The spreadsheet Group Report Data.xlsx contains monthly returns on ten Australian industry indices from January 2016 to July 2021. The industry abbreviations are in the table below. Investor utility is represented by: U = E(R) - A2 . There are two investors with different risk aversion coefficients (A). Angela has a risk aversion coefficient of 5 and Boris has a risk aversion coefficient of 2. Investors are able to short-sell each industry throughout the report. Investors are unable to borrow or lend at the risk-free rate except for part 5 of the report. The expected returns per month to be used throughout the report are in the following table.

Industry Abbreviation Expected Return

Consumer Discretionary COND 0.96%

Consumer Staples CONS 0.83%

Energy ENGY 1.09%

Health Care HC 0.86%

Industrials INDU 0.92%

Information Technology IT 1.00%

Materials MATL 0.87%

Telecom TELE 0.90%

Utilities UTIL 0.80%

Financials FIN 0.90%

Real Estate RE 0.96%

Calculate the expected utility for both investors if they invested solely in each industry. Which industries does each investor prefer? What are the reasons for their preference?

Consider the MATL and HC industries. What is the optimal portfolio for both Boris and Angela that contains these two industries? Discuss what happens to each investor's utility and portfolio risk for this portfolio compared holding these two industries individually. Will you always reach this conclusion or is specific to these two portfolios?

