CIMA Portfolio Theory and Construction 2 — Questions and Answers
Question 1: In mean-variance optimization, what does the global minimum variance portfolio represent?
- The portfolio with the highest Sharpe ratio
- The portfolio with the lowest attainable risk regardless of return (Correct answer)
- The portfolio on the efficient frontier with the highest expected return
- The tangency portfolio when the risk-free rate equals zero
Correct answer: The portfolio with the lowest attainable risk regardless of return
The global minimum variance portfolio is the point on the minimum variance frontier with the lowest possible standard deviation, regardless of expected return.
Question 2: Which of the following best describes the separation theorem in portfolio theory?
- Every investor should hold a different mix of risky assets based on their risk tolerance
- All investors hold the same risky portfolio (the market portfolio) and differ only in their allocation to the risk-free asset (Correct answer)
- The optimal risky portfolio changes as the risk-free rate changes
- Investors separate their portfolios into domestic and international assets
Correct answer: All investors hold the same risky portfolio (the market portfolio) and differ only in their allocation to the risk-free asset
Tobin's separation theorem states that the optimal risky portfolio is the same for all investors; risk tolerance only affects the split between the risk-free asset and that risky portfolio.
Question 3: A portfolio has an expected return of 12% and a standard deviation of 18%. The risk-free rate is 3%. What is the Sharpe ratio?
- 0.50 (Correct answer)
- 0.67
- 0.75
- 1.00
Correct answer: 0.50
The Sharpe ratio = (12% − 3%) / 18% = 9% / 18% = 0.50.
Question 4: When two assets have a correlation coefficient of +1.0, combining them in a portfolio:
- Eliminates all diversification benefit (Correct answer)
- Provides maximum risk reduction
- Reduces risk proportionally to the weight of the lower-risk asset
- Creates a risk-free portfolio
Correct answer: Eliminates all diversification benefit
Perfect positive correlation means the assets move in lockstep, so diversification provides no variance reduction benefit.
Question 5: Which risk measure captures only downside deviations from a target return and is preferred by some practitioners over standard deviation?
- Beta
- Semi-variance (Correct answer)
- Tracking error
- Value at Risk
Correct answer: Semi-variance
Semi-variance (or semi-deviation) measures dispersion of returns below a target, focusing exclusively on downside risk.
Question 6: In the context of factor models, what is the intercept term (alpha) in a single-factor regression of a portfolio's excess returns?
- The portfolio's sensitivity to the market factor
- The return attributable to systematic risk
- The average excess return unexplained by the factor (Correct answer)
- The standard deviation of residual returns
Correct answer: The average excess return unexplained by the factor
Alpha is the regression intercept representing average excess return not explained by exposure to the risk factor.
Question 7: A portfolio manager adds a new security to a well-diversified portfolio. The primary risk consideration is the security's:
- Total variance
- Unsystematic variance
- Covariance with the existing portfolio (Correct answer)
- Standard deviation in isolation
Correct answer: Covariance with the existing portfolio
In a well-diversified portfolio, idiosyncratic risk is diversified away, so a new security's contribution to portfolio risk is driven by its covariance with the portfolio.
CIMA Portfolio Theory and Construction 2
In mean-variance optimization, what does the global minimum variance portfolio represent?