) Based on your results and the graph, which portfolios appear to be more attractive considering their risk-return profile? (Analyze the position of the portfolios on the graph and the corresponding Sharpe ratios). Do you see any benefits to diversification compared to portfolios of 100% invested in individual stocks or equally-weighted portfolio? For the tangency portfolio with shorting, which stock is shorted? Why? Based on your results, what allocation would you recommend? Explain your conclusion. That allocation will be the clients Target portfolio.

Amazon (AMZN)	Apple (AAPL)	Walmart (WMT)	Microsoft (MSFT)	At&T. (T)	Benchmark SP 500 ETF (SPY)
4	Monthly Expected Return	2.70%	2.49%	1.14%	2.32%	0.51%	1.23%
5	Monthly Standard Deviation	8.18%	8.00%	4.95%	5.76%	4.80%	4.01%
6	Annualized Expected Return	32.41%	29.92%	13.64%	27.85%	6.10%	14.78%
7	Annualized standard deviation	28.33%	27.72%	17.13%	19.96%	16.62%	13.89%
8	Sharpe Ratio	0.0210	0.0249	0.0114	0.0232	0.0051	0.0123
9
10
11
12	2. Distributional Statistics
13	Worst monthly return	-20.22%	-18.40%	-15.56%	-13.02%	-17.23%	-13.00%
14	Best monthly return	26.89%	21.44%	14.78%	19.63%	10.37%	13.36%
15	Skewness	0.29	-0.14	-0.10	0.19	-0.53	-0.32
16	Kurtosis	0.395	-0.308	0.757	0.622	1.226	1.740
17	Probabillity of negative return	37%	38%	41%	34%	46%	38%
18	5% Var	-10.75%	-10.67%	-7.00%	-7.16%	-7.38%	-5.36%
19	10% Var	-7.78%	-7.76%	-5.20%	-5.06%	-5.64%	-3.91%
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21
22
23	3. Correlation Matrix
24		Amazon (AMZN)	Apple (AAPL)	Walmart (WMT)	Microsoft (MSFT)	At&T. (T)	Benchmark SP 500 ETF (SPY)
25	Amazon (AMZN)	1.0000	0.4156	0.1347	0.4718	0.0637	0.5460
26	Apple (AAPL)	0.4156	1.0000	0.1999	0.4849	0.1895	0.5541
27	Walmart (WMT)	0.1347	0.1999	1.0000	0.1154	0.2106	0.2981
28	Microsoft (MSFT)	0.4718	0.4849	0.1154	1.0000	0.1810	0.5985
29	At&T. (T)	0.0637	0.1895	0.2106	0.1810	1.0000	0.4356
30	Benchmark SP 500 ETF (SPY)	0.5460	0.5541	0.2981	0.5985	0.4356	1.0000
31