Portfolio management

  1. Your client wants to build an investment portfolio with his savings. He is being
    offered to buy 2 different funds, a fixed income fund and an equities fund, with
    the following information:
    Expected return Volatility Correlation
    Fixed income
    5,5% 5% -0,45
    Equities fund 14% 17%
    a. Which % would buy of each one if your client wants to get the
    maximum possible return? Which are the expected returns and
    volatility of this portfolio?
    b. If your client wants to follow a conservative path and have a portfolio
    that minimizes risk what % would buy of each fund (minimum variance
    portfolio)? What would be the expected return and the volatility of this
    portfolio of funds?
  2. Stock A and B have the following characteristics:
    Expected return Volatility
    Bond A 6% 12%
    Stock B 14% 20%
    Their correlation is 0. The risk-free interest rate is 2%.
    a. Consider a portfolio, with 80% in Bond A and 20% in the risk- free
    asset. What is the portfolio´s expected return and volatility?
    b. Consider another portfolio, which consists of 30% of Stock B and 70%
    in the risk free asset. What is the portfolio´s expected return and
    c. Consider another portfolio, which consists of 80% of Bond A and 20%
    of Stock B. What is the portfolio´s expected return and volatility?
    d. Calculate Sharpe ratio for the previous 3 portfolios. Which one is more
    e. Is it attractive for you to choose the risk free investment as part of your
    portfolio? Why do you think may be attractive for you?
  3. Given this stock and Index:
    Return Volatility Correlation
    BNPP 6% 14% 0,6
    CAC40 Index 3% 5%
  • Compute Beta. Explain what it means.
  • Compute BNPP Alpha. Explain what alpha means.
  • Provide the expected return for BNPP if the CAC40 grows a
  1. Describe the mean – variance portfolio theory (Markowitz).
  2. Describe the main difference between the Sharpe´s Market portfolio theory
    and the CAPM
  3. Explain if any of these 2 statements are correct or incorrect and briefly justify
    your why:
    Statement 1: The investment policy statement is an initial step of the portfolio
    management process. The investment process should be changed according
    to the change of market trends.
    Statement 2: The primary purpose of the monitoring process in portfolio
    management is to measure the performance of a client’s portfolio relative to
    the performance of the stock market benchmark over a comparable period of
  4. The asset risk free offers a return of 2%. If the Expected return for the market
    portfolio is 15% with a volatility of 20%
    a. Would it be reasonable buy shares on asset A with a Beta of 0,70
    with an expected return of 10%? Explain why
    b. And a share with a Beta of 1.25 with an expected return of 19%?
    Explain why
    c. And if risk free is 5% instead? Does a larger risk free change anything
    on your previous investment decisions? If so, why?
  5. Briefly describe what information each of the following 3 ratios measure:
    a. Sharpe Ratio
    b. Treynor Ratio
    c. Alpha Jensen
  6. Complete the table below. Risk free is 4% (show the steps followed on your
    Fund Return σf Βf Sharpe
    A 9% 7% 0,75
    B 15% 12% 1,1
    C 13% 10% 1,2
    D 17% 14% 1,3
    Market 11% 6% 1
    Has performed better than the market? (YES/NO)
    Fund Sharpe ratio Treynor ratio Alpha Jensen
  7. You can build a portfolio of two assets, A and B, whose returns have the
    following characteristics:
    Expected return Volatility Correlation
    Share A 10% 20% 0,4
    Share B 12% 25%
    If you demand an expected return of 11%, what are the portfolio weights?
    What is the portfolio’s standard deviation?
  8. Assume the following Characteristic Line equation for these 3 assets:
    a. RBNPP = 0,20% + 1,50 * RCAC40 + UBNPP
    b. RTotal= 0,05% + 1,10* RCAC40 + UTotal
    c. REDF = 0,50% + 0,90 * RCAC40 + UEDF
    d. Assume a portfolio of 30% BNPP, 30% Total and 40% EDF.
    i. Portfolio Beta
    ii. Portfolio Alpha
    iii. Expected return if CAC40 growth is 4%
  9. Business case:
    a. Consider the following indices:
    i. S&P 500 TR
    ii. Nikkei 225 Average PR JPY
    iii. FTSE 100 TR GBP
    vi. MSCI Pacific Ex Japan GR USD
    vii. S&P Latin America 40 TR
    b. Download historical daily or weekly data for each one of these indices
    from 2001 until today.
    c. You are a portfolio manager who advises a client to diversify his
    investments. Your client, who is watching every day many hours of
    CNBC and Bloomberg from 2001 when he retired, suspects your
    advise to buy all the indices above will not guarantee he will achieve
    much diversification. He does believe these indices tend to move
    strongly together and he does not buy your argument only sometimes
    in the past due to macro events his arguments may be true. How
    would you convince him?
    Hint: diversification is highly related to correlation, so you may need to
    consider looking at the correlation of these indices. Consider looking
    at the evolution of these indices between 2001 to today, but then the
    evolution of this correlation in sub periods (like 2001-2012, 2007- to
    2015, 2015-2017, 2018-19…)

Sample Solution