The CFO of Grupo Almeida asks his adviser at Casa de Bolsa INTEX to create a portfolio with shares of three companies, Grupo Max, Inditel and Industrias Pat.

The wealth adviser obtained sample estimates of the expected returns and risk (standard deviation) of the three stocks as well as the correlation between the returns of each pair of stocks, based on annual data information obtained from Bloomberg for the past five years. These estimates are shown in Tables 1 and 2.

Table 1. Expected Returns and Risk

Accin	Annual Expected Return (%)	Annual Standard Deviation (%)
Grupo Max	10.50%	10%
Inditel	12%	13%
Industrias Pat	20%	20%

Table 2. Correlation between the returns of stock i and stock j

Action i, Action j	Correlation
Grupo Max, Inditel	0.4
Grupo Max, Industrias Pat	0.1
Inditel, Industrias Pat	0.5

And it makes calculations of some possible portfolios to obtain assuming that short sales are allowed. The CFO of Grupo Almeida asks you to report the risk and weights of various minimum variance portfolios with a given expected return. A) Calculate the risk (annual standard deviation) of the minimum variance portfolio that has an expected annual return of 11%.

• 9.079%

• 9.237%

• 11.279%

• 13.653%

• 15.883%

b) Calculate the weight (proportion invested) in the Inditel share for this portfolio.

• 17.294%

• 24.393%

• 5.985%

• -4.005%

• -25.304%

On the other hand, Grupo Almeida's wealth advisor forms a portfolio with two bonds (government bond of an emerging country and AAAA corporate bond) in order to diversify the risk of the stock portfolio. The expected return and standard deviation (yearly) of the bond yields are shown in table 3. Table 3. Expected Returns and Risk

Bono i	Annual Expected Return (%)	Desviacin Estndar Anual Annual Standard Deviation (%)
Emerging Country Government	3%	2%
AAA Corporate	2%	1.50%

The correlation coefficient between these two bonds is equal to zero. C) If a portfolio of bonds is built with only these two types of bonds, calculate the expected annual return of the maximum return portfolio with risk of 1.6% (annual standard deviation) if no short sales are allowed.

• 2.842%

• 2.783%

• 2.897%

• 2.949%

• 3.014%

D) Calculate the weight (proportion invested) in AAA Corporate Bonds for this portfolio.

• 5.08%

• 10.33%

• 15.83%

• 21.67%

• 23.75%

D) If the annual risk-free rate is 1% and a portfolio is built with the two portfolios previously built (in questions A and C), that is, with the integrated portfolio of three stocks and the portfolio made up of two bonds, and assuming that the correlation between the stock portfolio and the bond portfolio is zero. Calculate the expected annual return of the optimal portfolio (tangent) if short sales are allowed.

• 3.967%

• 4.456%

• 4.632%

• 4.743%

• 4.874%

E) Calculate the slope of the Capital Allocation Line

• 1.4992

• 1.5019

• 1.5538

• 1.5876

• 1.6475

f) What is the weight (proportion invested) in the stock portfolio in the optimal portfolio?

• 10.32%

• 12.45%

• 14.73%

• 14.40%

• 19.82%