the expected return on BIG TIME TOYS is 9 percent and its standard deviation is
ID: 2710536 • Letter: T
Question
the expected return on BIG TIME TOYS is 9 percent and its standard deviation is 20 percent. the expected return on Chemical Industries is 8 percent and its standard deviation is 25 percent. a) suppose the correlation efficient for the two stocks' return is 2. what are the expected return and standard deviation of a portfolio with 30 percent invested in BIG TIME TOYS and the rest in Chemical industries? b) if the correlation efficient is 7. recalulate the portfolio expected return and standard deviation, assuming the portfolio weights are unchanged. c) explain the difference between your answers to (a) and (b).
Explanation / Answer
Er1 = 9% SD1 =20%
ER2= 8% SD2=25%
Portfolio return = W1 x Er1 + W2 x Er2
= 0.30 x 9% + 0.70 x 8%
= 8.30%
Variance = (W1xSD)^2 + (W2xSD2)^2 +2W1xW2xSD1xSD2xcorrel
= (0.30x20)^2 +(0.70 x25)^2 + 2x0.30x0.70x20x25x0.20
=36 +306.25 +42
= 384.25
Standard Deviation = Variance ^0.50
= 384.25^0.50
= 19.60%
Portfolio return = W1 x Er1 + W2 x Er2
= 0.30 x 9% + 0.70 x 8%
= 8.30%
Variance = (W1xSD)^2 + (W2xSD2)^2 +2W1xW2xSD1xSD2xcorrel
= (0.30x20)^2 +(0.70 x25)^2 + 2x0.30x0.70x20x25x0.70
=36 +306.25 +147
= 489.25
Standard Deviation = Variance ^0.50
= 489.25^0.50
= 22.12%
c) Because of high correlation, part b has higher risk.
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