Question

The past four years of stock returns for BHP and Rio Tinto are provided in the following table. The correlation between BHP and Rio Tinto is 0.4. Year BHP Rio Tinto 2015 4.50% 10.20% 2016 6.90% -5.70% 2017 8.70% 19.60% 2018 3.40% -7.70%

A. What is the average annual return for BHP and Rio Tinto?

B. What is the standard deviation of return for BHP and Rio Tinto?

C. Which stock would you invest? Explain.

D. Given the expected return for BHP and Rio Tinto calculated in part (a), what would be your portfolio return and standard deviation if you invested 50% of your capital in BHP and the remaining 50% in Rio Tinto?

E. What if you increase your capital invested in BHP from 50% to 70%? What is your portfolio return and standard deviation? Is this more or less favourable? Explain.

Answer 1

1. Average Annual Return = BHP = 5.875% and RIO = 4.10%

2. Standard Deviation BHP = 2.06% and RIO = 11.32 %

3. It would be better to invest in BHP because it has higher return and lesser standard deviation (risk).

4. Portfolio Return = 6%, and portfolio standard deviation = 4.19%

Return and Standard Deviation of a Security with given Probability

Expected Return = ∑(Ret * Probability)

Standard Deviation = pi*(Ret-Ret expected)2

Portfolio Return and Portfolio Standard Deviation with 2 Securities

Portfolio Return=Wa*Ra+Wb*Rb

Portfolio Standard Deviation =

where W_a = Weight of stock a ; W_b = Weight of Stock B; σ_a = Standard deviation of stock A; σ_b = Standard deviation of stock B; r_ab = Correlation Coefficient between a & b