Question

Investment A has an expected return of 10% with a standard deviation of 3.5%. Investment B has an expected return of 6% with a standard deviation of 1.2%. If you invest equally in both investments; a) What is the expected return and standard deviation of your portfolio assuming the rates of return are independent? b) If your initial total investment was $1000, what is the probability that your portfolio value is worth more than $1000? (hint: find the distribution of portfolio using the mean and variance of the rates you obtained in a)

          Investment A has an expected return of 10% with a standard
deviation of 3.5%. Investment B has an expected return of 6% with a
standard deviation of 1.2%. If you invest equally in both
investments; a) What is the expected return and standard deviation
of your portfolio assuming the rates of return are independent? b)
If your initial total investment was $1000, what is the probability
that your portfolio value is worth more than $1000? (hint: find the
distribution of portfolio using the mean and variance of the rates
you obtained in a)
        
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Elementary Statistics a Step by Step Approach
Elementary Statistics a Step by Step Approach
Allan G. Bluman 9th Edition
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Investment A has an expected return of 10% with a standard deviation of 3.5%. Investment B has an expected return of 6% with a standard deviation of 1.2%. If you invest equally in both investments; a) What is the expected return and standard deviation of your portfolio assuming the rates of return are independent? b) If your initial total investment was $1000, what is the probability that your portfolio value is worth more than $1000? (hint: find the distribution of portfolio using the mean and variance of the rates you obtained in a)
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Transcript

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00:01 Hello, let's have a look on the question.
00:02 So we have the following data.
00:04 For a and b, we have er and sd, that is standard deviation.
00:09 So this is 10%.
00:11 Standard deviation, 3 .5%, this is 6 % and 1 .2%.
00:18 Now the expected return of a portfolio is represented by erp is equal to wa, er of a plus wb, r of b so when we put the values we will get this value is equal to 0 .5 multiplied by 10 plus 0 .5 multiplied by 6 so this will be equal to 8 now standard deviation of the portfolio is given by standard deviation of portfolio is given by sigma p is equal to under root of w a square plus multiplied by sigma a square plus w b squared multiplied by sigma b square plus 2 w a w b multiplied by sigma of a and sigma of b so when we put the values here we will get sigma p is equal to under root of 5 .5 2 .25 which is equal to 2 .35 percent this is the standard deviation of portfolio now return on portfolio follows normal distribution.
01:41 Normal distribution with mean 8 % and standard deviation, 2 .35%...
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