Question

In: Statistics and Probability

(Covering concepts for Chapter 3 and 8) The following attached file presents the annual returns for...

(Covering concepts for Chapter 3 and 8)

The following attached file presents the annual returns for two mutual funds offered by the investment giant Fidelity. The Fidelity Select Automotive Fund invests primarily in companies engaged in the manufacturing, marketing, or sales of automobiles, trucks, specialty vehicles, parts, tires and related services. The Fidelity Gold Fund invests primarily in companies engaged in exploration, mining, processing, or dealing in gold and, to a lesser degree, in other precious metals and minerals.

In a report, use the above information and attached file to

  1. Calculate descriptive statistics to compare the returns of the mutual funds using the Data Analysis Descriptive Box.
  2. Compare and interpret the mean, median and skewness of Fidelity Select Automotive Fund and Fidelity Select Gold Funds.
  1. Compare and interpret the range and the standard deviation of Fidelity Select Automotive Fund and Fidelity Gold Funds.
  2. Discuss the range of each funds returns? Is the range the best descriptive measure? Why or Why not?
  3. Assess reward by constructing and interpreting 95% confidence intervals for the population mean return. What assumption did you make for interval estimates?

Example p. 314/ Note Use standard deviation as a measure of risk!

Year Automotive Gold
2001 22.82 24.99
2002 -6.48 64.28
2003 43.53 32.09
2004 7.11 -9.79
2005 -1.75 40.7
2006 13.33 25.43
2007 0.01 24.93
2008 -61.2 -20.49
2009 122.28 38
2010 46.18 35.25
2011 -26.16 -16.34
2012 26.17 -12.43
2013 46.67 -51.41
2014 2.79 -8.51
2015 0.17 -17.88
2016 -5.83 47.28

Solutions

Expert Solution

The descriptive statistics are given below:

The mean median and skeness of automobile are 16.8525,8.06 and 0.77 respectively. For gold it is 12.256, 24.96 and -0.3 respectively

It means the mean return of automobile is greater than that of gold. The median return of automobile is less than that of gold.

Also return of automobile is positively skewed and that of gold is negatively skewed. Skewness gives the measure of assymetry of the probability distribution of the random variable under consideration.

The range and standard deviation of automobile are 183.48 and 40.61 respectively. For gold it is 115.69 and 31.83 respectively.

Range and standard deviation are measures of dispersion. Range is the difference between max and min of the observations and standard deviation shows how much dispersed the data is about its mean.

Here, automobile has greater range and standard deviation than gold. So automobile is more dispersed as compared to gold.

Range is the difference between max and min of the observations .  For gold it is 115.69 and for automobile it is 183.48. Range is a measure of dispesion. It is a simple measure as only 2 observations (min amd max) are considered, so it cannot be stated as a best descriptive measure. Standard deviation is a better measure as it uses all data points as opposed to range which use only 2 data points.

The 95% confidence interval is given by :

mean ± confidence level(95%)

For automobile, it is

16.8525  ±  21.637 = [ -4.7845 , 38.4895 ]

For gold, it is

12.256   ±  16.963 = [ -4.707 , 29.219 ]

So with 95% confidence, the mean return of automobile can go upto 38.4895 and can come down to -4.7845 as oppossed to that of gold which is between 29.219 and -4.707.

So, automobile return seems to be more than that of gold.

The interval estimates are obtained by assuming the data follows normal distrbution.


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