Calculate covariance of returns and correlation coefficient

Reference no: EM132492695

Assessment: Statistical Group Report-Risk, Return & Equity Analysis

Question 1: Using the information given in Exhibit 1,calculate the historical returns for each company and the market index. With the use of the excel functions, calculate the average monthly return and standard deviation of returns for each company and the market index.

Month	Market index (points)	Land Ltd ($)	Sea Ltd ($)	Market In	Land Ltd	Sea Ltd
1	5600	10	16.12	0.02142857	-0.04	0.04652605
2	5720	9.6	16.87	0.01573427	-0.0625	0.05927682
3	5810	9	17.87	0.02237522	-0.03333333	-0.04196978
4	5940	8.7	17.12	-0.01262626	0.045977011	0.0146028
5	5865	9.1	17.37	-0.01653879	0.054945055	0.04317789
6	5768	9.6	18.12	0.04282247	-0.03125	0.04856512
7	6015	9.3	19	0.01995012	-0.04301075	-0.07894737
8	6135	8.9	17.5	-0.01059495	0.08988764	0.03542857
9	6070	9.7	18.12	0.0214168	0.051546392	0.04139073
10	6200	10.2	18.87	0.0233871	-0.05392157	0.02013778
11	6345	9.65	19.25	-0.0323089	0.082901554	-0.09090909
12	6140	10.45	17.5	0.01710098	-0.03827751	0.03542857
13	6245	10.05	18.12	0.03122498	-0.04975124	0.04856512
14	6440	9.55	19	0.01863354	-0.05235602	0.01315789
15	6560	9.05	19.25	-0.02591463	0.077348066	0.01298701
16	6390	9.75	19.5	-0.02816901	0.082051282	0.02564103
17	6210	10.55	20	0.02657005	-0.04265403	0.0525
18	6375	10.1	21.05	0.01803922	-0.03960396	0.04513064
19	6490	9.7	22	0.01694915	-0.0257732	0.02272727
20	6600	9.45	22.5	-0.01666667	0.052910053	-0.02666667
21	6490	9.95	21.9	-0.01617874	0.050251256	-0.07305936
22	6385	10.45	20.3	0.01801096	0.052631579	0.06896552
23	6500	11	21.7	0.02384615	0.031818182	0.05529954
24	6655	11.35	22.9	0.01728024	0.035242291	0.05240175
25	6770	11.75	24.1
		Total	Returns	0.19577186	0.195078746	0.43035786
		Average	Returns	0.00815716	0.008128281	0.01793158
		Variance of returns		0.00045941	0.002926346	0.00211138
		Standard Deviation		0.0214339	0.054095713	0.04594971

Question 2: Using the Question 1 above, and assuming that investors can only invest in one of the two alternative shares in Exhibit 1, use the average return and standard deviation to determine which share would be the most appropriate for a risk-averse investor. Provide numerical justification for your selection based on the coefficient of variation.

	Market Ind	Land Ltd	Sea Ltd
Total returns	0.328449	0.56448	0.835477
Average returns	0.01564	0.02688	0.039785
Variance of returns	0.000459	0.002926	0.002111
Standard deviation	0.04583	0.063324	0.098126

Question 3: Calculate the covariance of returns and correlation coefficient between all shares. Provide an explanation of your results and the implications for diversification.

