An investor is evaluating the possibility of buying shares in two companies. Com

Question

An investor is evaluating the possibility of buying shares in two companies. Company c and company d. the following probability distribution of returns covering different economic conditions is provided

excellent (probability) 0.2 Coy c returns 10% Coy D returns 19%

normal (probability) 0.5 13% 18

poor (probability) 0.3 14% 14

cal : weighted average for both 70% in company C and 30% invested in company D

:weighted risk  both 70% in company C and 30% invested in company D

:the portfolio return  both 70% in company C and 30% invested in company D

:the portfolio risk  both 70% in company C and 30% invested in company D

:using some your answers to the above, show how dersification has reduced risks

Explanation / Answer

Table construction for further calculations

Note : X - represents returns of stock - C and Y - represents returns of stock - D. Now we have Dx - representing (X - 12.7) and Dy - representing ( Y - 17). Finally Dx2 = Dx*Dx & Dy2 = Dy*Dy

P = Probability ( given in the question )

(1) Expected retun = sum of the products of probability and returns. P = probablity and X represent returns of Stock - C. Then SUM (X*P) = 12.7 is the expected return on stock - C. Similarly expected return on stock - D = 17

(2) Standard deviation = Square root over ( SUM of P * Dx2 ) =

Stock - C ............ Sqrt over 2.01 = 1.42

Stock - D ............. Sqrt over (4) = 2

The portfolio return  both 70% in company C and 30% invested in company D

= 70% ( 12.7) + 30% ( 17) = 13.99 %

The portfolio risk  both 70% in company C and 30% invested in company D

Standard deviation = Square Root [ (0.70)2 * (1.42)2 + (0.30)2 * (2)2 ] = SQRT [ 0.988 + 0.36 ] = 1.16 %

show how dersification has reduced risks

Individual stock standard deviations are 1.42% ( lowest) and 2% (highest). The standard deviation of the portfolio as calculated above is (1.16%) is lower then these individual standard deviations. Thus risk is reduced, hence said to be diversified with portfolio.

P X Y X*P Y*P Dx Dy Dx2 Dy2 P*Dx2 P*Dy2 Excellent 0.2 10 19 2 3.8 -2.7 2 7.29 4 1.458 0.8 Normal 0.5 13 18 6.5 9 0.3 1 0.09 1 0.045 0.5 Poor 0.3 14 14 4.2 4.2 1.3 -3 1.69 9 0.507 2.7 12.7 17 2.01 4

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