Question

Using the most appropriate type of graph to present weekly closing price of the Bitcoin and provide a general description. Hint: What are the main features of this graph, is there a trend? [Topic 1]                                  

Calculate the weekly return and construct a histogram. Does the data appear normally distributed?   Is there evidence of outliers? Hint: the formula for a return is (Current Price – Previous price)/Previous price multiplied by 100 [Topics 1-3]                                                         

Calculate and interpret the three aspects of Descriptive Analysis, Location, Shape and Spread, for weekly return. [Topic 1]

What is the empirical probability of a loss? [Topic 2]

Repeat the same steps (steps 1-4 above) for three share prices in the Australia Securities Exchange: BHP Billiton (BHP) from the mining sector, Commonwealth Bank of Australia (CBA) from the bank sector, and Telstra Corporation (TLS) from the telecom sector.

Construct a 95% confidence interval of the return to Bitcoin, and interpret the interval. How does your interval change if the level of confidence is 90% and 95% respectively, and explain why. [Topics 6-7]

Construct a 95% confidence interval of the return to BHP, CBA, and TLS respectively. [Topics 6-7]

An investment advisor claimed that the return to Bitcoin is 4% while the returns to other three shares are no different from zero. Do you agree? Justify your reasoning using a two-tailed hypothesis test approach at the significance level of 5%. [Topic 8]

Data source: Yahoo Finance
Data frenquecy: weekly closing price
Data measurement unit: AU$
Short Name	Full Name
BIT	Bitcoin
BHP	BHP Billiton
CBA	Commonwealth Bank of Australia
TLS	Telstra Corporation

