Examining Stock Returns for Normal Distributions
Examining Stock Returns for Normal Distributions
July11, 2012
Part A. A1 (CRSP 2000-2008) | VW Daily | EW Daily | VW Monthly | EW Monthly | Mean | 0.00% | 0.05% | -0.12% | 0.50% | σ | 1.35% | 1.12% | 4.66% | 6.14% | Table A1 shows return means and standard deviations for the CRSP market portfolio from 2000-2008. In comparing daily vs monthly returns in both cases, equally weighted (EW) and value weighted (VW), Table A1 shows the mean and standard deviation are bigger for the monthly data than daily. This is due to the collection interval of the data. There are higher mean returns in the monthly than daily simply because the prices moved more in a month than in a day. There is also more deviation from the mean on a monthly basis than on a daily basis, because of the time period, more movement is possible.
In comparing EW to VW, in both the monthly and daily case. EW seems to have higher means signaling that smaller firms in general have higher returns which bring up the mean significantly more in the EW than in the VW because they have less influence over the VW. But there is not a large difference in daily standard deviations. Meaning, small and large stocks differ from their means (distribution) in a similar fashion on a daily basis. But on a monthly basis smaller stocks move more than larger ones, as indicated by higher st. dev on the monthly basis attributed to the EW portfolio.
Part B.
In this experiment I analyzed stock returns to determine if they follow a normal distribution. The result of this experiment could be extremely beneficial. If they do follow such a distribution one could develop a strategy based on historical performance and forecast future performance. To develop an accurate conclusion I used market indexes’, and individual stock’s, performance over different time periods. After this analysis I have concluded that stock returns are not normal and therefore cannot be forecasted on the basis of
July11, 2012
Part A. A1 (CRSP 2000-2008) | VW Daily | EW Daily | VW Monthly | EW Monthly | Mean | 0.00% | 0.05% | -0.12% | 0.50% | σ | 1.35% | 1.12% | 4.66% | 6.14% | Table A1 shows return means and standard deviations for the CRSP market portfolio from 2000-2008. In comparing daily vs monthly returns in both cases, equally weighted (EW) and value weighted (VW), Table A1 shows the mean and standard deviation are bigger for the monthly data than daily. This is due to the collection interval of the data. There are higher mean returns in the monthly than daily simply because the prices moved more in a month than in a day. There is also more deviation from the mean on a monthly basis than on a daily basis, because of the time period, more movement is possible.
In comparing EW to VW, in both the monthly and daily case. EW seems to have higher means signaling that smaller firms in general have higher returns which bring up the mean significantly more in the EW than in the VW because they have less influence over the VW. But there is not a large difference in daily standard deviations. Meaning, small and large stocks differ from their means (distribution) in a similar fashion on a daily basis. But on a monthly basis smaller stocks move more than larger ones, as indicated by higher st. dev on the monthly basis attributed to the EW portfolio.
Part B.
In this experiment I analyzed stock returns to determine if they follow a normal distribution. The result of this experiment could be extremely beneficial. If they do follow such a distribution one could develop a strategy based on historical performance and forecast future performance. To develop an accurate conclusion I used market indexes’, and individual stock’s, performance over different time periods. After this analysis I have concluded that stock returns are not normal and therefore cannot be forecasted on the basis of