You believe that the volatility in the monthly returns on the S&P 500 Index is higher this year than it was during the Financial Crisis.
finance
Description
1.
You believe that the volatility in the monthly returns
on the S&P 500 Index is higher this year than it was during the Financial
Crisis. You compare the standard
deviation of monthly returns on the S&P 500 Index for the 6 months ending May
31, 2020 to the period from June 2008 through October 2011 (financial
crisis). The sample standard deviations
of the monthly returns are as follows:
Recent 6 months: 9.13%
(6 observations)
Financial crisis standard
deviation: 6.32% (41 observations)
a.
State the null and alternative hypotheses to
test your conjecture (one-sided test)
b.
Test the hypothesis at a 95% level of
significance (
, showing the test statistic
and comparing it to the critical value
2. You
are considering the relationship between annual returns on the S&P 500
index (January 31 to January 31) and annual changes in the unemployment rate.
You define:
S = annual % change in the S&P500 (SPX)
U = annual % change in the unemployment rate
You consider the following univariate relationship:
Si = b0 + b1Ui +
εi
You have data on annual changes in the unemployment rate and the S&P500
(SPX) from 2002 through 2020 (19 observations) and you want to use the data to
estimate the regression coefficients (intercept b0
and slope b1)
You are given the following statistics:
|
Statistic |
Value |
|
Cov(U,S) |
-0.025043 |
|
Var(U) |
0.034590 |
|
E(U) |
-0.001530 |
|
E(S) |
0.064267 |
|
TSS |
0.627907 |
|
RSS |
0.326368 |
a.
Compute the estimated coefficients for the
intercept (b0)
and slope (b1)
and the R2
b.
So far in 2020, the unemployment rate has increased
by 280% (from 3.6 percent to 13.3 percent).
If the unemployment rate increase for the year ends up at 100%, what is
the expected value of S (annual return on the S&P500)?
