In: Statistics and Probability

(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

- Calculate descriptive statistics to compare the returns of the mutual funds using the Data Analysis Descriptive Box.
- Compare and interpret the mean, median and skewness of Fidelity Select Automotive Fund and Fidelity Select Gold Funds.

- Compare and interpret the range and the standard deviation of Fidelity Select Automotive Fund and Fidelity Gold Funds.
- Discuss the range of each funds returns? Is the range the best descriptive measure? Why or Why not?
- 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 | |

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.

Chapter 3 presents the concept of financial analysis through the
use of ratios. The chapter presents 13 ratios in four categories.
Briefly explain the four categories and discuss why they would be
important in making a stock purchase. In preparing your comments,
assume you have $10,000 to invest in the stock market and you are
trying to choose between companies in the same industry. How would
you use the ratios presented in chapter 3 to decide what stock to
purchase?...

The attached Excel sheet contains data on annual returns on IBM
and 3M stocks over the period 1990-2002, as well as annual returns
on S&P 500 Index and one-year U.S. Treasury bills for this
period. You are asked to evaluate performance of IBM and 3M stocks
using the CAPM’s Security Market Line with S&P 500 Index as
proxy for the market return.
(i) Compute the annual excess returns of IBM, 3M, and the
S&P 500.
(ii) Use Excel to compute...

EXCEL FILE ONLY
Refer to the table below. The table below shows the annual
returns (in percentages) for 2 major market indices. For each
index, calculate the arithmetic mean return and the geometric mean
return of full-year returns from 2005-2015. What is the
relationship between the arithmetic and geometric mean returns?
2015
2014
2013
2012
2011
2010
2009
2008
2007
2006
2005
Nasdaq Composite Index
1.37
8.59
50.0
-31.5
-21.1
-39.3
85.6
39.6
21.6
22.7
39.9
Dow Jones Industrial Average...

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2. How much investment should firms really put into
reducing emissions.
3. From a strategic standpoint, what are the practical
implications of these changes/predicted changes?
Sea transport has a relatively green image because ships emit
less carbon dioxide per tonne and per kilometre than rail, truck or
air transport. Yet, given its scale and rapid growth, it’s a major
source...

Please answer the following questions using the data in the
attached Excel file.
You are thinking of investing in Abercrombie and Fitch Co.
(ANF). The returns for ANF are embedded in an Excel document below
(Source: yahoo.com).
1. For the investment in ANF that
you are considering, for all of 2012 determine the following
items:
a) the mean return
b) the median return
c) the standard deviation
d) the variance
e) the coefficient of variation
The weekly rates of return...

This chapter discusses "Firms in a competitive market," concepts
like monopolies, etc.
3) Determine whether the following statements are true or false.
Explain your answers.
a) A firm will make a profit when the price it charges exceeds
the average variable cost of the chosen output level.
b) To maximize profits in the short run, a firm must minimize
its costs.
c) if economic profit is positive, firms will exit the market in
the short run
d) A firm that...

ABC Inc. has provided returns of 6%, 12%, -16%, 4%, 8%, 3%, -5%,
8%, -11%, and 14% over the past ten years. Compute the arithmetic
and geometric means of the returns. What was the standard deviation
of the returns?

Question: Find √A for the following matrix A=[12 -3 8 ; 8 1 8 ;
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Problem 12-8 Risk Premiums [LO2, 3]
Suppose we have the following returns for large-company stocks
and Treasury bills over a six year period:
Year
Large
Company
US Treasury
Bill
1
4.00
4.62
2
14.49
4.96
3
19.33
3.88
4
–14.35
7.00
5
–31.84
5.38
6
37.04
6.43
a.
Calculate the arithmetic average returns for large-company
stocks and T-bills over this period. (Do not round
intermediate calculations. Enter your answers as a percent rounded
to 2 decimal places, e.g., 32.16.)
Average...

Table 3 (below) shows annual returns for the S&P 500 for
the years 2000-2016:
Table 3: Annual Returns
Year
Returns
2000
-9.0%
2001
-11.9%
2002
-22.0%
2003
28.4%
2004
10.7%
2005
4.8%
2006
15.6%
2007
5.5%
2008
-36.6%
2009
25.9%
2010
14.8%
2011
2.1%
2012
15.9%
2013
32.2%
2014
13.5%
2015
1.4%
2016
11.7%
Calculate:
The cumulative return over the 17 years;
The average annual return;
The standard deviation;
The Sharpe Ratio (assuming a risk free rate of 2.3% on...

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