Answer only questions 4,5,6,7,8

write the Excel formulas

Say you are a stock investor. You are considering to invest in TESLA. To that end, you download the stocks historical price data given in Computer Exercise 2.xlsx. More precisely, you analyze the daily market-closing stock prices from June 29, 2010 to December 31, 2019. Please answer the following questions.

1. To start, you want to get an idea of the daily return that you could have obtained by buying on one trading day and selling on the next (assuming that there are no dividends). Compute the daily net return; i.e. the proportionate change in prices.

2. Now you want to know on how many of the total trading days in your sample you would have made a positive net return. What is the number of days on which your net return would have been positive?

3. You decided that you want to invest in TESLA. Say that the outcome of your experiment (i.e. your investment) that you are interested in is whether you will win a positive net return on the first day or not. That is, you define a Bernoulli random variable, X, that can take on values 1 (positive net return on first day), and 0 (zero or negative net return on first day).

Since you dont know how to otherwise approach the question (you are a first-time investor), you decide that the likelihood of successes in the past should be an indication of the future probability of success. Hence, what is the probability of success (i.e. positive net return) based on the 2010-2019 sample?

4. What is the expected value/population mean of your Bernoulli variable X?

5. What are the (population) variance and standard deviation of X? Having computed the latter, comment on how good your guess for X (i.e. the expected value in 4.) really is.

6. Is the distribution of X symmetric about its mean? Why or why not?

7. Instead, now assume that your investment horizon is 15 trading days, where on each day you either can gain a positive net return (Xi=1) or a negative net return (Xi=0). Assume that the random variables Xi, i=1, 2,,15, are independent. The probability of success is still the same as in question 3. above, and it is the same for all i.

What is the probability that you will make a positive net return on 10 (out of the in total 15) following trading days?

8. Under the same assumptions as in question 7. above, what is the probability that you will make a positive net return on more than 11 (out of the in total 15) following trading days?

Date	Closing Price
20100629	23.89
20100630	23.83
20100701	21.96
20100702	19.2
20100706	16.11
20100707	15.8
20100708	17.46
20100709	17.4
20100712	17.05
20100713	18.14
20100714	19.84
20100715	19.89
20100716	20.64
20100719	21.91
20100720	20.3
20100721	20.22
20100722	21
20100723	21.29
20100726	20.95
20100727	20.55
20100728	20.72
20100729	20.35
20100730	19.94
20100802	20.92
20100803	21.95
20100804	21.26
20100805	20.45
20100806	19.59
20100809	19.6
20100810	19.03
20100811	17.9
20100812	17.6
20100813	18.32
20100816	18.78
20100817	19.15
20100818	18.77
20100819	18.79
20100820	19.1
20100823	20.13
20100824	19.2
20100825	19.9
20100826	19.75
20100827	19.7
20100830	19.87
20100831	19.48
20100901	20.45
20100902	21.06
20100903	21.05
20100907	20.54
20100908	20.9
20100909	20.71
20100910	20.17
20100913	20.72
20100914	21.12
20100915	21.98
20100916	20.94
20100917	20.23
20100920	21.055
20100921	20.77
20100922	19.87
20100923	19.56
20100924	20.1
20100927	20.53
20100928	21.4
20100929	21.98
20100930	20.405
20101001	20.6
20101004	20.99
20101005	21.12
20101006	20.46
20101007	20.43
20101008	20.43
20101011	20.24
20101012	20.24
20101013	20.54
20101014	20.75
20101015	20.54
20101018	20.23
20101019	20.05
20101020	20.65
20101021	20.75
20101022	20.72
20101025	20.85
20101026	21.36
20101027	21
20101028	21.19
20101029	21.84
20101101	21.41
20101102	21.25
20101103	21.77
20101104	24.9
20101105	24.44
20101108	24.98
20101109	24.63
20101110	29.36
20101111	28.035
20101112	29.84
20101115	30.8
20101116	29.67
20101117	29.49
20101118	29.89
20101119	30.99
20101122	33.4
20101123	34.57
20101124	35.47