## 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)?

Once you have the forecast value for S, calculate a 95% confidence interval for your forecast