Question

You are investigating the stability of stock index returns over a multi-decade horizon. You collect the following information about monthly index returns:

Time	N. observations	Mean return (%)	St.Dev (%)
1990-1999	120	-0.07	3.61
2000-2009	120	0.08	3.4

Assuming equal variances between periods, calculate the statistic for differences between means, to test the hypothesis that the means are equal. Bonus thinking question: can you reject the equal means hypothesis? Enter answer accurate to 3 decimal places. PLEASE SHOW STEPS AND DO THE PROBLEM ON EXCEL.

Answer 1

Time No. of obs Mean % St Dev

1990-99 120 -0.07 3.61

2000-09 120 0.08 3.40

The relevant statistic is the t statistic wherein

t = ((x-bar - y-bar)-(mu-x-mu-y))/(s*sqrt(1/nx + 1/ny)

df = nx+ny-2

s^2 = ((nx-1)sx^2+(ny-1)sy^2)/((nx-1)+(ny-1))

Here

nx 120

ny 120

df 238

x bar -0.07 sx 3.61

y bar 0.08 sy 3.4

s^2 12.29605

s 3.5066

t = ((0.08+0.07)-0)/(3.5066*sqrt(1/120 + 1/120))

t = 0.3313

df 238

T crit 1.970

Since t value is less than T crit, we cannot reject null hypothesis of both means being equal