You are given the following data for rates of return on a risky asset, a risk free rate and a market rate of return. Your aim is to calculate a regression line and estimate beta from the capital asset pricing for the rates of return on Asset Y. Task One Copy the table below into Excel and calculate the excess returns for risky Asset Y and the Market X. Year 2 30 day Treasury Bill Rate 15 Excess return on Market 2.0 15 2.0 15 Natural logarithm of returns Asset Year 20.7 46.8 14.5 17.2 Market rate of return 12.5 Excess return on Asset 24.2 2.3 7.6 Task Two Create a scatter diagram from the data and calculate the following for Y and X (the excess returns). 1. The mean 2. The median 3. The standard deviation 4. The correlation coefficient between Y and X Summarise your findings in a short note of approximately 100 words in length. Asset Task Three In the table below, input the missing values using the data from the table above. You will need to insert the excess return for the asset and the market that you calculated earlier. Excess return on Market Excess Returns Market X², ΣΧΥ,
You are given the following data for rates of return on a risky asset, a risk free rate and a market rate of return. Your aim is to calculate a regression line and estimate beta from the capital asset pricing for the rates of return on Asset Y. Task One Copy the table below into Excel and calculate the excess returns for risky Asset Y and the Market X. Year 2 30 day Treasury Bill Rate 15 Excess return on Market 2.0 15 2.0 15 Natural logarithm of returns Asset Year 20.7 46.8 14.5 17.2 Market rate of return 12.5 Excess return on Asset 24.2 2.3 7.6 Task Two Create a scatter diagram from the data and calculate the following for Y and X (the excess returns). 1. The mean 2. The median 3. The standard deviation 4. The correlation coefficient between Y and X Summarise your findings in a short note of approximately 100 words in length. Asset Task Three In the table below, input the missing values using the data from the table above. You will need to insert the excess return for the asset and the market that you calculated earlier. Excess return on Market Excess Returns Market X², ΣΧΥ,
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:You are given the following data for rates of return on a risky asset, a risk free rate and a
market rate of return. Your aim is to calculate a regression line and estimate beta from the
capital asset pricing for the rates of return on Asset Y.
Task One
Copy the table below into Excel and calculate the excess returns for risky Asset Y and the
Market X.
Year
1
2
3
30 day Treasury
Bill Rate
15
2.0
Excess return
on Market
X
15
2.0
15
Year
T
Natural logarithm of returns
1
Asset
2
20.7
3
46.8
8.6
14.5
17,2
Market rate of return
12.5
24.2
Excess return
on Asset
Y
2.3
Task Two
Create a scatter diagram from the data and calculate the following for Y and X (the excess
returns).
1. The mean
2.
The median
3. The standard deviation
4. The correlation coefficient between Y and X
Summarise your findings in a short note of approximately 100 words in length.
7.6
8.4
Task Three
In the table below, input the missing values using the data from the table above. You will
need to insert the excess return for the asset and the market that you calculated earlier.
Asset
Y
Excess Returns
Excess return
on Market
Market
Xx
X²
ΣΧΥ,

Transcribed Image Text:medi
3. The standard deviation
4. The correlation coefficient between Y and X
Summarise your findings in a short note of approximately 100 words in length.
Task Three
In the table below, input the missing values using the data from the table above. You will
need to insert the excess return for the asset and the market that you calculated earlier.
Excess return
on Market
B₁ =
Year
T
=
1
2
3
5
Sum
Mean
Excess return
on Asset
Excess return
on Market
Use the following expressions to calculate estimates for the regression line.
ΣXtYt - TXY
Σ(XtX) (Yt-Y)
Σ(Xt-X)²
Σ(X)² – TX²
X²,
=
ΣΧΥ,
Bo =Y - BiX
Once you have results for the regression line, put your results together in a narrative with the
two tables you completed. Your narrative should outline the capital asset pricing model and
what your estimate of one means in the context of the model.
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Transcribed Image Text:Task Two
Complete the values in the table below:
X
(X minus the mean
of X)
Sum
(X minus the mean
of X)'
Calculate the standard errors for the estimated parameters:
Standard error of (B₁) =
Standard error of (Bo)
X²
S
V Σ(Χ. – Χ.)2
Σ(Χ)2
sx Tx E(XtXt)²
Task Three
Calculate a t-statistic for each of the coefficients. Using a 0.05 level of significance, decide if
you can reject the null hypothesis for each estimated parameter.
Once you have completed the above tasks, put the content together in a narrative
|

Transcribed Image Text:Using the data you constructed in the previous activity and the linear regression line you
produced when estimating the parameters associated with the capital asset pricing model for
Asset Y, complete the tasks below. You will recall that you are interested in the following:
E(R) - rf
Y
B₁
These are the hypotheses:
Actual value for
excess return for
Asset
ß(E(Rm) – rf)
Bo+B1(X)
equals E(R) - rf
equals E(Rm) - rf
equals & the estimate of riskiness
Ho
B₁0 versus H₂ : B₁
Ho: Po 0 versus H₂ : Bo
Excess return
on Market
X
Task One
Using the data from the previous activity, complete the table below:
Fitted value for
excess return for
Asset Y
Sum
0
Calculate the sample variance.
0
Estimated residual
squared
Solution
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