Arbor Systems and Gencore stocks both have a volatility of 40%. Compute the vola

Question

Arbor Systems and Gencore stocks both have a volatility of 40%. Compute the volatility of a portfolio with 50% invested in each stock if the correlation between the stocks is (a) +1.0, (b) 0.50, (c) 0, (d) - 0.50, and (e) - 1.0. In which of the cases is the volatility lower than that of the original stocks? If the correlation is +1.0, the volatility of the portfolio is %. (Round to one decimal place.) If the correlation is 0.50, the volatility of the portfolio is %. (Round to one decimal place.) If the correlation is 0, the volatility of the portfolio is %. (Round to one decimal place.) If the correlation is - 0.50, the volatility of the portfolio is %. (Round to one decimal place.) If the correlation is - 1.0, the volatility of the portfolio is %. (Round to one decimal place.) In which of the cases is the volatility lower than that of the original stocks? (Select the best choice below.) In cases (d) and (e). In cases (b), (c), (d) and (e). In all of the cases. In none of the cases.

Explanation / Answer

To compute the volatility of the portfolio is nothing but the standard deviation of the portfolio

Hence we will compute the variance and square root of variance will be the volatility

1) If correlation is 1 ie perfectly co related then Variance = .5^2 *.4 + .5^2*.4 + 2*.5*.5*1 = .7 hence volatility = SQRt(.7)

= If correlation is 1 then volatility of portfolio = .837

= If correaltion is is .5 then = .1+ .1+.5*correlation = .45 = sqrt (.45 ) =.670

= If correaltion is is 0 then = .1+ .1+.5*correlation = .2 = sqrt (.2 ) =.448

= If correaltion is is -.5 then = .1+ .1+.5*correlation = -.05 = sqrt (-.05 ) =0

= If correaltion is is -1.0 then = .1+ .1+.5*correlation = -.3 = sqrt (-.3 ) =.0

Hence the cases in which the volatility is lower than the original stock is

when the corelation is negative hence in case of D and E

Option A) is the right answer

Thank you.

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