3. Stock market analysts have suggested that January is a good indicator of the

Question

3. Stock market analysts have suggested that January is a good indicator of the behaviour of the stoc market during the entire year. The data shown in the attached figure consists of the changes in stock in the Standard and Poor’s (S&P) 500 index during January and the corresponding changes in the same index for the entire year. Data are provided for the years 1950 to 2010.

Conduct an analysis of the reported data and answer the following questions.

a) What percentage of the variation in the yearly performance of the S&P 500 can be explained by the performance of this index in January? (In other words, find the R2). Explain the relevance of this percentage.

b) Do you believe that January can serve as a predictor of the stock market’s performance for the entire year? (In other words, is there a relationship?) Explain.

c) In January of 2011, the S&P 500 index increased by 2.3%. Predict the performance of the index for the entire year. Also give a 95% prediction interval.

d) Based on the 95% prediction interval, comment on the usefulness of the January indicator.

Year January Change (%) Annual Change (%) 1950 2.3 22.5 1951 4.3 14.4 1952 1.4 11.6 1953 -0.6 -6.5 1954 4.5 44.2 1955 -0.3 23.8 1956 -3.0 3.3 1957 -3.2 -13.4 1958 3.4 36.9 1959 0.0 8.0 1960 -7.2 -3.0 1961 7.3 24.3 1962 -3.8 -11.8 1963 4.9 18.9 1964 2.7 13.0 1965 3.3 9.1 1966 0.5 -13.1 1967 7.8 20.1 1968 -4.4 7.7 1969 -0.8 -11.4 1970 -7.6 0.1 1971 4.0 10.8 1972 1.8 15.6 1973 -1.7 -17.4 1974 -1.0 -29.7 1975 12.1 31.4 1976 11.8 19.1 1977 -5.1 -11.5 1978 -6.2 1.1 1979 4.0 12.3 1980 5.8 25.8 1981 -4.6 -9.7 1982 -1.8 14.8 1983 3.3 17.3 1984 -0.9 1.4 1985 7.4 26.4 1986 0.2 14.6 1987 13.2 2.0 1988 4.0 12.4 1989 7.1 27.3 1990 -6.9 -6.6 1991 4.2 26.3 1992 -2.0 4.5 1993 0.7 7.1 1994 3.2 -1.6 1995 2.4 34.1 1996 3.3 20.3 1997 6.1 31.0 1998 1.0 26.7 1999 4.1 19.5 2000 -5.1 -10.0 2001 3.5 -13.0 2002 -1.6 -23.4 2003 -2.7 26.4 2004 1.7 9.0 2005 -2.5 3.0 2006 2.5 13.6 2007 1.4 3.5 2008 -4.7 -37.6 2009 -8.8 23.5 2010 -4.0 12.6 2011 2.3 0.0

Explanation / Answer

Answer

(a) R2=0.268 ,i.e., 26.8% of the variation in the yearly performance of the S&P 500 can be explained by the performance of this index in January

(b)since the value of R is .517 ,i.e., the correlation between annually and januaryis 51% so we can believe that January can serve as a predictor of the stock market’s performance for the entire year

(c)the performance of the index for the entire year 2011 is : 11.083.

A 95% prediction interval for coefficints is(3.099,10.732)

and A 95% prediction interval for january is(1.029,2.587)

d) since from 95% prediction interval we can claim that our mean value will lie between these two values.

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