Date	COND	CONS	ENGY	HC	INDU	IT	MATL	TELE	UTIL	FIN	RE
1/29/16	-0.0265	-0.0018	-0.0649	-0.0258	-0.0269	-0.0491	-0.0912	0.0070	0.0073	-0.0737	0.0022
2/29/16	-0.0157	-0.0484	0.0028	0.0064	0.0584	-0.0546	0.0912	-0.0547	0.0123	-0.0532	0.0276
3/31/16	0.0513	0.0300	0.0616	0.0035	0.0227	0.0563	0.0605	0.0471	0.0130	0.0589	0.0278
4/29/16	-0.0171	0.0105	0.0747	0.0334	0.0151	0.0258	0.1430	0.0046	-0.0032	0.0169	0.0207
5/31/16	0.0564	-0.0089	-0.0161	0.0939	0.0256	0.0705	-0.0301	0.0496	0.0354	0.0470	0.0278
6/30/16	-0.0018	-0.0402	-0.0081	-0.0248	-0.0099	-0.0760	0.0059	-0.0128	0.0563	-0.0418	0.0291
7/29/16	0.0890	0.0855	0.0023	0.0700	0.0717	0.0389	0.0779	0.0423	0.0704	0.0589	0.0545
8/31/16	-0.0046	0.0186	0.0236	-0.0317	-0.0427	0.0458	0.0001	-0.0650	-0.0568	-0.0165	-0.0230
9/30/16	0.0028	0.0162	0.0009	-0.0033	-0.0025	0.0146	0.0568	-0.0395	-0.0324	-0.0065	-0.0399
10/31/16	-0.0613	-0.0383	-0.0198	-0.0805	-0.0411	-0.0659	0.0116	-0.0433	-0.0303	0.0074	-0.0737
11/30/16	-0.0033	0.0056	0.0329	-0.0163	0.0135	0.0010	0.0225	-0.0041	0.0366	0.0600	0.0069
12/30/16	0.0421	0.0173	0.0608	0.0086	0.0243	0.0403	0.0383	0.0052	0.0868	0.0551	0.0671
1/31/17	-0.0430	-0.0104	0.0072	0.0456	-0.0441	-0.0418	0.0477	-0.0168	0.0108	-0.0205	-0.0460
2/28/17	0.0151	0.0602	-0.0213	0.0390	0.0341	0.0185	-0.0319	-0.0314	0.0307	0.0413	0.0433
3/31/17	0.0473	0.0547	0.0433	0.0560	0.0435	0.0363	0.0022	0.0028	0.0628	0.0389	0.0095
4/28/17	0.0070	-0.0253	-0.0055	0.0340	0.0409	0.0352	-0.0025	-0.0948	0.0308	0.0191	0.0249
5/31/17	-0.0032	-0.0044	0.0152	-0.0238	0.0469	0.0022	-0.0024	0.0338	0.0100	-0.0771	-0.0075
6/30/17	0.0087	-0.0243	-0.0684	0.0608	-0.0025	0.0188	0.0063	-0.0166	-0.0269	0.0167	-0.0413
7/31/17	-0.0063	0.0097	0.0062	-0.0750	-0.0274	-0.0049	0.0348	-0.0421	-0.0528	0.0125	-0.0017
8/31/17	-0.0154	0.0517	0.0518	0.0025	0.0457	0.0099	0.0452	-0.0720	0.0322	-0.0212	0.0137
9/29/17	-0.0006	-0.0187	0.0112	0.0227	-0.0111	0.0060	-0.0138	-0.0446	-0.0364	0.0111	0.0119
10/31/17	0.0544	0.0534	0.0641	0.0548	0.0418	0.0844	0.0444	0.0235	0.0496	0.0326	0.0132
11/30/17	0.0087	0.0324	0.0433	0.0296	0.0221	0.0450	0.0201	-0.0158	0.0298	0.0000	0.0474
12/29/17	0.0368	0.0167	0.0652	-0.0048	-0.0095	0.0294	0.0611	0.0546	-0.0448	0.0042	0.0038
1/31/18	-0.0020	0.0021	-0.0028	0.0311	-0.0201	0.0249	0.0046	0.0077	-0.0435	-0.0074	-0.0323
2/28/18	-0.0119	0.0210	-0.0375	0.0696	-0.0037	0.0166	0.0037	-0.0620	-0.0159	0.0064	-0.0187
3/30/18	-0.0226	-0.0135	-0.0249	-0.0332	-0.0114	-0.0219	-0.0424	-0.0620	-0.0075	-0.0585	-0.0013
4/30/18	0.0295	0.0574	0.1072	0.0719	0.0308	0.0276	0.0744	0.0194	0.0216	0.0011	0.0410
5/31/18	0.0527	-0.0000	0.0041	0.0545	0.0124	0.0203	0.0197	-0.1005	0.0103	-0.0006	0.0301
6/29/18	0.0209	0.0594	0.0774	0.0250	0.0064	0.0590	0.0165	-0.0549	0.0591	0.0399	0.0256
7/31/18	0.0175	-0.0088	0.0118	0.0223	0.0316	-0.0112	-0.0025	0.0759	-0.0143	0.0204	0.0099
8/31/18	0.0359	0.0264	-0.0122	0.1042	0.0326	0.1221	-0.0486	0.1302	0.0061	0.0005	0.0261
9/28/18	-0.0383	-0.0267	0.0427	-0.0730	-0.0215	-0.0065	0.0406	0.0297	-0.0310	-0.0222	-0.0186
