Compute the covariances between the S&P; 500 index and the CPI and between the t

Question

Compute the covariances between the S&P; 500 index and the CPI and between the three-month Treasury bill rate and the CPI. Are these population or sample covariances? Compute the correlation coefficients between the S&P; 500 index and the CPI and between the three-month Treasury bill rate and the CPI. A priori, would you expect these correlation coefficients to be positive or negative? Why? If there is a positive relationship between the CPI and the three-month Treasury bill rates, does that mean inflation, as measured by the CPI, is the cause of higher T bill rates? CONSUMER PRICE INDEX (CPI, 1982-1984 = 100). STANDARD AND POOR'S COMPOSITE INDEX (S&P; 500, 1941-1943 = 100), AND THREE-MONTH TREASURY BILL RATE (3-m T BILL, %)

Explanation / Answer

a) Both sample and population covariances are calculated

b) The correlation should be of the same sign as the covariance

c) T-bill rates and CPI are negatively related. Thus, if CPI increases, T-bill rates decreases.

Year CPI S&P 500 T-bill 1980 82.4 118.78 12 Sample 1981 90.9 128.05 14 Covariances S&P 500 T-bill 1982 96.5 119.71 11 CPI 15700.19 -91.4366 1983 99.6 160.41 8.63 1984 103.9 160.46 9.58 Population 1985 107.6 186.84 7.48 Covariances S&P 500 T-bill 1986 109.6 236.34 5.98 CPI 15139.47 -88.171 1987 113.6 286.83 5.82 1988 118.3 265.79 6.69 1989 124 322.84 8.12 Correlation S&P 500 T-bill 1990 130.7 334.59 7.51 CPI 0.929853 -0.81218 1991 136.2 376.14 5.42 1992 140.3 415.74 3.45 1993 144.5 451.41 3.02 1994 148.2 460.42 4.29 1995 152.4 541.72 5.51 1996 156.9 670.5 5.02 1997 160.5 873.43 5.07 1998 163 1085.5 4.81 1999 166.6 1327.33 4.66 2000 172.2 1427.22 5.85 2001 177.1 1194.18 3.45 2002 179.9 993.94 1.62 2003 184 965.23 1.02 2004 188.9 1130.65 1.38 2005 195.3 1207.23 3.16 2006 201.6 1310.46 4.73 2007 207.3 1477.19 4.41

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