Lecture 6 - Understanding Risk Flashcards
Risk and Return
- The relationship between risk and return is considered one of the
fundamental concepts in finance - Risk along with a measure of performance such as returns or profit, forms a dual criterion for making investment decisions
Ex post
Financial analysts have enormous quantity of historical data allowing them to explore this relationship retrospectively
Ex ante
- For decision-making purposes, it is important to understand this relationship beforehand (ex-ante) to assess the potential trade-offs between risk and return before committing capital
- The ex-ante risk-return relationship refers to the relationship between the expected risk and expected return of an investment before it is actually made
Risk and returns for stocks
The higher returns for stocks donβt come for free because stocks are riskier than long term government bonds or Treasury bills
Histogram
Is a graphical representation of data distribution where data is divided into intervals or bins and the frequency or count of observations falling within each interval is depicted by the height of corresponding bars, providing a visual summary of the dataβs frequency distribution
Variance
Is a measure of risk because it quantifies the extent of dispersion or spread of data points around the mean or expected value
Variance as a measure of risk
In finance, higher variance indicates greater volatility, implying increased
uncertainty and potential for larger deviations from the expected outcome, hence greater risk
Standard Deviation
- Is a statistical measure of the dispersion or spread of
a set of data points from the mean - Standard deviation is expressed in the same units as the original data, making it more intuitive to comprehend compared to variance, which is in squared units
Expected Return of an Investment
The expected return (π) is the average outcome calculated by multiplying
each possible outcome π (out of π possible outcomes) by its respective probability and summing up the results
Diversification
- Efficient Diversification: construct risky portfolios to provide the lowest possible risk for any given level of expected return
- The risk of a portfolio is not a weighted average of the individual asset variances that comprise the portfolio
Benefits of diversification
One factor on which the degree of risk reduction from diversification depends on is: the extent of statistical interdependence between the returns of the different investments
Covariance
Covariance between investments A and B (ππ΄,π΅) measures how their returns vary together; positive values indicate they tend to move in the same direction, while negative values indicate the opposite
Correlation
- Correlation between investments A and B (ππ΄,π΅) measures the strength and direction of their linear relationship; it ranges from -1 to 1, where 1 indicates a perfect positive correlation, -1 indicates a perfect negative correlation and 0
is no linear correlation - The more negatively correlated the 2 assets, the higher the benefits of diversifications
Benefits of diversification - a general rule
- Portfolio returns are a weighted average of the expected returns on the individual investment BUT
- Portfolio standard deviation is LESS than the weighted average risk of the
individual investments, except for perfectly positively correlated investments
Types of Risks
- Specific Risk
- Market Risk
Total risk for a firm is the sum of specific and systematic risk
Specific Risk
- Risk factors affecting only a firm
- Also called idiosyncratic/
diversifiable/residual/unique /unsystematic risk - This risk can be diversified away
Market Risk
- Economywide sources of risk that affect the overall stock market
- Also called systematic risk
- This risk cannot be diversified away
Diversification with many stocks
- The higher the number of assets in a portfolio N, the portfolio variance
approaches average covariance (this is the systematic risk), while the
assetsβ specific risk (average variance) is eliminated - Average risk (standard deviation) of portfolios containing different
numbers of stocks - This is because diversification can
only eliminate specific risk - It cannot eliminate systematic risk
Systematic risk vs Total risk
- The total risk of holding one asset e.g. a stock in a company, denoted by
A is its standard deviation: ππ΄ - But investors do not hold individual stocks, but they hold portfolios consisting of multiple assets
- When you add a stock to a diversified portfolio you donβt simply add its total risk because some of that risk can be mitigated through diversification
- Instead, what matters more is the systematic risk that the stock contributes to the portfolio
Investment opporunity set
The line representing all combinations of portfolio expected returns + standard deviations that can be constructed from the 2 (or more) available assets
Efficient Frontier
The efficient frontier is that part of the investment opportunity set that lies above the the portfolio with the global minimum variance
