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Svetllana [295]
3 years ago
9

Stock A ‘s returns have a standard deviation of 0.5, and stock B’s returns have standard deviation of 0.6.The correlation coeffi

cient between A and B equals 0.5. What is the variance of a portfolio composed of 70 percent Stock A and 30 percent Stock B?
Mathematics
1 answer:
galben [10]3 years ago
4 0

Answer:

The variance of the profile is 0.2179.

Step-by-step explanation:

We are given the following in the question:

\sigma_A = 0.5\\\sigma_B = 0.6\\\rho_{A,B} = 0.5\\w_A = 70\% = 0.7\\w_B = 30\% = 0.3

Variance of portfolio is given by:

w_A^2\sigma_A^2 +w_B^2\sigma_B^2 + 2w_Aw_BCov_{A,B}

Cov_{A,B} = \rho_{A,B} \times \sigma_A \times \sigma_B \\=0.5\times 0.5 \times 0.6\\=0.15

Putting values, we get,

w_A^2\sigma_A^2 +w_B^2\sigma_B^2 + 2w_Aw_BCov_{A,B}\\=(0.7)^2(0.5)^2 + (.3)^2(0.6)^2 + 2(0.7)(0.3)(0.15)\\=0.2179

Thus, the variance of the profile is 0.2179.

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3 years ago
In a chemical plant, 24 holding tanks are used for final product storage. Four tanks are selected at random and without replacem
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a) P(A) = 0,4607     or   P(A) = 46,07 %

b) P(B) = 0,7120   or 71,2 %

c) P(C) = 0,2055  or P(C) = 20,55 %

Step-by-step explanation:

We will use two concepts in solving this problem.

1.- The probability of an event (A) is for definition:

P(A) = Number of favorable events/ Total number of events FE/TE

2.- If A and B are complementary events ( the sum of them is equal to 1) then:

P(A) = 1 - P(B)

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C ( 24,4) = 24! / 4! ( 24 - 4 )!    ⇒  C ( 24,4) = 24! / 4! * 20!

C ( 24,4) = 24*23*22*21*20! / 4! * 20!  

C ( 24,4) = 24*23*22*21/4*3*2

C ( 24,4) = 24*23*22*21/4*3*2    ⇒  C ( 24,4) =  10626

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FE = 6* C ( 18, 3)  = 6 * 18! / 3!*15!  =  18*17*16*15!/15!

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P(A) = 4896/10626

P(A) = 0,4607     or   P(A) = 46,07 %

b) P(B) will be the probability of at least 1 tank contains h-v

P(B) = 1 - P ( no one tank with h-v)

Again Total number of events is 10626

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FE = C (18,4) = 18! / 14!*4! = 18*17*16*15*14!/14!*4!

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reasoning the same way but now having 4 with t-i (impurities) number of favorable events is:

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P(C) = 2184/ 10626

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