Question

1. Use the Data for Two Stocks to determine the following:
   1. Create a one-way data table that determines the different means and standard deviations for portfolios consisting of combinations of Stock A and Stock B by varying the correlation coefficient value between Stock A and Stock B through the full range of possible correlation coefficient values. Use increments of 0.1 for the possible correlation coefficient values.
   2. Graph the means and the standard deviations of the portfolios from the one-way data table. Be sure to include a title for the graph and label the axes.
   3. Explain how the portfolio means are affected by changing the correlation coefficient values.
   4. Explain how the portfolio standard deviations are affected by changing the correlation coefficient values.

Data for Two Stocks

		A	B
Expected return		12.00%	18.00%
Variance of return		0.49	0.64
Standard deviation of return		70.00%	80.00%
Correlation		0.8
Proportion of A		0.4

Answer 1

Solution: The solution Has been provided in the following sheets.

First Five Sheet is the working of the correlation coefficient of both the Stocks along with some explanation,

Sheet 6 is the table for correlation , sheet 7 is the excel sheet for the relationship between standard deviation and mean with correlation coefficient.

Sheet 8 is the answer for the remaining questions.

folulin a to t h order to find out the possible combinations of Stoch A and stock B by varying dutelahian cofficinh ly inertnesh sine, correlation coefficient varies from therefore by merement of o.1, we can and have to find out the standard deviations of narious correlation coefficient. Correlation coefficients (incremento. 1) -0.9 0.4 - 0.5 - - 0.4 0.3 0.9

Ashanians of the portfolio 7 6 ²p 2 WC + Wp + WA WBC where, spa nariance of Portfolio was weight of A (i propanking 4 we weight of B (ic poopoction mgr AB t correlation of stock A and stod Now Ar narious conclation coefficient

I weocan apply the formula above correlation instanes for the A 0.9.11 Byou - As that proportion of wAt WB 7 0.4+ Wpal Now, applying the names of WA and WB along with the nonlance of a = 0.49 given and nariams of B = 0.64 ginen, in the above formula at nasions correlation Instances floo r 00 AL1-1) → 62 (0.4) x 0.49 + (0-6) x 0.64 +2x0. 1 0 6 x 0.7 x 0.87 sowing 7 6 p 2 0.16x0.49 + 0.36 x 0.64 0.2688 x 6-1) 0.0784+0.2304 -0.2688 - 0.04 1 Ep2loom

dimilarly, for the rest of the correlatim cofficient, we can put the names as provided and calculated entory with the respective correlation coefficient, we will At (r= -0.9) = 0.26g t Co-0.8) P0.31 (mer -0.70) 20:39 Cr -0.60 0.38 (o= -0.50) 0.42 fra -0.40 -0.45 (72- 0.30) 2 0:48 (man0.20) 0.51 Ir = -0. 10) = 0.53 nos (rzo), 0.57

AF (r = 0 (0) 0.58 (na 0-10 2 060 fra 0.80 20.62 (ne 0.402 Fron Crie 0-50) 2 067. Cra0-70) = 0.70 20.80220172 coreo.90 0.74

Return and Variability Table of Different correlation of Stock A and Stock Mean Correlation coefficient (AS computed from previous pages) Standard Deviation of Stock A and B -0.9 0.26 0,31 0.35 0.38 15.6% 0.45 15.6% 15.6 15.6% 15.6% 15.6% 15.6% 15.6% 15.6% 115.6% 0.65 0.67 0.69 0.70 0.72 0.74 0.76 Celul Note Mean = weight of Stock A. Return of Stock A+ Weight of Stock B. Return of Stock B Weight of Stock A = 0.4 Return of Stock A - 12 weight of Stock 5 0.6, as (1-Weight of Stock A that is (1-0.4) Return of Stock B - 15 Using the above date in the above formula for Mean, we get 0.412+0.5 18 = 4.8-10.B 15.595

A4 fe Standard Deviation н 0.60 Series 0.45 A Ser Standard Deviation Mean of A and B 0.20 15.60% 0.26 15.60% 0.31 15.60% 0.35 15.60% 0.38 15.60% 0.42 15.60% 15.60% 0.48 15.60% 0.51 15.60% 0.53 15.60% 0.56 15.60% 0.58 15.60% 0.60 15.60% 0.62 15.60% 0.65 15.60% 0.67 15.60% 0.69 15.60% 0.70 15.60% 0.72 15.6096 0.74 15.60% 0.76 15.60% Standard deviation of ABB Series Series 0.00 0.00 0.10 0.15 020 025 Return of Stock ABB Activate Windows Sheet1 Sheet2 Sheet3 Sheet 4

The correlation coefficient of stock A and Stock B and its charging rates will not effect the portfolio means, as the correlation coefficicur is not a factor for computing the portfolio of stock A and stoch B for mean. Hence, there will be no affect of the changing correlation with portfolio means, as weights are not dependent upon correlation. d) deviatim of As the standard portfolio is poulff. 6p = VWn2G42 + wg² 6 ² + 2 TAB WAWACASA therefore, change in standard he each time, when correlation as we can comprehend from deviatin will coefficient changes, the above formula. Therfore, it will be affected.