Date	BIT	CBA	BHP	TLS
15/6/14	690	80.9812	33.5932	5.17
22/6/14	665	81.031	34.0324	5.26
29/6/14	661.2	81.5084	35.107	5.34
6/7/14	692.14	80.7923	35.1163	5.33
13/7/14	614.12	80.832	35.8732	5.43
20/7/14	600.84	81.8366	36.4432	5.45
27/7/14	665.93	82.3737	35.8919	5.44
3/8/14	687.76	79.6982	35.2658	5.39
10/8/14	584.97	80.7624	36.4899	5.58
17/8/14	543	80.1756	35.3219	5.71
24/8/14	510.53	80.8818	34.266	5.56
31/8/14	537.92	80.8619	33.3128	5.64
7/9/14	562.43	79.7977	33.4437	5.54
14/9/14	424.44	77.3907	33.154	5.41
21/9/14	460.15	74.8544	31.9205	5.31
28/9/14	353.36	76.237	31.2571	5.39
5/10/14	481.64	74.3969	30.1918	5.29
12/10/14	485.55	76.1275	31.2103	5.38
19/10/14	449.98	78.3455	31.528	5.5
27/10/14	419.9	80.0463	31.7336	5.63
3/11/14	440.98	82.314	32.2289	5.77
10/11/14	463.96	81.3294	31.0702	5.8
17/11/14	448.09	79.6584	29.6218	5.65
24/11/14	471.5	80.285	28.8929	5.69
1/12/14	476	81.2001	28.4257	5.67
8/12/14	419.55	81.2995	26.5942	5.7
15/12/14	434.97	83.2589	27.0801	5.89
22/12/14	443.46	84.4624	27.0708	5.91
29/12/14	362.8	85.278	27.6034	5.97
5/1/15	350.09	85.5763	27.2483	6.07
12/1/15	290.02	83.1197	25.2766	6.22
19/1/15	480.51	85.7653	27.4539	6.34
26/1/15	289.48	88.8486	27.3418	6.5
2/2/15	309.59	92.479	29.4816	6.59
9/2/15	323.9	92.648	30.061	6.59
16/2/15	323.5	89.7239	30.1825	6.61
23/2/15	354.85	91.4247	31.444	6.37
2/3/15	351.34	90.5991	30.5002	6.28
9/3/15	405.86	90.8279	27.809	6.2
16/3/15	349.82	95.8009	28.6593	6.37
23/3/15	380	93.8316	28.7341	6.38
29/3/15	320.56	93.8913	28.2388	6.32
5/4/15	379.94	93.6227	28.1641	6.28
12/4/15	365	91.5838	28.0052	6.14
19/4/15	300	91.6037	29.9489	6.32
26/4/15	324.68	88.4408	30.3694	6.24
3/5/15	295.91	82.1947	29.248	6.17
10/5/15	345.03	84.2933	30.36	6.2
17/5/15	327.36	82.6621	29.25	6.2
24/5/15	369.69	84.6315	29.59	6.22
31/5/15	328.8	79.8573	27.9	6.01
7/6/15	320.5	80.9812	27.9	6.03
14/6/15	312.87	84.0148	28.41	6.13
21/6/15	325.62	86.1831	27.5	6.2
28/6/15	362.18	86.193	26.59	6.13
5/7/15	443.58	85.3277	26.65	6.21
12/7/15	412.15	87.5059	27.1	6.42
19/7/15	401.96	85.3476	25.27	6.36
26/7/15	415	87.0882	26.45	6.49
2/8/15	362.04	80.8619	25.93	6.29
9/8/15	329.08	81.6775	25.32	6.08
16/8/15	357.53	75.59	24.1	6.07
23/8/15	320.4	76.36	25.49	5.82
30/8/15	349.46	72.15	24.69	5.61
6/9/15	330.8	75.13	23.71	5.55
13/9/15	323.27	75.83	24.46	5.65
20/9/15	346.48	71.44	22.93	5.67
27/9/15	350.66	73.39	22.6	5.62
4/10/15	339.59	75.53	25.6	5.64
11/10/15	373.53	76.55	25	5.44
18/10/15	400.01	77.35	24.59	5.58
26/10/15	477.69	76.73	23.02	5.4
2/11/15	551.39	76.59	22.7	5.31
9/11/15	471.79	75.76	20.23	5.14
16/11/15	476.89	79.83	20.5	5.41
23/11/15	518.39	80.12	18.77	5.4
30/11/15	540.58	80.22	17.93	5.41
7/12/15	605.46	78.95	17.2	5.2
14/12/15	616.24	81.57	16.87	5.48
21/12/15	581.21	83.32	18.34	5.46
28/12/15	582.38	85.53	17.86	5.61
4/1/16	642.2	79.42	16.35	5.3
11/1/16	554.28	78.88	15.07	5.33
18/1/16	573.92	76.56	15.26	5.54
25/1/16	532.58	78.67	15.35	5.63
1/2/16	529.39	76.6	16.2	5.65
8/2/16	567.05	73.33	15.09	5.57
15/2/16	609.61	73.43	16.61	5.28
22/2/16	606.68	70.72	15.59	5.27
29/2/16	548.07	75.74	17.67	5.13
7/3/16	543.69	76.37	17.61	5.16
14/3/16	584.58	78.16	18.1	5.22
21/3/16	589.97	74.82	17	5.25
27/3/16	585.82	72.99	16.97	5.26
3/4/16	555.66	70.76	16.18	5.16
10/4/16	574.93	75	19.28	5.24
17/4/16	616.19	75.04	20.36	5.4
24/4/16	588.28	73.89	20.68	5.36
1/5/16	655.87	74.35	18.46	5.6
8/5/16	642.67	77.39	18.2	5.68
15/5/16	612.75	78.12	18.85	5.66
22/5/16	701.27	78.9	19.37	5.67
29/5/16	788.69	75.75	18.53	5.59