C Co-variance of returns		Co-variance of returns		Co-variance of returns
Market Index versus Land		Sea Ltd versus Land Ltd		Sea Ltd versus Market Index
Market Index	Land Ltd	Sea Ltd	Land Ltd	Sea Ltd	Market Index
0.021428571	-0.04	0.04652605	-0.04	0.046526	0.021429
0.015734266	-0.0625	0.05927682	-0.0625	0.059277	0.015734
0.022375215	-0.0333333	-0.04196978	-0.03333333	-0.04197	0.022375
-0.01262626	0.04597701	0.0146028	0.045977011	0.014603	-0.01263
-0.01653879	0.05494505	0.04317789	0.054945055	0.043178	-0.01654
0.042822469	-0.03125	0.04856512	-0.03125	0.048565	0.042822
0.019950125	-0.0430108	-0.07894737	-0.04301075	-0.07895	0.01995
-0.01059495	0.08988764	0.03542857	0.08988764	0.035429	-0.01059
0.021416804	0.05154639	0.04139073	0.051546392	0.041391	0.021417
0.023387097	-0.0539216	0.02013778	-0.05392157	0.020138	0.023387
-0.0323089	0.08290155	-0.09090909	0.082901554	-0.09091	-0.03231
0.017100977	-0.0382775	0.03542857	-0.03827751	0.035429	0.017101
0.03122498	-0.0497512	0.04856512	-0.04975124	0.048565	0.031225
0.01863354	-0.052356	0.01315789	-0.05235602	0.013158	0.018634
-0.02591463	0.07734807	0.01298701	0.077348066	0.012987	-0.02591
-0.02816901	0.08205128	0.02564103	0.082051282	0.025641	-0.02817
0.026570048	-0.042654	0.0525	-0.04265403	0.0525	0.02657
0.018039216	-0.039604	0.04513064	-0.03960396	0.045131	0.018039
0.016949153	-0.0257732	0.02272727	-0.0257732	0.022727	0.016949
-0.01666667	0.05291005	-0.02666667	0.052910053	-0.02667	-0.01667
-0.01617874	0.05025126	-0.07305936	0.050251256	-0.07306	-0.01618
0.018010963	0.05263158	0.06896552	0.052631579	0.068966	0.018011
0.023846154	0.03181818	0.05529954	0.031818182	0.0553	0.023846
0.01728024	0.03524229	0.05240175	0.035242291	0.052402	0.01728

-0.00090497		-0.00042865		0.000435


Correlation Coefficient		Correlation Coefficient		Correlation Coefficient
Market Ind V Land Ltd		Sea Ltd V Land Ltd		Sea Ltd V Market Ind
Market In	Land Ltd	Sea Ltd	Land Ltd	Sea Ltd	Market In
0.021429	-0.04	0.046526	-0.04	0.046526	0.021429
0.015734	-0.0625	0.059277	-0.0625	0.059277	0.015734
0.022375	-0.03333	-0.04197	-0.03333	-0.04197	0.022375
-0.01263	0.045977	0.014603	0.045977	0.014603	-0.01263
-0.01654	0.054945	0.043178	0.054945	0.043178	-0.01654
0.042822	-0.03125	0.048565	-0.03125	0.048565	0.042822
0.01995	-0.04301	-0.07895	-0.04301	-0.07895	0.01995
-0.01059	0.089888	0.035429	0.089888	0.035429	-0.01059
0.021417	0.051546	0.041391	0.051546	0.041391	0.021417
0.023387	-0.05392	0.020138	-0.05392	0.020138	0.023387
-0.03231	0.082902	-0.09091	0.082902	-0.09091	-0.03231
0.017101	-0.03828	0.035429	-0.03828	0.035429	0.017101
0.031225	-0.04975	0.048565	-0.04975	0.048565	0.031225
0.018634	-0.05236	0.013158	-0.05236	0.013158	0.018634
-0.02591	0.077348	0.012987	0.077348	0.012987	-0.02591
-0.02817	0.082051	0.025641	0.082051	0.025641	-0.02817
0.02657	-0.04265	0.0525	-0.04265	0.0525	0.02657
0.018039	-0.0396	0.045131	-0.0396	0.045131	0.018039
0.016949	-0.02577	0.022727	-0.02577	0.022727	0.016949
-0.01667	0.05291	-0.02667	0.05291	-0.02667	-0.01667
-0.01618	0.050251	-0.07306	0.050251	-0.07306	-0.01618
0.018011	0.052632	0.068966	0.052632	0.068966	0.018011
0.023846	0.031818	0.0553	0.031818	0.0553	0.023846
0.01728	0.035242	0.052402	0.035242	0.052402	0.01728

-0.78049		-0.17245		0.441509

Question 4: Determine the expected return and standard deviation of two-asset portfolios comprised of Sea Ltd and Land Ltd. Assume equal weightings of each share within the portfolio. Interpret your results and comment and illustrate the impact on risk when combining shares into a portfolio.

Total Returns	0.19577186	0.195078746	0.43035786
Average Returns	0.00815716	0.008128281	0.01793158
Standard Deviation	0.0214339	0.054095713	0.04594971
Covariance of return	-0.00086726	-0.00041079	0.00041672
Correlation coefficients	-0.78049196	-0.17244605	0.44150908

Question 5: Determine the systematic risk (Beta) for both shares. Interpret your answers. The use of excel functions should be used to calculate Beta.

Question 6: Assuming a risk-free rate of 3% and market risk premium of 12%. Calculate the required return for both shares. If the growth in dividends is expected to continuously average 2%, what value would you place on each share (use the dividend growth model). What concerns do you have in regards to your valuations?

Reference no: EM132492695

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