Portfolio Theory Flashcards
(21 cards)
Returns
Broadly speaking, we can classify returns as follows: (2/2,2)
Realised returns
- based on actual prices that have been observed, so we are looking back in time
- sometimes called ex post returns
Expected returns
- based on expectations regarding future prices, so we are looking forward in time
- sometimes called ex ante returns
What is risk?
The higher the variance/standard deviation…
Likelihood of loss (negative return)
The higher the variance/standard deviation the higher the spread so more outcomes and more risk
Formulas
Average return: (Historical stock returns)
Population standard deviation: (Historical stock returns)
Sample standard deviation: (Historical stock returns)
Realised returns example
Minnesota Company (MC) has been in business for over fifty years. Their historical annual returns for the past three years are: MC: -5%, 15%, 20%;
What are the variances of return for MC?
Example: Suppose that Big Oil’s share price is $100. At the end of the year, there is an equal chance that it could be $80, $120, or $160. Assume that no dividends will be paid.
What is the expected return and standard deviation of investing in Big Oil’s share?
Total Risk formula
Firm-specific Risk
Definition
Aka (4)
Affects only that firm and its close competitors
Also known as:
- Idiosyncratic Risk
- Unique Risk
- Unsystematic Risk
- Diversifiable Risk
Systematic Risk
Due to?
Aka (3)?
Due to market-wide effects
Also known as:
- Common Risk
- Non-diversifiable Risk
- Market Risk
Managing Risk
What method?
Does it work for both types of risk?
Diversification:
- Strategy designed to reduce risk by spreading the portfolio across many investments
“Firm-Specific Risk”:
- Risk factors affecting only that firm
- Can be diversified away
“Systematic Risk”:
- Economy-wide sources of risk that affect the overall stock market
- Is not diversified away
Return on a portfolio of two risky assets:
Formula and what it means?
When we move on to consider more than one asset – or a portfolio of assets – the …is very important
(3) more imporant than (1)
When we move on to consider more than one asset – or a portfolio of assets – the relationship between the returns is very important
Covariance, correlation, comovement among stocks are more important than individual stock risk
Assume that another company, Big Retail, has an equal chance of the following possible returns:
24%, 33%, -27%
Big Oil from previous slides examples (At the end of the year, there is an equal chance that the big oil return can be -20%, +20%, +60%) has expected return of 20% , σ2 = 1066.6 %2 and σ = 32.66%
What is the covariance between Big Oil and Big Retail?
What is the correlation coefficient?
The closer the coefficient is to -1, the better as the risk will be lower as they offset each others negative return periods
Correlation coefficient = -0.79
Diversification
As the correlation decreases, the ___________ of the portfolio _____.
The maximum benefit from forming a portfolio (in terms of risk reduction) occurs when rho = __.
When does diversification lead to reduction in risk?
What is the central idea of Portfolio Theory?
What does the extent of risk reduction depend on?
As the correlation decreases, the volatility of the portfolio falls.
The maximum benefit from forming a portfolio (in terms of risk reduction) occurs when rho = -1.
Diversification leads to a reduction in risk if the securities are not perfectly positively correlated
Individual risk is not important, leading to the central idea of Portfolio Theory: ‘don’t put all your eggs in one basket’
The extent of risk reduction depends upon the correlation between the securities
Markowitz Portfolio Theory
What is any investors goal?
How can risk be reduced?
What is the theory about? (2)
Any investor’s goal is to maximize Return for any level of Risk
Risk can be reduced by creating a diversified portfolio of unrelated securities
It is a graphical representation of all the** possible mixtures of risky assets** for an optimal level of Return given any level of Risk, as measured by standard deviation.
Mean Variance Efficient portfolio - It’s the best possible portfolio!. The set of all risky portfolios having minimum risk (standard deviation of returns) for a given level of expected return.
How Should We Choose The Best Weights?
- All feasible portfolios lie inside a __________-___________ _________, called the …
- The ____________ ___________ is the…
- Rational investors should select portfolios from the __________ ___________
How Should We Choose The Best Weights?
- All feasible portfolios lie inside a bullet-shaped region, called the minimum-variance boundary or frontier
- The efficient frontier is the top half of the minimum-variance boundary
- Rational investors should select portfolios from the efficient frontier
Efficient Frontier
Investing in risky assets and the risk-free asset CML
What does the CML show?
What is the tangency point?
The capital market line (CML), in thecapital asset pricing model(CAPM): shows the trade-off between risk and return for a portfolio of the risk free and the market portfolio
The tangency point is the optimal portfolio of risky assets, known as the market portfolio.
The Tangent or Efficient Portfolio
What does the optimal portfolio consist of? (2)
Why is this portfolio optimal?
- The optimal portfolio consists of a risk-free asset and an optimal risky asset portfolio.
- The optimal risky asset portfolio is M at the point where the CML is tangent to the efficient frontier.
- This portfolio is optimal because the slope of CML is the highest, which means we achieve the highest returns per unit of risk (sharp ratio).
Summary
- What is the best risky portfolio and what does it offer?
- How do you find this point
Separation theorem
Each investor should put money into two benchmark investments: (2 +1)
- M is the best risky portfolio and offers the highest risk premium (r – rf) to sigma
- To find this point, find the tangency point by drawing a line from the risk-free return to the efficient risky portfolios
Separation theorem
Each investor should put money into two benchmark investments:
- Risk-free asset (borrowing or lending)
- Portfolio M
The exact combination will depend upon the preferences for risk
