A contention expressed commonly by academics (and practitioners) is that international portfolio diversification pushes out the efficient frontier, or, in other words, enables an investor to maintain the same level of expected return with a lower level of risk (or, alternatively, the same level of risk with a higher expected return).Take historical monthly returns (the investable market index IMI) for the stock markets in the U.S., Europe, and Asia/Pacific and examine the risk vs. return possibilities that can be obtained by combining these markets into 20 different portfolios (where the portfolios differ in the weight allocated to each foreign market).

Your results should include both the expected return and standard deviation for each of the 20 portfolios, as well as a graph (in expected return vs. standard deviation space) that contains the 20 points (Note: this is time series data. For your probabilities, assume each observation has a 1/60th probability of occurring). (The variance of return for a 3 asset portfolio consisting of stocks a, b, and c can be calculated as: Wa2a2 + Wb2b2 + Wc2c2 + 2WaWba,b + 2WaWca,c + 2WbWcb,c) Do you think, over the 60 month time period, that international diversification was a worthwhile endeavor? Why, or why not?

	Date	USA IMI	AC EUROPE IMI	AC ASIA PACIFIC IMI
1	Oct 31, 2014	0.0261	-0.0262	0.0064
2	Nov 28, 2014	0.0217	0.0215	-0.0096
3	Dec 31, 2014	-0.0023	-0.0440	-0.0181
4	Jan 30, 2015	-0.0286	-0.0027	0.0184
5	Feb 27, 2015	0.0564	0.0646	0.0402
6	Mar 31, 2015	-0.0123	-0.0300	0.0017
7	Apr 30, 2015	0.0044	0.0425	0.0492
8	May 29, 2015	0.0122	-0.0128	-0.0095
9	Jun 30, 2015	-0.0186	-0.0304	-0.0330
10	Jul 31, 2015	0.0153	0.0272	-0.0316
11	Aug 31, 2015	-0.0624	-0.0700	-0.0827
12	Sep 30, 2015	-0.0310	-0.0461	-0.0431
13	Oct 30, 2015	0.0777	0.0680	0.0829
14	Nov 30, 2015	0.0035	-0.0189	-0.0172
15	Dec 31, 2015	-0.0222	-0.0238	0.0024
16	Jan 29, 2016	-0.0575	-0.0679	-0.0792
17	Feb 29, 2016	-0.0033	-0.0177	-0.0167
18	Mar 31, 2016	0.0687	0.0649	0.0810
19	Apr 29, 2016	0.0055	0.0177	0.0188
20	May 31, 2016	0.0161	-0.0130	-0.0152
21	Jun 30, 2016	0.0007	-0.0513	-0.0012
22	Jul 29, 2016	0.0386	0.0421	0.0567
23	Aug 31, 2016	0.0002	0.0020	0.0079
24	Sep 30, 2016	0.0002	0.0093	0.0149
25	Oct 31, 2016	-0.0231	-0.0341	-0.0060
26	Nov 30, 2016	0.0407	-0.0229	-0.0266
27	Dec 30, 2016	0.0175	0.0517	-0.0035
28	Jan 31, 2017	0.0188	0.0220	0.0477
29	Feb 28, 2017	0.0349	0.0090	0.0259
30	Mar 31, 2017	-0.0005	0.0351	0.0123
31	Apr 28, 2017	0.0095	0.0354	0.0128
32	May 31, 2017	0.0077	0.0385	0.0248
33	Jun 30, 2017	0.0072	-0.0128	0.0121
34	Jul 31, 2017	0.0183	0.0315	0.0354
35	Aug 31, 2017	-0.0004	0.0003	0.0051
36	Sep 29, 2017	0.0227	0.0314	0.0022
37	Oct 31, 2017	0.0208	0.0037	0.0419
38	Nov 30, 2017	0.0278	0.0009	0.0164
39	Dec 29, 2017	0.0087	0.0176	0.0204
40	Jan 31, 2018	0.0524	0.0556	0.0569
41	Feb 28, 2018	-0.0391	-0.0583	-0.0352
42	Mar 30, 2018	-0.0216	-0.0159	-0.0244
43	Apr 30, 2018	0.0031	0.0188	0.0072
44	May 31, 2018	0.0260	-0.0384	-0.0099
45	Jun 29, 2018	0.0055	-0.0095	-0.0370
46	Jul 31, 2018	0.0324	0.0300	0.0040
47	Aug 31, 2018	0.0324	-0.0297	-0.0085
48	Sep 28, 2018	0.0001	0.0013	-0.0032
49	Oct 31, 2018	-0.0745	-0.0796	-0.0972
50	Nov 30, 2018	0.0170	-0.0130	0.0290
51	Dec 31, 2018	-0.0944	-0.0475	-0.0468
52	Jan 31, 2019	0.0850	0.0699	0.0656
53	Feb 28, 2019	0.0331	0.0286	0.0136
54	Mar 29, 2019	0.0134	0.0008	0.0069
55	Apr 30, 2019	0.0383	0.0311	0.0144
56	May 31, 2019	-0.0666	-0.0611	-0.0596
57	Jun 28, 2019	0.0684	0.0634	0.0472
58	Jul 31, 2019	0.0140	-0.0202	-0.0091
59	Aug 30, 2019	-0.0223	-0.0295	-0.0332
60	Sep 30, 2019	0.0162	0.0261	0.0216

fill in this section (using data above)

	summary statistics
		US	Europe	Asia/Pac
	Expected (average) Return
	var
	std
		covariance table
		US	Europe	Asia/Pac
	US
	Europe
	China
		correlation table
		US	Europe	Asia/Pac
	US	1
	Europe		1
	China			1

Portfolio Weights Percent of wealth invested in: Portfolio Europe US Asia/Pac port ret port var port std 100 fill this in - it's your final output section AWNA 80 60 40 20 20 40 60 80 0 100 80 20 60 0 SOO 40 20 40 60 80 11 100 10 12 13 80 60 40 20 10 20 30 14 15 40 50 20 30 40 50 30 0 16 17 18 10 60 60 40 40 10 30 40 20 19 20 20 40 Portfolio Weights Percent of wealth invested in: Portfolio Europe US Asia/Pac port ret port var port std 100 fill this in - it's your final output section AWNA 80 60 40 20 20 40 60 80 0 100 80 20 60 0 SOO 40 20 40 60 80 11 100 10 12 13 80 60 40 20 10 20 30 14 15 40 50 20 30 40 50 30 0 16 17 18 10 60 60 40 40 10 30 40 20 19 20 20 40