance can be calculated with the help of below formula -

(Note: here, n- 1 is used in the denominator as the returns are given for few years and these are assumed to be of a sample)

**Mean = Total of all years returns / No. of
years**

Returns are shown in below table-

No. of
years |
Return |
( Return - Mean return) |
( Return - Mean
return)^{2} |

1 | 0.06 | 0.018 | 0.000324 |

2 | -0.05 | -0.092 | 0.008464 |

3 | -0.16 | -0.202 | 0.040804 |

4 | 0.28 | 0.238 | 0.056644 |

5 | 0.08 | 0.038 | 0.001444 |

Total
return |
0.21 |
Total |
0.10768 |

Mean 0.21/ 5= | 0.042 |

Variance = **0.10768 / (5 -
1)**

**= 0.10768 /
4**

= 0.02692

**Variance of the portfolio = 0.0269**

Hope it helps!

4. Calculate the variance of the following
returns.
Year Return
1 -0.20
2 0.04
3 -0.14
4 0.25
5 0.14
Enter the answer with 6 decimals,
e.g. 0.123456.
5. A stock has an expected return of 0.10, its beta is 0.95, and
the expected return on the market is 0.05. What must the risk-free
rate be? (Hint: Use CAPM) Enter the answer in 4 decimals e.g.
0.0123.
1. The Down and Out Co. just issued a dividend of $1.17 per...

Stocks A and B have the following? returns:
Stock A
Stock B
1
0.10
0.06
2
0.07
0.02
3
0.15
0.05
4
?0.05???
0.01
5
0.08
?0.02???
a. What are the expected returns of the two?
stocks?
b. What are the standard deviations of the
returns of the two? stocks?
c. If their correlation is 0.46?, what is the
expected return and standard deviation of a portfolio of 70?% stock
A and 30% stock? B?

Consider the following information:
State Probability Stock A Stock B Stock C
Boom 0.65 0.01 0.16 0.22
Bust 0.35 0.20 -0.06 0.10
What is the expected return on an equally weighted portfolio of
these three stocks? (Hint: Equally means that each stock has the
same weight. Given that there are only 3 stocks, each has a weight
of 1/3) Enter the answer with 4 decimals (e.g. 0.1234).

Returns
Year X Y
1 11 % 23 %
2 15 26
3 10 11
4 –13 –14
5 10 16
Using the returns shown above, calculate the arithmetic average
returns, the variances, and the standard deviations for X and Y.
(Do not round intermediate calculations. Enter your average return
and standard deviation as a percent rounded to 2 decimal places,
e.g., 32.16, and round the variance to 5 decimal places, e.g.,
32.16161.)

Returns
Year
X
Y
1
17
%
22
%
2
31
32
3
12
16
4
–
24
–
29
5
10
23
Using the returns shown above, calculate the arithmetic average
returns, the variances, and the standard deviations for X and Y.
Fill in the table below. (Do not round intermediate
calculations. Enter your average return and standard deviation as a
percent rounded to 2 decimal places, e.g., 32.16, and round the
variance to 5 decimal places, e.g., .16161.)...

Consider the following information:
State Probability Stock A Stock B Stock C
Boom 0.32 -0.05 0.08 -0.02
Bust 0.68 0.07 -0.12 0.22
What is the expected return of a portfolio that has invested
$12,403 in Stock A, $15,943 in Stock B, and $18,914 in
Stock C? (Hint: calculate weights of each stock first). Enter the
answer with 4 decimals (e.g. 0.1234).

A). A stock has a beta of 1.02, the expected return on the
market is 0.09, and the risk-free rate is 0.05. What must the
expected return on this stock be? Enter the answer with 4 decimals
(e.g. 0.1234).
B).
You own a portfolio that has $4100 invested in Stock A and $4900
invested in Stock B. If the expected returns on these stocks are
0.18 and 0.01, respectively, what is the expected return on the
portfolio?
Enter the answer...

A portfolio produces the following returns in years 1-5:
Year
Return (%)
1
-8
2
7
3
5
4
3
5
-2
What is the sample semideviation of returns?
Enter answer in percents, accurate to 2 decimal places.

Consider the following information:
State Probability Stock A Stock B Stock C
Boom 0.32 0 0.25 0.19
Bust 0.68 0.25 0.08 0.16
What is the expected return of a portfolio that has invested
$9,242 in Stock A, $7,934 in Stock B, and $7,984 in
Stock C? (Hint: calculate weights of each stock first). Enter the
answer with 4 decimals (e.g. 0.1234).

Using the following returns, calculate the standard deviation of
returns for Spotify:
Year
Return
1
14%
2
20%
3
-9%
4
3%
5
17%
According to the Fisher effect, what is the relationship between
real and nominal returns when inflation is greater than zero?
Real returns < Nominal returns
Real returns > Nominal returns
Real returns = Nominal returns

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