Question

Make sure the answers are correct, well written, clear, and easy to understand. DO NOT USE EXCEL. Use formulas, math and written explanation to solve the problem. Again, DO NOT USE EXCEL.

There are three securities in the market. The following chart shows their possible payoffs: State Probability petur y Return on Return on Return on Outcome me Security 1 Security 2 Security 3 .16 191 191 041 .141 .091 .091 .091 .141 .041 .041 .191 NM .34 141

Answer 1

		Return on securities			Expected return = probability *return			0 = Pi (Ri - R			Covariance
	probability of outcome	1	2	3	1	2	3	1	2	3	12	13	23
1	0.16	0.191	0.191	0.041	0.03056	0.03056	0.00656	0.0009	0.0009	0.0009	0.0009	-0.0009	-0.0009
2	0.34	0.141	0.091	0.091	0.04794	0.03094	0.03094	0.000213	0.000213	0.0002125	-0.00021	-0.00021	0.000213
3	0.34	0.091	0.141	0.141	0.03094	0.04794	0.04794	0.000213	0.000213	0.0002125	-0.00021	-0.00021	0.000213
4	0.16	0.041	0.041	0.191	0.00656	0.00656	0.03056	0.0009	0.0009	0.0009	0.0009	-0.0009	-0.0009
	total				0.116	0.116	0.116
	standard deviation							0.002225	0.002225	0.002225
	covariance										0.001375	-0.00223	-0.00138

Put values in formulaes and get the above table.

$\sigma _{p}=\sqrt{W_{1}^{2}*\sigma _{1}^{2}+W_{2}^{2}*\sigma _{2}^{2}+2W_{1}W_{2}Cov_{12}}$

$Cov=\sum \left [ P_{i}*(R_{1}-\bar{R_{1}})*(R_{2}-\bar{R_{2}}) \right ]$