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Investment Theory problems 2011-2012, Ejercicios de Administración de Empresas

Universitat de València (UV)Administración de Empresas
Prof. Gustavo Cuello

Asignatura: teoria de la inver, Profesor: Cuello, Gustavo, Carrera: Administració i Direcció d'Empreses, Universidad: UV

Tipo: Ejercicios

2013/2014

Subido el 14/06/2014

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Investment Theory (35805). Course 2011-12
-----------------------------------------------------------------------------------------------------------------------------------------------------------------
1
CORPORATE FINANCE DEPARTMENT
FACULTAT D’ECONOMIA
UNIVERSITAT DE VALÈNCIA
_________________________________________________________________________________
EXERCISES (2)
INVESTMENT THEORY
35805
Gustavo Cuello Albornoz
COURSE 2011-2012
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Investment Theory (35805). Course 2011- -----------------------------------------------------------------------------------------------------------------------------------------------------------------

CORPORATE FINANCE DEPARTMENT

FACULTAT D’ECONOMIA

UNIVERSITAT DE VALÈNCIA

_________________________________________________________________________________

EXERCISES (2)

INVESTMENT THEORY

Gustavo Cuello Albornoz

COURSE 2011-

Investment Theory (35805). Course 2011- -----------------------------------------------------------------------------------------------------------------------------------------------------------------

RETURN AND RISK ON SECURITIES AND PORTFOLIOS

Exercise 1

Consider the following information:

State of Economy

Probability of State of Economy

Rate of return X

Rate of return Y I 60,00% 25,00% 15,00% II 40,00% 10,00% 11,00%

Calculate :

  1. Expected return and standard deviation for each stock. Calculate also covariance and correlation between both securities.
  2. Calculate expected return and standard deviation of a portfolio with 50% of each stock..
  3. Explain if it is posible to have a riskless portfolio with these two securities. Explain the weights of each security in this portfolio (if it exists) and the expected return of the portfolio.
  4. Calculate the composition (weight of each security) of a portfolio with a risk (measured by standard deviation) of 5,192918%. Calculate expected return of this portfolio.
  5. Calculate the composition (weight of each security) of a portfolio with an expected return of 13,96%. Calculate the risk (measured by standard deviation) of this portfolio.

Exercise 2

Consider the following information:

State of the Economy

Probability of State of Economy

Rate of Return of stock X

Rate of Return of stock Y I 60,00% 20,00% 5,00% II 40,00% 10,00% 8,00%

Calculate :

  1. Expected return and standard deviation for each stock. Calculate also covariance and correlation between both securities.
  2. Calculate expected return and standard deviation of a portfolio with 50% of each stock..
  3. Explain if it is posible to have a riskless portfolio with these two securities. Explain the weights of each security in this portfolio (if it exists) and the expected return of the portfolio.
  4. Calculate the composition (weight of each security) of a portfolio with a risk (measured by standard deviation) of 2,35151%. Calculate expected return of this portfolio.
  5. Calculate the composition (weight of each security) of a portfolio with an expected return of 7,18%. Calculate the risk (measured by standard deviation) of this portfolio.

Investment Theory (35805). Course 2011- -----------------------------------------------------------------------------------------------------------------------------------------------------------------

  1. Explain if it is posible to have a riskless portfolio with these two securities. Explain the weights of each security in this portfolio (if it exists) and the expected return of the portfolio.
  2. Calculate the composition (weight of each security) of a portfolio with a risk (measured by standard deviation) of 13,94274%. Calculate expected return of this portfolio.
  3. Calculate the composition (weight of each security) of a portfolio with an expected return of 11%. Calculate the risk (measured by standard deviation) of this portfolio.

Exercise 5

Consider the following information:

Expected Return

Risk (standard deviation) Stock X

Stock Y

Considering also :

  • case 1: correlation between stocks X and Y = -1.
  • case 2: correlation between stocks X and Y = -0,5.
  • case 3: correlation between stocks X and Y = 1.

If you, investor, expects a return of 12%: a) Calculate weights and risk of the portfolio in each case (1,2, 3) b) Which one of three cases is better considering diversification effect? c) In which of three cases standard deviation of the portfolio is the weighted average of standard deviations of each security?

If you, investor, assumes a risk (measured by standard deviation) of 4%:

a) Calculate weights and expected return of portfolios in each case (1, 2, 3)

Exercise 6

100 Stocks are traded in the Stock Exchange Market. These stocks have different combinations or Expected Return and Standard Deviation. The average variance of all the stocks, is 0,2556 and average covariance is 0,05112. Calculate :

  1. Total risk of the portfolio composed of 10 stocks (randomly chosen), with same weight each one, Calculate also systematic and unsystematic risk of that portfolio.

  2. Total risk of the portfolio composed of all 100 stocks, with same weight each. Calculate also systematic and unsystematic risk of this portfolio.