5/6/16	903.09	75.49	18.8	5.46
12/6/16	1053.05	72.03	18.08	5.31
19/6/16	905.65	72.57	17.54	5.35
26/6/16	897.08	73.83	19.09	5.58
3/7/16	871.54	72.41	19.05	5.59
10/7/16	895.01	75.94	20.37	5.75
17/7/16	893.52	77.14	19.3	5.8
24/7/16	823.18	77.35	19.52	5.77
31/7/16	787.93	76.15	20.03	5.66
7/8/16	750.5	76.01	20.68	5.45
14/8/16	760	73.45	21.29	5.48
21/8/16	770	73.26	20.88	5.3
28/8/16	815.6	70.91	19.85	5.12
4/9/16	814	70.87	20.78	5.06
11/9/16	834.99	72.24	20.09	5.1
18/9/16	786.2	73.4	21.53	5.19
25/9/16	819.42	72.4	22.38	5.18
2/10/16	815.57	74.38	23.3	5.01
9/10/16	854	74.58	22.54	5.08
16/10/16	861.02	74.9	23.04	5.04
23/10/16	925	72.75	22.98	4.95
31/10/16	925.83	70.99	22.27	4.9
7/11/16	931.9	75.78	24.94	4.72
14/11/16	1000.52	76.86	24.1	4.93
21/11/16	1002.97	78.17	26.5	5.03
28/11/16	1024.27	78.6	25.02	4.95
5/12/16	1075.2	80.67	25.98	4.99
12/12/16	1106.2	81.06	25	4.91
19/12/16	1235.94	82.5	24.63	5.04
26/12/16	1381.4	82.41	25.06	5.1
2/1/17	1244.41	84.13	25.5	5.26
9/1/17	1095.16	83.86	26.33	5.22
16/1/17	1223.2	81.58	26.35	5.14
23/1/17	1238.34	82.98	27.52	5.11
30/1/17	1347.74	81.68	26.2	5.08
6/2/17	1341.48	82.9	25.88	5.16
13/2/17	1375.95	85.39	26.64	4.84
20/2/17	1553.46	83.02	25.06	4.81
27/2/17	1690.27	83.2	25.34	4.59
6/3/17	1649.1	84.5	23.67	4.64
13/3/17	1362.27	84.77	24.84	4.76
20/3/17	1277.61	83.38	24.26	4.59
26/3/17	1472.88	85.91	24.04	4.66
2/4/17	1612.83	84.77	24.59	4.56
9/4/17	1588.75	86.25	24.31	4.16
16/4/17	1683.46	85.64	24.04	4.23
23/4/17	1781.71	87.4	23.72	4.22
30/4/17	2196.67	84.4	22.62	4.4
7/5/17	2595.07	81.67	23.75	4.36
14/5/17	2860.85	80.23	24.28	4.43
21/5/17	3094.79	80.14	24.01	4.48
28/5/17	3493.27	80.38	24.07	4.49
4/6/17	3889.46	79.19	23.54	4.37
11/6/17	3588.86	81.86	22.99	4.38
18/6/17	3503.31	81.25	22.41	4.35
25/6/17	3342.76	82.81	23.28	4.3
2/7/17	3415.51	82.13	24.59	4.32
9/7/17	2510	83.12	25.13	4.3
16/7/17	3541.5	83.97	24.49	4.1
23/7/17	3529.74	83.76	25.33	4.11
30/7/17	4060.53	80.72	25.72	4.07
6/8/17	5318.14	80.5	25.55	4.15
13/8/17	5298.76	79.09	25.39	3.9
20/8/17	5620	77.72	26.68	3.92
27/8/17	6018.4	75.48	27.42	3.67
3/9/17	5319.46	73.24	27.29	3.7
10/9/17	4593.05	76.28	26.26	3.65
17/9/17	4625.38	76.62	25.95	3.58
24/9/17	5565.36	75.25	25.78	3.49
1/10/17	5887.35	76.3	26.61	3.44
8/10/17	7226.76	76.66	26.36	3.52
15/10/17	7713.93	78.97	26.68	3.52
22/10/17	8018.65	78.24	26.59	3.55
30/10/17	9692.39	77.79	27.69	3.5
6/11/17	7924.89	80.85	28.07	3.46
13/11/17	10693.55	80.92	27.12	3.45
20/11/17	12297.99	80.57	27.97	3.48
27/11/17	15024.19	79.17	27.58	3.42
4/12/17	21184.87	79.62	27.17	3.69
11/12/17	25986.55	79.94	27.71	3.69
18/12/17	18939.79	80.39	29.1	3.66
25/12/17	19050.74	80.34	29.57	3.63
1/1/18	22862.21	81.16	30.58	3.73
8/1/18	19041.51	80.88	31.53	3.74
15/1/18	15148.37	79.83	30.69	3.57
22/1/18	14445.12	78.65	30.85	3.56
29/1/18	10225.82	80.79	30.81	3.67
5/2/18	10382.72	76.25	29.13	3.49
12/2/18	13338.45	74.02	31.52	3.43
19/2/18	12300.72	75.46	30.68	3.48
26/2/18	14763.94	75.73	29.63	3.27
5/3/18	12143.73	76.87	28.32	3.44
12/3/18	10646.88	75.34	29.16	3.35
19/3/18	11039.19	72.81	28.77	3.22
25/3/18	8835.98	72.31	28.21	3.14
1/4/18	9130.39	73.49	28.64	3.1
8/4/18	10654.32	73.16	29.73	3.1
15/4/18	11357.21	72.06	30.86	3.08
22/4/18	12432.76	71.54	31.11	3.15
29/4/18	12682.62	72.76	31.49	3.24
6/5/18	11560.03	70.53	33.16	3.2
13/5/18	11318.46	70.5	34.08	2.85
20/5/18	9752.02	69.87	33.07	2.87
27/5/18	10233.1	68.7	33.08	2.78
3/6/18	8956.31	69.37	34.07	2.77
10/6/18	8717.19	68.98	33.56	2.94
17/6/18	9008.23	69.88	32.36	2.77

