a. Plot the frequency chart of monthly excess stock returns, and compute mean, volatility (i.e., standard deviation), skewness and kurtosis of excess stock returns, and perform a test for whether the excess stock returns are normally distributed; b. Perform a test and discuss your findings for the difference in means of the excess stock returns across periods of economic expansion and recession as indicated by the NBER recession index; f. Run a multivariate OLS regression of the excess stock return on all the three factor returns (Mkt_RF, SMB, HML). Explain and discuss the economic significance (i.e., the magnitude) and statistical significance of the intercept and the relations between the excess stock return and the three factor returns;
Minimization
In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.
Maxima and Minima
The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.
Derivatives
A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.
Concavity
In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.
please solve the three sub-parts (a,b,f) by using given data in pictures
a. Plot the frequency chart of monthly excess stock returns, and compute
b. Perform a test and discuss your findings for the difference in means of the excess stock returns across periods of economic expansion and recession as indicated by the NBER recession index;
f. Run a multivariate OLS regression of the excess stock return on all the three factor returns (Mkt_RF, SMB, HML). Explain and discuss the economic significance (i.e., the magnitude) and statistical significance of the intercept and the relations between the excess stock return and the three factor returns;
![a.
ESR
variable
sd skewness kurtosis
N
nean
ESR
275 .0013146 .0862379 .2246285 5.499584
b.
Two-sample t test with unequal variances
obs
Mean std. Err.
std. Dev. (95% conf. Interval]
36
-.0222395
.0238602
.143161
-.0706782
.0261992
y
239
.0048625
.0047759
.0738333
-.0045459
.0142709
combined
275
.0013146
.0052003
.0862379
-.0089231
.0115523
diff
-.027102
.0243334
-.0763688
.0221648
diff - mean(x) - nean(y)
HO: diff - e
t- -1.1138
satterthwaite's degrees of freedom - 37.8518
Ha: diff !- e
Pr(|T| > |t|) = 0.2724
Ha: diff > e
Pr(T > t) = 0.8638
Ha: diff < e
Pr(T < t) = 0.1362
08
09
Kouanbəs](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4aa9933b-5161-42cf-95bc-c2946d028b2e%2F81e7e200-de04-4bc5-ae34-1b028385aea4%2F67rcdgh_processed.jpeg&w=3840&q=75)
![f.
Source
df
MS
Number of obs
275
F(3, 271)
59.16
Model
.806408775
3 .268802925
Prob > F
e.0000
Residual
1.23132076
271 .004543619
R-squared
0.3957
Adj R-squared =
0.3890
Total
2.03772953
274 .007436969
Root MSE
.06741
ESR
Coef.
std. Err.
t
P>|t|
[95% Conf. Interval]
Mkt_RF
1.215893
.0922072
13.19
0.000
1.03436
1.397427
SMB
-.1911945
.1317904
-1.45
0.148
-.4506576
.0682687
HML
.2817048
.1301661
2.16
0.031
.0254394
.5379701
_cons
-.0064722
.0041153
-1.57
0.117
-.0145742
.0016298](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4aa9933b-5161-42cf-95bc-c2946d028b2e%2F81e7e200-de04-4bc5-ae34-1b028385aea4%2Fcwsaul_processed.jpeg&w=3840&q=75)
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