Summary: Portfolio Management

Read the summary and the most important questions on Portfolio management

• 1 READING 83 Portfolio Risk and Return: Part I

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• What does an indifference curve represent in portfolio theory?

  An indifference curve plots combinations of risk (standard deviation) and expected return that provide the investor with the same level of expected utility (happiness).
  
  

• What does the capital allocation line show?

  The capital allocation line shows all possible risk–return combinations achievable by combining the risk-free asset with the optimal risky portfolio.

• How does an investor’s degree of risk aversion affect the shape of indifference curves and the optimal portfolio?

  Back (Answer):
  

  • More risk-averse investors have steeper indifference curves because they require a large increase in expected return to accept additional risk.
    
  • Less risk-averse investors have flatter indifference curves and optimally choose portfolios with higher risk and higher expected return.
    
  • Compared to more risk-averse investors, less risk-averse investors allocate more to the risky asset portfolio and less to the risk-free asset.
    

• Why is the tangency point between the CAL and an indifference curve optimal?

  Because it represents the highest utility the investor can achieve given available portfolios. At this point, the market’s risk–return tradeoff equals the investor’s required compensation for risk.

• Please explain the difference between variance and standard deviation

  
  Variance measures dispersion in squared units, while standard deviation—its square root—expresses risk in the same units as returns, making it easier to interpret and compare.

• Please explain covariance (also measured in squared units), a positive one, a negative one and one of zero

  Covariance measures the extent to which two variables move together over time. A positive covariance means that the variables (e.g., rates of return on two stocks) tend to move together. Negative covariance means that the two variables tend to move in opposite directions. A covariance of zero means there is no linear relationship between the two variables. To put it another way, if the covariance of returns between two assets is zero, knowing the return for the next period on one of the assets tells you nothing about the return of the other asset for the period.

• Why is covariance difficult to interpret, and how do we obtain a comparable measure of co-movement between two securities?

  Covariance measures how two securities’ returns move together, but it is expressed in units of return squared, which makes it difficult to interpret or compare across assets. To standardize covariance, we divide it by the product of the standard deviations of the two securities, which gives correlation, a unit-free measure of co-movement.
  ρXY=Cov(X,Y)σXσY ρ XY​ = σ X​ σ Y​ Cov(X, Y)​ Correlation is bounded between −1 and +1, making it easy to interpret.

• When will you have the greatest portfolio risk, when the asset returns are positively or negatively correlated?

  
  
  
  The lower the correlation of asset returns, the greater the risk reduction (diversification) (So, positively will increase risk)

• What do the minimum-variance frontier, the efficient frontier, and the global minimum-variance portfolio represent?

  
  

  • The minimum-variance frontier shows the portfolios with the lowest risk for each level of expected return.
    
  • The efficient frontier is the upper portion of the minimum-variance frontier that offers the highest expected return for each level of risk. (Risk-averse investors would only choose a portfolio that lies on the efficient frontier.)
  • The global minimum-variance portfolio is the portfolio on the frontier with the lowest risk of all possible portfolios.
    

• 2 READING 84: Portfolio Risk and Return: Part II

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• What is the Capital Market Line (CML) and what does it represent? Please also provide the equation of this line

  The Capital Market Line (CML) shows all possible combinations of expected return and risk that can be achieved by combining the risk-free asset with the market portfolio. (market portfolio has the steepest possible Capital Allocation Line, the highest Sharpe ratio and touches the effcient frontier line)