You put half of your money in a stock portfolio that has an expected return of...

You put half of your money in a stock portfolio that has an expected return of 14% and a standard deviation of 23%. You put the rest of your money in a risky bond portfolio that has an expected return of 6% and a standard deviation of 11.3%. The stock and bond portfolios have a correlation of 0.42. What is the standard deviation of the resulting portfolio?

Solutions

Expert Solution

	Stock	Bond
Expected return	14.00%	6.00%
SD	23.00%	11.30%

Coorelation co-efficient	0.42

weights are
Stock	50.00%
Bond	50.00%

	Expected return	Weight	Weight * Expected return
Stock	14.00%	50.00%	7.00%
Bond	6.00%	50.00%	3.00%
		Total	10.00%

So expected return is 10%


Calculation of standard deviation

The first step is to calculate the covariance:

COVAB = SDA × SDB × rAB, where rAB is the correlation coefficient between securities A and B.

Now, calculate the standard deviation for the portfolio:

[(SDA2 × WA2) + (SDB2 × WB2) + 2 (WA)(WB)(COVAB)]½


Let's calcualte the co-variance	=23% * 11.3% * 0.42
	0.010916

Now lets calculate the SD
SD portfolio=	((23%^2 * 50%^2)+(11.3%^250%^2)+(250%50%0.010916))^(0.5)
SD portfolio=	14.79%

jeff jeffy answered 1 year ago

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