Question No : 31 I have a portfolio of two stocks. The weights are equal. The...

Question No : 31 I have a portfolio of two stocks. The weights are equal. The one volatility is 30% while the other is 40%. The minimum and maximum possible values of the volatility of my portfolio are:

A. 30% and 40% B. 5% and 35% C. 10% and 40% D. 10% and 70%

Expert Solution

SD [Volatility] of a two asset portfolio [asset 'a' and asset 'b'] is given by the formula, sdp = [sda^2wa^2+sdb^2wb^2+sdasdbwawbCor(a,b)]^0.5
Where,
sda and sdb are the standard deviations, wa and wb are the weights of the two assets in the portfolio and Cor(a,b) the correlation of the returns of the two assets.
Given two assets, their volatilities and their weights, the maximum SD of the portfolio is gi ven when the correlation is +1 and the minimum SD of the portfolio is given when the correlation is -1.
The SD with correlation of -1 [minimum portfolio SD and with correlation of +1 [maximum portfolio SD] are caculated below.
SD of the portfolio with correlation of -1 = (0.5^230^2+0.5^240^2+20.50.53040*-1)^0.5 =	5.00
Sd of the portfolio with correlation of +1 = (0.5^230^2+0.5^240^2+20.50.53040*1)^0.5 =	35.00
Answer: Option [B] 5% and 35%

jeff jeffy answered 5 months ago

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