Answer 1

1.)

We can best represent the return with the help of line graph.

The graph is displayed below at broad level:

The price of butcoin remains almost constant till 2016 December but after that it is showing increasing trend till November 2017 From there it has started decreasing and from start of 2018 year it has decreased drastically from its peak closing value.

2.)

The weekely returns are given in below table:

Return	Week
-3.62%	1
-0.57%	2
4.68%	3
-11.27%	4
-2.16%	5
10.83%	6
3.28%	7
-14.95%	8
-7.17%	9
-5.98%	10
5.37%	11
4.56%	12
-24.53%	13
8.41%	14
-23.21%	15
36.30%	16
0.81%	17
-7.33%	18
-6.68%	19
5.02%	20
5.21%	21
-3.42%	22
5.22%	23
0.95%	24
-11.86%	25
3.68%	26
1.95%	27
-18.19%	28
-3.50%	29
-17.16%	30
65.68%	31
-39.76%	32
6.95%	33
4.62%	34
-0.12%	35
9.69%	36
-0.99%	37
15.52%	38
-13.81%	39
8.63%	40
-15.64%	41
18.52%	42
-3.93%	43
-17.81%	44
8.23%	45
-8.86%	46
16.60%	47
-5.12%	48
12.93%	49
-11.06%	50
-2.52%	51
-2.38%	52
4.08%	53
11.23%	54
22.48%	55
-7.09%	56
-2.47%	57
3.24%	58
-12.76%	59
-9.10%	60
8.65%	61
-10.39%	62
9.07%	63
-5.34%	64
-2.28%	65
7.18%	66
1.21%	67
-3.16%	68
9.99%	69
7.09%	70
19.42%	71
15.43%	72
-14.44%	73
1.08%	74
8.70%	75
4.28%	76
12.00%	77
1.78%	78
-5.68%	79
0.20%	80
10.27%	81
-13.69%	82
3.54%	83
-7.20%	84
-0.60%	85
7.11%	86
7.51%	87
-0.48%	88
-9.66%	89
-0.80%	90
7.52%	91
0.92%	92
-0.70%	93
-5.15%	94
3.47%	95
7.18%	96
-4.53%	97
11.49%	98
-2.01%	99
-4.66%	100
14.45%	101
12.47%	102
14.51%	103
16.61%	104
-14.00%	105
-0.95%	106
-2.85%	107
2.69%	108
-0.17%	109
-7.87%	110
-4.28%	111
-4.75%	112
1.27%	113
1.32%	114
5.92%	115
-0.20%	116
2.58%	117
-5.84%	118
4.23%	119
-0.47%	120
4.71%	121
0.82%	122
7.43%	123
0.09%	124
0.66%	125
7.36%	126
0.24%	127
2.12%	128
4.97%	129
2.88%	130
11.73%	131
11.77%	132
-9.92%	133
-11.99%	134
11.69%	135
1.24%	136
8.83%	137
-0.46%	138
2.57%	139
12.90%	140
8.81%	141
-2.44%	142
-17.39%	143
-6.21%	144
15.28%	145
9.50%	146
-1.49%	147
5.96%	148
5.84%	149
23.29%	150
18.14%	151
10.24%	152
8.18%	153
12.88%	154
11.34%	155
-7.73%	156
-2.38%	157
-4.58%	158
2.18%	159
-26.51%	160
41.10%	161
-0.33%	162
15.04%	163
30.97%	164
-0.36%	165
6.06%	166
7.09%	167
-11.61%	168
-13.66%	169
0.70%	170
20.32%	171
5.79%	172
22.75%	173
6.74%	174
3.95%	175
20.87%	176
-18.24%	177
34.94%	178
15.00%	179
22.17%	180
41.01%	181
22.67%	182
-27.12%	183
0.59%	184
20.01%	185
-16.71%	186
-20.45%	187
-4.64%	188
-29.21%	189
1.53%	190
28.47%	191
-7.78%	192
20.03%	193
-17.75%	194
-12.33%	195
3.68%	196
-19.96%	197
3.33%	198
16.69%	199
6.60%	200
9.47%	201
2.01%	202
-8.85%	203
-2.09%	204
-13.84%	205
4.93%	206
-12.48%	207
-2.67%	208
3.34%	209

Freuency table is shown below:

Frequency Table
Class	Count
-40--28.01	2
-28--16.01	13
-16--4.01	43
-4-7.99	95
8-19.99	40
20-31.99	11
32-43.99	4
44-55.99	0
56-67.99	1

Histogram is shown below:

The histogram looks normal from shape but there is one value which is abnormal

The return of 65.68% is abnormal and is an outlier

3.)

Descriptive Statistics:

Mean: 0.02

Median: 0.015

Spread:

Standard deviation: 0.1

Range	1.054374
Minimum	-0.39756
Maximum	0.656817

Shape:

Kurtosis	3.122755
Skewness	0.613819

4.)

Empirical Probability of loss means ratio of total number of negative weekely returns to total number of returns

EP_L = 89/209 = 0.425