Monthly Prices		Monthly Returns
	AAPL	AMZN	MSFT			AAP	AMZN	MSFT
Date	adj. prc	adj. prc	adj. prc		Date	ret	ret	ret
11/1/16	25.91	750.57	55.75		11/1/16
12/1/16	27.29	749.87	57.88		12/1/16
1/1/17	28.60	823.48	60.22		1/1/17
2/1/17	32.28	845.04	59.60		2/1/17
3/1/17	34.00	886.54	61.72		3/1/17
4/1/17	34.00	924.99	64.16		4/1/17
5/1/17	36.16	994.62	65.45		5/1/17
6/1/17	34.23	968.00	64.97		6/1/17
7/1/17	35.35	987.78	68.52		7/1/17
8/1/17	38.98	980.60	70.47		8/1/17
9/1/17	36.77	961.35	70.58		9/1/17
10/1/17	40.33	1105.28	78.81		10/1/17
11/1/17	41.00	1176.75	79.75		11/1/17
12/1/17	40.52	1169.47	81.46		12/1/17
1/1/18	40.09	1450.89	90.48		1/1/18
2/1/18	42.65	1512.45	89.30		2/1/18
3/1/18	40.34	1447.34	87.32		3/1/18
4/1/18	39.73	1566.13	89.48		4/1/18
5/1/18	44.93	1629.62	94.57		5/1/18
6/1/18	44.68	1699.80	94.75		6/1/18
7/1/18	45.93	1777.44	101.93		7/1/18
8/1/18	54.94	2012.71	107.94		8/1/18
9/1/18	54.68	2003.00	110.32		9/1/18
10/1/18	53.01	1598.01	103.03		10/1/18
11/1/18	43.25	1690.17	106.96		11/1/18
12/1/18	38.34	1501.97	98.40		12/1/18
1/1/19	40.45	1718.73	101.17		1/1/19
2/1/19	42.08	1639.83	108.53		2/1/19
3/1/19	46.37	1780.75	114.74		3/1/19
4/1/19	48.98	1926.52	127.06		4/1/19
5/1/19	42.73	1775.07	120.33		5/1/19
6/1/19	48.50	1893.63	130.81		6/1/19
7/1/19	52.20	1866.78	133.07		7/1/19
8/1/19	51.15	1776.29	134.62		8/1/19
9/1/19	55.09	1735.91	136.22		9/1/19
10/1/19	61.19	1776.66	140.47		10/1/19
11/1/19	65.73	1800.80	148.32		11/1/19
12/1/19	72.44	1847.84	155.03		12/1/19
1/1/20	76.36	2008.72	167.35		1/1/20
2/1/20	67.44	1883.75	159.27		2/1/20
3/1/20	62.88	1949.72	155.47		3/1/20
4/1/20	72.65	2474.00	176.66		4/1/20
5/1/20	78.62	2442.37	180.64		5/1/20
6/1/20	90.45	2758.82	201.17		6/1/20
7/1/20	105.39	3164.68	202.66		7/1/20
8/1/20	127.98	3450.96	222.94		8/1/20
9/1/20	115.07	3148.73	208.42		9/1/20
10/1/20	108.16	3036.15	200.63		10/1/20
11/1/20	118.29	3168.04	212.12		11/1/20
12/1/20	132.07	3256.93	220.97		12/1/20
1/1/21	131.34	3206.20	230.45		1/1/21
2/1/21	120.69	3092.93	230.87		2/1/21
3/1/21	121.76	3094.08	234.78		3/1/21
4/1/21	131.04	3467.42	251.12		4/1/21
5/1/21	124.21	3223.07	248.63		5/1/21
6/1/21	136.76	3440.16	270.38		6/1/21
7/1/21	145.64	3327.59	284.37		7/1/21
8/1/21	151.60	3470.79	301.30		8/1/21
9/1/21	141.50	3285.04	281.92		9/1/21
10/1/21	148.64	3320.37	308.13		10/1/21

	AAPL	AMZN	MSFT
Mean
Variance
Standard Deviation
Covariance between AAPL and AMZN:
Covariance between AMZN and MSFT:
Covariance between MSFT and AAPL:
Three-Asset Portfolio	A	B	C
Weight in AAPL	0.2500	0.333	0.1
Weight in AMZN	0.3333	0.333	0.3
Weight in MSFT	0.4167	0.333	0.6
Total Weights	1	1	1
Portfolio mean	0	0
Portfolio Variance	0
Portfolio Standard Deviation
Sharpe Ratio
Risk-Free Rate	0.13%	0.13%	0.13%

Portfolio Mathematics

1) Convert the stock prices to returns

2) To the left are the returns for three stocks. Calculate the mean, variance, standard deviation for each return series in the appropriates spaces.

3) Find the covariance between stocks.

4) Find the mean, variance, and standard deviation for the return of three portfolios A,B, and C.

5) Given the risk free rate of 0.13%, figure out the Sharpe ratio and find the best portfolio.