Question

You decide to invest in a portfolio consisting of 18 percent Stock X, 39 percent Stock Y, and the remainder in Stock Z. Based on the following information, what is the standard deviation of your portfolio?

State of Economy	Probability of State			Return if State Occurs
	of Economy
				Stock X			Stock Y			Stock Z
Normal		.74			9.30%			2.70%			11.70%
Boom		.26			16.60%			24.60%			16.10%

Multiple Choice

• 6.44%

• 7.51%

• 5.15%

• 1.99%

• 2.65%

Answer 1

Explanation and answer

Stock return for Normal state of economy, (Wx*Rx+Wy*Ry+Wz*Rz)

= 0.18 × 9.3% + 0.39 × 2.7% + 0.43 × 11.7%

= 7.758%

Stock return for Boom state of economy, (Wx*Rx+Wy*Ry+Wz*Rz)

= 0.18 × 16.6% + 0.39 × 24.6% + 0.43 × 16.1%

= 19.505%

Weighted average return, (Wn*Rn+Wb*Rb)

= 0.74 × 7.758% + 0.26 × 19.505%

= 10.812%

Standard deviation = Normal probability state of economy × (Stock return for Normal state of economy - Weighted average return)^number of years + Boom probability state of economy × (Stock return for Boom state of economy - Weighted average return)^number of years)^percentage

= (0.74 × (7.758 - 10.812)^2 + 0.26 × (19.505 - 10.812)^2)^1/2

= 5.15%

Answer is 3rd option