Question

Currently the level of the S&P 500 Index is 1300, and the yield on the 90-day treasury bill is 2.75%. The following table lists the forecasts of an economist for the S&P 500 in the coming year.

Economic Environment	Probability of Occurance	Expected return of the S&P
Above Average	30%	22%
Average	45%	8%
Poor	25%	-35%

Calculate the expected return and standard deviation for the S&P 500. Construct the Security Market Line graph (from your findings) and show what the market risk premium is. Label your graph to receive full credit.

What would happen to the expected return on stocks if investors perceived an increase in the volatility of stocks? Why?

Answer 1

S&P 500 Index is 1300
yield on the 90-day treasury bill is 2.75%
	Pi	E®	Pi * E®
Economic Environment	Probability of Occurance	Expected return of the S&P	Weighted Expected Return	Expected Weighted Return	Expected Return in points	Difference from Mean	Sq. Difference from Mean
Above Average	30%	22%	6.600%	1300 * 22% * 30%	85.8	80	6,323
Average	45%	8%	3.600%	1300 * 8% * 45%	46.8	41	1,642
Poor	25%	-35%	-8.7500%	1300 * -35% * 25%	-113.75	-120	14,408
Expected Return of the portfolio		Σ Pi * E®	1.450%	Mean	6		22,373
				Standard Deviation = Sq. Rt. (Sum of Squared Differences of Mean/ N - 1) where n is the number of population.
				S.d. = (22373 / (3-1))^(1/2)
				S.d. =	106

Security Market Line Graph
Data for Chart
Economic Environment	Probability of Occurance / risk	Expected return of the S&P	Weighted Expected Return
Above Average	30%	22%	6.600%
Average	45%	8%	3.600%
Poor	25%	-35%	-8.7500%

For an increased volatility of stocks it would adversely affect the Security Market Line and the investors can expect to generate better returns.