Calculating Expected Return, Variance, and Standard Deviation for Stock YSJ Inc.

Q1: You are presented with the following data for stock YSJ Inc.:

Probability of occurrence(s) Return(s)
0.15 – 22%
0.25 + 4%
0.25 + 17%
0.35 + 26%

Calculate: the expected return, variance and standard deviation; also, explain your  results.

Q2: Assume that you combine stock YSJ Inc. (from Q1) with stock YFK Inc., whose E(r) and  are 14% and 19%, respectively; if the correlation between each stock = + 0.38, what is the portfolio’s standard deviation and E(r) (*50% of the funds are allocated to each stock)?

Q3: While doing research, you identify a stock opportunity for company YGR Inc., whose E(r) and  are the same as YFK Inc., but it has a covariance of – 0.01572 with YSJ Inc.; should you replace stock YFK Inc. (from Q2) with YGR Inc. (assume a 50% distribution to each stock, and show all your work)?

Q4: Your colleague re-computes the statistics for YGR Inc., and the covariance of YSJ Inc., YGR Inc. = -0.02218; how does this impact the portfolio’s standard deviation, and would your answer from Q3 change?

Q5: Compute the Sharpe Ratios (reward-to-variability) for the portfolios in Q #’s 2 & 4 (i.e., YSJ Inc. + YFK Inc., and YSJ Inc. + YGR Inc.)- assume 90-day Treasury bills are yielding 3%, and that 30-year long-term Government of Canada bonds = 5.5%.