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prisoha [69]
3 years ago
7

You are creating a portfolio of two stocks. The first one has a standard deviation of 20% and the second one has a standard devi

ation of 37%. The correlation coefficient between the returns of the two is 0.1. You will invest 43% of the portfolio in the first stock and the rest in the second stock. What will be the standard deviation of this portfolio's returns? Answer in percent, rounded to two decimal places (e.g., 4.32%=4.32).
Business
1 answer:
Drupady [299]3 years ago
8 0

Answer:

23.56

Explanation:

Standard deviation of  the first stock (σ1) = 20%

Standard deviation of  the second stock (σ2) = 37%

The correlation coefficient between the returns (ρ) = 0.1.

Proportion invested in the first stock (W1) = 43%

Proportion invested in the second stock (W2) = 57%

The standard deviation of a two-stock portfolio's returns is given by

\sigma_{portfolio} = \sqrt{w_1^2\sigma_1^2+w_2^2\sigma_2^2+2w_1w_2\rho\sigma_1\sigma_2} \\\sigma_{portfolio} = \sqrt{0.43^2*0.2^2+0.57^2*0.37^2+2*0.43*0.57*0.1*0.2*0.37}\\\sigma_{portfolio} =0.2356=23.56\%

The standard deviation of this portfolio's returns IS 23.56%

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Answer:

SD = 0.0740270 or 7.40270 percent rounded off to 7.403 percent

Explanation:

To calculate the standard deviation of the investment, we must first calculate the expected or mean return of the investment. The expected or mean return can be calculated as follows,

r = pA * rA  +  pB * rB  +  ...  +  pN * rN

Where,

  • pA, pB, ... represents the probability of state occurrence
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r = 0.2 * 0.16  +  0.4 * 0.12  +  0.2 * 0.05  +  0.2 * -0.05

r = 0.08 or 8%

The formula to calculate the standard deviation of a stock/investment is as follows,

SD = √pA * (rA - r)²  +  pB * (rB - r)²  +  ...  +  pN * (rN - r)²

SD = √0.2 * (0.16 - 0.08)²  +  0.4 * (0.12 - 0.08)²  +  0.2 * (0.05 - 0.08)²  +  0.2 * (-0.05 - 0.08)²

SD = 0.0740270 or 7.40270 percent rounded off to 7.403 percent

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3 years ago
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Answer:

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Number of hours the plant would have to work to produce 1000 parts = 1000/120 = 8.33 hours

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