Reference no: EM132345658

1. Based on historical data, you have estimated the following probability distributions for the returns on two individual securities (SMALL and BIG) and the value-weighted market portfolio:

State               probability                 Small             Big                 Market

Expansion                  0.30                25%                8%                  12%

Normal                       0.50                15%                6%                  10%

Recession                   0.20                0%                  2%                  3%

a) Calculate the expected return and standard deviation of return for Small, Big and the market portfolio

b) Calculate the covariance between Small and Big; between Small and the market, and between Big and the market.

c) Calculate the expected return and standard deviation of return for a portfolio that consists of ½ Big and ½ Small.

d) Calculate the expected return and standard deviation of return for a portfolio that consists of 3/4 Big and 1/4 Small.

e) Compare the five investment opportunities: the two portfolios in c) and d), the individual securities Small and Big, and the market portfolio. Without performing any calculations, can you recommend buying (or not buying) any of these investments?