10/31/18	-0.0834	-0.0490	-0.1028	-0.0725	-0.0529	-0.1137	-0.0518	-0.0398	-0.0403	-0.0602	-0.0380
11/30/18	-0.0453	-0.0292	-0.1068	-0.0397	-0.0060	0.0099	-0.0475	-0.0412	-0.0176	0.0141	-0.0259
12/31/18	-0.0194	0.0120	-0.0220	0.0272	-0.0029	-0.0408	0.0513	-0.0326	0.0277	-0.0313	0.0107
1/31/19	0.0428	0.0273	0.1146	0.0391	0.0338	0.0882	0.0697	0.0809	0.0592	-0.0025	0.0585
2/28/19	0.0669	-0.0139	0.0784	0.0133	0.0644	0.0748	0.0640	0.0338	0.0403	0.0907	0.0219
3/29/19	0.0139	0.0368	-0.0415	0.0131	0.0198	0.0255	0.0340	0.0551	0.0132	-0.0262	0.0541
4/30/19	0.0546	0.0733	0.0155	0.0314	0.0315	0.0735	-0.0205	0.0178	-0.0049	0.0440	-0.0167
5/31/19	0.0204	-0.0416	-0.0380	0.0354	0.0025	-0.0312	0.0311	0.0711	-0.0062	0.0262	0.0258
6/28/19	-0.0151	0.0292	0.0217	0.0442	0.0555	0.0105	0.0617	0.0302	0.0308	0.0342	0.0324
7/31/19	0.0475	0.0959	0.0149	0.0596	0.0335	0.0511	0.0117	0.0204	0.0185	0.0177	0.0319
8/30/19	0.0064	0.0010	-0.0562	0.0343	-0.0250	0.0067	-0.0734	-0.0460	-0.0224	-0.0258	0.0240
9/30/19	0.0333	0.0174	0.0446	-0.0215	-0.0013	0.0011	0.0295	-0.0425	0.0201	0.0423	-0.0229
10/31/19	0.0055	-0.0224	0.0031	0.0727	0.0289	-0.0319	-0.0176	-0.0081	0.0123	-0.0288	0.0177
11/29/19	0.0422	0.0810	0.0729	0.0881	0.0397	0.1055	0.0444	0.0945	-0.0053	-0.0201	0.0233
12/31/19	-0.0221	-0.0775	-0.0138	-0.0266	-0.0305	-0.0389	0.0182	-0.0761	0.0078	-0.0156	-0.0448
1/31/20	0.0427	0.0781	0.0057	0.1201	0.0186	0.1024	0.0163	0.0872	0.0098	0.0474	0.0600
2/28/20	-0.0874	-0.0740	-0.1742	-0.0395	-0.0841	-0.1631	-0.1169	-0.0744	-0.0396	-0.0492	-0.0449
3/31/20	-0.2642	-0.0355	-0.3764	-0.0564	-0.2301	-0.1758	-0.1325	-0.1062	-0.0674	-0.2770	-0.3558
4/30/20	0.1644	0.0259	0.2521	0.0487	0.1282	0.2184	0.1437	0.0095	0.0323	0.0289	0.1412
5/29/20	0.0690	-0.0049	0.0474	-0.0510	0.0381	0.1431	0.0839	0.0642	0.0305	0.0535	0.0706
6/30/20	0.0506	0.0475	-0.0212	0.0339	-0.0157	0.0370	0.0217	-0.0256	0.0085	0.0434	-0.0145
7/31/20	0.0288	0.0323	-0.0626	-0.0384	-0.0380	0.0484	0.0591	0.0530	-0.0023	-0.0102	-0.0010
8/31/20	0.0971	-0.0031	0.0342	0.0402	0.0462	0.1515	0.0116	-0.0853	-0.0480	0.0135	0.0761
9/30/20	-0.0242	-0.0658	-0.1074	0.0082	-0.0032	-0.0639	-0.0286	-0.0359	-0.0332	-0.0613	-0.0134
10/30/20	0.0107	0.0456	-0.0097	0.0096	-0.0348	0.0858	-0.0105	-0.0344	-0.0149	0.0627	0.0029
11/30/20	0.0843	-0.0066	0.2824	0.0289	0.1198	0.0414	0.0766	0.1290	0.0147	0.1612	0.1323
12/31/20	0.0139	0.0221	-0.0069	-0.0469	-0.0218	0.0857	0.0877	-0.0280	-0.0538	-0.0050	0.0012
1/29/21	0.0478	0.0202	0.0096	-0.0170	-0.0307	0.0020	-0.0100	0.0448	-0.0009	0.0226	-0.0428
2/26/21	-0.0262	-0.0450	0.0250	-0.0282	-0.0184	-0.0802	0.0706	0.0150	-0.0802	0.0515	-0.0146
3/31/21	0.0668	0.0274	-0.0022	0.0243	0.0344	-0.0267	-0.0307	0.0587	0.0681	0.0429	0.0556
4/30/21	0.0344	-0.0237	-0.0468	0.0287	0.0415	0.0979	0.0748	0.0304	-0.0116	0.0320	0.0278
5/31/21	0.0316	0.0237	-0.0154	0.0347	-0.0112	-0.0910	0.0179	0.0206	-0.0662	0.0565	0.0147
6/30/21	0.0453	0.0543	0.0415	0.0214	0.0310	0.1236	0.0008	0.0563	0.0345	-0.0018	0.0481
7/31/21	-0.0055	0.0150	-0.0241	0.0111	0.0409	-0.0636	0.0706	-0.0148	0.0160	-0.0142	0.0085