Question

Returns and Variances - Consider the following information:

State of Economy	Probability of State of Economy	Rate of Return If State Occurs
		Stock A	Stock B	Stock C
Boom	.75	.06	.15	.25
Bust	.25	.11	−.04	−.08

1. What is the expected return on an equally weighted portfolio of these three stocks?

2. What is the variance of a portfolio invested 20 percent each in A and B and 60 percent in C?

Answer 1

Weight 0.333333 0.333333 0.333333 Total probability Rate of Return If State Occurs Return weight State of EXPECTED PORTFOLIO с ТОTAL Probability А C A в Economy RETURN 0.05 0.083333 0.153333 Вoom 0.75 0.06 0.15 0.25 0.02 0.115 -0.08 0.036667 -0.04 -0.026670.00333 Bust 0.25 0.11 -0.01333 0.000833333 0.114166667 11.42% 0.114167 Expected return

Weight 0.2 0.2 0.6 Total probability Total-Expected return Rate of Return If State Occurs Return weight d2*probability State of EXPECTED PORTFOLIO DEVIATIO Probability А В C A В C ТОTAL VARIANCE Economy RETURN DEVIATION NA2 0.0565 0.003192 0.012 0.144 Boom 0.75 0.06 0.15 0.25 0.03 0.002394188 0.15 0.192 Bust 0.25 0.022 0.11 -0.04 -0.08 0.007182563 -0.008 -0.048 -0.034 -0.0085 -0.1695 0.02873 0.1355 0.00957675 13.55% Expected return 0.1355 variance 0.00958