Question

Your investment advisor believes that recent stock returns should be given more consideration when calculating future returns and risk than older returns. The historical returns for Lately Lighthouse, Inc. are given in the table below, along with the weights that your advisor believes are appropriate. Use the corresponding weights in all calculations.

Year	Lately Stock				Weight
2012		12.50	%			5	%
2013		13.91	%			15	%
2014		7.75	%			20	%
2015		11.32	%			25	%
2016		6.85	%			35	%

a. What is the expected return for Lately Lighthouse, Inc.? (Enter your answer as a percent rounded to two decimal places.)

b. What is the standard deviation of returns for Lately Lighthouse, Inc.? (Enter your answer as a percent rounded to two decimal places.)

Answer 1

Expected return = sum of (probability of state * return of state)

= 0.05 * 12.5% + 0.15 * 13.91% + 0.2 * 7.75% + 0.25 * 11.32% + 0.35 * 6.85%

= 9.489%

= 9.49%

E(X^2) =  sum of (probability of state * return of state^2)

= 0.05 * 12.5%^2 + 0.15 * 13.91%^2 + 0.2 * 7.75%^2 + 0.25 * 11.32%^2 + 0.35 * 6.85%^2

= 0.009730669

variance = E(X^2) - (E(X))^2

= 0.009730669 - 0.0949^2

= 0.000724659

Standard deviation = sqrt(variance)

= sqrt(0.000724659)

= 2.69%