Graded Assignment Descriptions & Instructions Instructions: In no more than 500

Question

Graded Assignment Descriptions & Instructions Instructions: In no more than 500 words, use the data distributions below to calculate the following for Portfolio 1 and Portfolio 2. Both portfolios contain 50 stocks Portfolio 1 Portfolio2 Annual Returns Annual Returns Frequency (f Frequency (f) 4 -2 4 12 4 10 12 15 16 19 21 23 26 28 Total 50 Total 50 A. Calculate the: Mode Arithmetic Mean . Median Standard Deviation B. Write a report comparing your findings for the two portfolios. Indicate which of the two portfolios you would recommend a company to invest in and the reasons for such favorable investment option

Explanation / Answer

A. Calculate the

1. Mode :Mode is the value from the given data that occures the most often.

Now, based on given information, we have two portfolios with 50 stocks each. We have data of the annual return and frequency of the return occuring. From these, we have to find the return which occurs most often for both portfolios to calculate mode.

Mode for Portfolio 1 = 2% (Since the frequecy for this is 12)

Mode for Portfolio 2 = 21% and 23% (This database is biomodal because the frequency for both these returns is 9)

2. Arithmetic Mean - avaerage of all the datapoints

Simple mean of the given datapoints for both the portfolios can be calculates as follows:

Portfolio 1 = [(-3%*4)+(-2%*5)+(-1%*8)+(2%*12)+(5%*10)+(8%*5)+(11%*2)+(15%*2)+(16%*1)+(19%*1)]/50 = 3.42%

Portfolio 2 = [(-1%*1)+(2%*3)+(4%*3)+(7%*4)+(12%*6)+(19%*6)+(21%*9)+(23%*9)+(26%*7)+(28%*)]/50 = 17.3%

3. Median - The median is an exact middle data point from data which is arranged in an ascending order

Position of median = (n+1)/2 (n= Totalnumber of data points)

Applying the above formula, = (50+1)/2 = 25.5 i.e. Median is the mean of 25th and 26th number.

Based on the frequency , we can calculate 25tth and 26th number for both the portfolios.

Median for Portfolio 1 = (2+2)/2 = 2% (If we add the frequencies, 4+5+8 = 17< 25, 4+5+8+12 = 29>25 i.e. return for frequency 12 is 25th and 26th number)

Median for Portfolio 2 = (21+21)/2 = 21% (If we add the frequencies, 1+3+3+4+6+6 = 23<25 , 1+3+3+4+6+6+9 = 32>25 i.e. return for frequency 12 is 25th and 26th number)

4. Standard Deviation

For Portfolio 1 :

Mean in below table is as calculated in option 2

From above data, standard deviation = Sqrt (1406.18/50) = 5.3031

For Portfolio 2:

From above data, standard deviation = Sqrt (12985.22/50) = 16.11534

B. From above calculations it is clear that , the standard deviation for portfolio 1 = 5.3031 < Standrd deviation for portfolio 2 = 16.11535

That means portfolio 2 is more volatile than the portfolio 1. And hence, portfolio 1 is preferable to invest in.

Annual Return (x) Frequency (f) f*x X-mean (x-mean)^2 f*(x-mean)^2 -3 4 -12 -6.42 41.2164 164.8656 -2 5 -10 -5.42 29.3764 146.882 -1 8 -8 -4.42 19.5364 156.2912 2 12 24 -1.42 2.0164 24.1968 5 10 50 1.58 2.4964 24.964 8 5 40 4.58 20.9764 104.882 11 2 22 7.58 57.4564 114.9128 15 2 30 11.58 134.0964 268.1928 16 1 16 12.58 158.2564 158.2564 19 1 19 15.58 242.7364 242.7364 Total 50 171 1406.18

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