Question

Two assets' correlation is -0.2. The first has expected return of 9% and standard deviation of 16%, the second has expected return of 13% and standard deviation of 20%.

Calculate the minimum amount of risk (standard deviation) you'll need to take if investing in these two assets. (Provide your answer in percent rounded to two decimals omitting the % sign)

Answer 1

So actually your query asks for the minimum risk portfolio comprising 2 assets. The allocation to security a in a portfolio comprising securities a & b will be expressed as follows:

where V represents Variance while SD represents Standard Deviation.

If you're wondering what Variance is, It's actually just the Square of Standard Deviation. Now If we take the data we're given, and plug it in the values above, you'll get the following result:

	Expected Return	Standard Deviation	Variance (Squared of SD)	Correlation
A	0.09	0.16	0.0256	-0.2
B	0.13	0.2	0.04
		Weight of A:	59.18%

So naturally the weight of B will be 100%-59.18% = 40.82%.

At this point, the portfolio standard deviation will be as follows:

	Expected Return	Standard Deviation	Variance (Squared of SD)	Correlation
A	0.09	0.16	0.0256	-0.2
B	0.13	0.2	0.04
		Weight of A:	59.18%
		Weight of B:	40.82%
		Portfolio SD:	12.44%

There you go. The answer to that would be 12.44%

Hope that helps!