L5 - Optimal Risky Portfolio Flashcards
What are the two types of uncertainty that affect firms?
•Most risky assets, such as stocks and bonds, have two components of risk:
- General economic uncertainty
- Business cycle, inflation rate, interest rate, exchange rate, etc.
- Affect all firms in the economy, cannot be diversified away
- Systematic risk, non-diversifiable risk, or market risk
- Firm-specific uncertainty
- Sales growth, R&D, relative performance, etc.
- Peculiar to the firm, and can be eliminated by diversification in a portfolio
- Idiosyncratic risk, diversifiable risk, or unsystematic risk
What do the benefits of diversification depends on?
- The correlation coefficient between the two assets
- •The smaller the correlation, the greater the risk reduction potential.
- If r = 1, no risk reduction is possible.
- The case r = -1 generates the maximum risk reduction.
What is the portfolio frontier?
- it is the budget constraint that depicts all the possible portfolios that can be formed between two risky assets
What does the nose on the portfolio frontier represent?
- the tip/nose of the portfolio frontier represents the minimum variance portfolio.
- Points above the nose are called the efficient frontier
- Those below the nose are called the inefficient frontier
How do you calculate the minimum variance portfolio?
- want to minimise the variance equations
- differentiate with respect to w1 setting it equal to zero
How do you find the optimal risky portfolio?
- The tangent point between the investor indifference curve and the portfolio frontier (or portfolio opportunity set)
How do you calculate the optimal portfolio including a riskless asset?
- By drawing the CAL using the risk-free asset and a risky asset –> by including the risk-free assets we have a larger portfolio opportunity set (everything on and below the line is now an available combination)
- We can keep allocating more of the portfolio to the risky asset to the point that the CAL is tangent to the portfolio frontier
This becomes a tangency(complete?) portfolio!
How do you find the Most optimal portfolio including risk-free assets algebraically?
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What is the optimal complete portfolio?
- The point when the indifference curve is tangent to the CAL fro the optimal risky portfolio
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How do you calculate the optimal risky portfolio with multiple risky securities?
The large variance equation is actually just the sum of all the variance and covariance terms in the variance-covariance matrix multiplied by their specific weights
How is portfolio constuction different in the real world?
- Lots of different types of funda with different goals
- hedge funds like to adopt complicated trading strategies to generate alpha
- Nonprofit organisations or pension funds limit risk exposure more than pursuing alpha
- Hold a lot of different assets
- Modern-day portfolio management requires knowledge in finance, maths and coding
- Everything is computerised due to the amount of assets
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- Everything is computerised due to the amount of assets
What is the efficient frontier?
- (help to choose the optimal portfolio from all securities)
- Is the combination of portfolio that give the highest return for a given level of risk
- Portfolios on the efficient froniter dominate those inside the frontier
What is separation properties?
In absence of risk-free security, the advisor will recommend different combinations of risky securities to different clients.
•But when the risk-free asset is available, he will recommend the same combination of risky securities to all clients.
By combination, he means the makeup of the risky portfolio not the weight between that portfolio and the risk-free rate
•The CAL(P) thus becomes the separating line between the return dynamics and the risk aversion. (choice on the portfolio is separate from the risk attitudes)
- Basically, they are no longer confined to the efficient frontier - can get better returns or the same return with less risk
