Optimal risky portfolios and Markowitz Portfolio Optimisation Flashcards
(25 cards)
What are the two key decisions in portfolio design?
Capital Allocation – Between risk-free and risky assets (Week 1).
Asset Allocation – Among risky assets (Week 2, using Markowitz optimization).
What is the main objective of the Markowitz procedure?
To find the optimal weights of risky assets that maximize the Sharpe Ratio of the portfolio.
How is the Sharpe Ratio calculated?
SharpeRatio=
E(Rp)−rf/σp
Where E(Rp) is is the expected portfolio return,
rf is the risk-free rate, and
σ P is the portfolio’s standard deviation.
What is the optimization constraint in Markowitz theory?
The sum of the portfolio weights must equal 1. The portfolio must also lie on the efficient frontier.
How are optimal weights calculated in a 2-asset portfolio?
Long formula but it is in the formula sheet for both wE and wD.
What is the Portfolio Opportunity Set?
It is the full set of possible risk-return combinations from different portfolio weights across assets.
What is the Efficient Frontier?
It is the upper boundary of the Portfolio Opportunity Set where portfolios offer the highest return for a given level of risk.
What is the Tangency Portfolio?
It is the point on the Efficient Frontier where the Capital Allocation Line (CAL) is tangent. It maximizes the Sharpe Ratio.
What is the Global Minimum Variance Portfolio (GMVP)?
It is the portfolio on the Efficient Frontier with the lowest possible risk among all combinations of risky assets.
Asset allocation
Find the optimal risky portfolio
Capital allocation
Find an optimal complete portfolio
What is the Capital Market Line (CAL)?
The CAL shows the best possible combinations of the risk-free asset and the tangency portfolio. It represents the new efficient frontier when a risk-free asset is available.
Its slope is the Sharpe ratio of the tangency portfolio, and it reflects the maximum increase in return per unit of risk.
How do investors use the Efficient Frontier in practice?
Investors:
Use historical data to estimate expected returns and covariances.
Use tools like Excel Solver to calculate the frontier.
Choose a portfolio on the frontier (or on the CAL if using a risk-free asset) based on their risk tolerance.
Combine the optimal risky portfolio with the risk-free asset to form a complete portfolio.
How does adding a risk-free asset affect the Efficient Frontier?
With a risk-free asset:
The Efficient Frontier becomes a straight line called the Capital Market Line (CAL).
CAL starts at the risk-free rate and is tangent to the efficient frontier.
The tangency point is the only risky portfolio needed; all other points on the original frontier become suboptimal.
What is the Tangency Portfolio?
The Tangency Portfolio lies at the point where the Capital Allocation Line (CAL) is tangent to the efficient frontier.
It represents the optimal risky portfolio with the highest Sharpe ratio. When combined with a risk-free asset, it forms the best complete portfolio for all investors, regardless of risk preference.
What differentiates efficient portfolios from inefficient ones?
Efficient portfolios offer better return for the same level of risk or less risk for the same level of return compared to inefficient ones.
Inefficient portfolios lie below the efficient frontier and are dominated by at least one efficient portfolio.
What is the Global Minimum Variance Portfolio (GMVP)?
The GMVP is the portfolio on the minimum variance frontier that has the lowest risk (standard deviation) among all possible portfolios, regardless of return. It is the most diversified in terms of risk reduction, but not necessarily the best in terms of return.
What is the Minimum Variance Frontier?
The Minimum Variance Frontier is the boundary of the portfolio opportunity set showing the lowest possible risk for each level of return. It includes both efficient (upper part) and inefficient (lower part) portfolios.
The lowest point on this frontier is the Global Minimum Variance Portfolio (GMVP).
What is the Efficient Frontier in portfolio theory?
The Efficient Frontier is the set of portfolios that offer the highest expected return for a given level of risk or lowest risk for a given level of return. It lies on the upper portion of the risk-return graph derived from all possible combinations of risky assets. Portfolios on this curve are optimal and well-diversified.
How is the Efficient Frontier constructed?
Using the Markowitz procedure, the Efficient Frontier is derived by:
Estimating expected returns, variances, and covariances of all assets.
Generating all possible portfolios (varying weights).
Calculating each portfolio’s expected return and risk (standard deviation).
Identifying the minimum variance frontier and selecting the upper half as the efficient frontier.
What is the sharpe ratio used for?
Compare Investments:
It helps investors compare which portfolios or assets provide better return per unit of risk.
Higher Sharpe Ratio = better risk-adjusted performance.
Portfolio Optimization:
In Markowitz theory, the optimal risky portfolio is the one that maximizes the Sharpe Ratio.
Capital Allocation:
It’s the slope of the Capital Allocation Line (CAL):
SlopeofCAL=SharpeRatioofTangencyPortfolio
What is a separation property and its benefit?
Risky portfolio managers can design their optimal risky
portfolio without considering clients’ risk aversion. Indeed, all
clients use the same optimal risky portfolio as their
investment vehicle regardless of their risk aversion level.
* Optimal complete portfolio reflects clients’ risk aversion level,
but optimal risky portfolio does not. More risk averse client
will invest more in the risk-free asset and less in risky asset.
Q: If there are no risk-free assets in the market,
how would portfolio managers design an optimal
risky portfolio?
If there is no risk-free asset, then managers
need to consider their clients’ risk aversion level.
In this situation, the risky portfolio must
maximize utility, not the Sharpe ratio. At an
optimal portfolio, the slope of the indifference
curve and the slope of the opportunity set are
the same, i.e., they are tangent to each other.
Which evaluation measure is most important for
you? Sharpe, Treynor, or Jensen’s alpha? Why?
Explain. Are there any other performance measures
you would use?
If the portfolio is well diversified, we would focus
only on systematic risk. Therefore, the Treynor
ratio is the appropriate measure.
* If the portfolio is not well diversified, we would
focus on both non-systematic (diversifiable) and
systematic (undiversifiable) risks. Thus, we need
to consider total risk. Therefore, the Sharpe ratio
is the appropriate measure.
* If an investor wants to know how much extra
return she can earn, compared to the CAPM
prediction, the Jensen’s alpha is better.
