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Midas is considering two stocks. The expected return on LAN is 15% with a standard deviation...

Midas is considering two stocks. The expected return on LAN is 15% with a standard deviation of 32%. The expected return on GBT is 9% with a standard deviation of 23%. The correlation between the returns on LAN and GBT is 0.15. The betas of LAN and GBT are 1.2 and 0.8 respectively.
a. Assume that Midas would like to have a portfolio with a beta of 0.9. Recommend how he can invest in two stocks to achieve his objective. Determine the expected return and standard deviation on this portfolio.

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Expert Solution

Beta for LAN = 1.2

Beta of GBT = 0.8

Beta for the Portfolio = 0.9

There can be various weight combination through which we can come to a portfolio beta of 0.9 from the 2 stocks however we will use a Linear Equation to calculate the same.

Assume Weight given to LAN is w

Then weight for GBT will be (1-w), since the total for weight has to be equal to 1.

Using a Linear Equation we get :

Beta of Portfolio = Weight of LAN * Beta of LAN + Weight of GBT * Beta of GBT

0.9 = w * 1.2 + (1-w) * 0.8

0.9 = 1.2w + 0.8 - 0.8w

0.9-0.8 = 0.4w

0.1 = 0.4w

w = 0.1 / 0.4 = 0.25 or 25%

Weight of LAN = 25%

Weight of GBT = (1-w) = 75%

So He will have to invest 25% in LAN and 75% in GBT to have a portfolio Beta of 0.9.

I would like to again repeat myself saying that this is one of the 100's of combination that we can create.

Expected Return of the Portfolio = Weight of LAN * Return of LAN + Weight of GBT * Return of GBT

Expected Return = 25% * 15% + 75% * 9%

Expected Return = 3.75% + 6.75% = 10.5%

Standard Deviation of the Portfolio = (Weight ^ 2 * Variance of LAN + Weight ^ 2 * Variance of GBT + 2* Weight of LAN *Weight of GBT * Correlation between LAN and GBT * Standard Deviation of LAN * Standard Deviation of GBT)^0.5

SD of Portfolio = ((0.25^2* .32^2) + (0.75^2 * 0.23^2) + 2*0.25*0.75*0.15*.32*.23)^0.5

SD of Portfolio = (0.0625*.1024 + 0.5625*.0529 + 0.00414)^0.5

SD of Portfolio = (0.0064 + 0.03 + 0.00414)^0.5

SD of Portfolio = (0.04054)^0.5 = 0.2013 = 20.13%

SD of Portfolio = 20.13%

jeff jeffy answered 6 months ago
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