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What happens to portfolio risk when stock correlations are below 1?
What happens to portfolio risk when stock correlations are below 1?
You can completely eliminate all types of risk in a diversified portfolio.
You can completely eliminate all types of risk in a diversified portfolio.
False
What are the two components of total risk in a portfolio?
What are the two components of total risk in a portfolio?
Non-diversifiable Risk and Diversifiable Risk
The variance of a well-diversified portfolio of N stocks is denoted by Var(RP) and can be expressed using _______ and _______.
The variance of a well-diversified portfolio of N stocks is denoted by Var(RP) and can be expressed using _______ and _______.
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Match the risk components with their definitions:
Match the risk components with their definitions:
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What is the expected effect of increasing the number of stocks in a portfolio on diversifiable risk?
What is the expected effect of increasing the number of stocks in a portfolio on diversifiable risk?
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What does a negative portfolio weight indicate?
What does a negative portfolio weight indicate?
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Positive correlation between stocks always leads to effective risk reduction through diversification.
Positive correlation between stocks always leads to effective risk reduction through diversification.
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A portfolio weight can only be positive or zero.
A portfolio weight can only be positive or zero.
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In a well-diversified portfolio, what weight does each stock approximately have?
In a well-diversified portfolio, what weight does each stock approximately have?
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What is the formula for calculating realized portfolio returns?
What is the formula for calculating realized portfolio returns?
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In a short sale, you borrow a unit of stock from a ______.
In a short sale, you borrow a unit of stock from a ______.
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Match the following terms with their descriptions:
Match the following terms with their descriptions:
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If you start with £1,000 and sell £250 of a stock short, what will the portfolio weight of the shorted stock be?
If you start with £1,000 and sell £250 of a stock short, what will the portfolio weight of the shorted stock be?
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You can profit from a short sale if the price of the stock rises.
You can profit from a short sale if the price of the stock rises.
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In a short sale, what happens to the investor's position if the stock price rises?
In a short sale, what happens to the investor's position if the stock price rises?
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What characterizes the set of efficient portfolios on the frontier?
What characterizes the set of efficient portfolios on the frontier?
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Inefficient portfolios lie on the left side of the efficient frontier.
Inefficient portfolios lie on the left side of the efficient frontier.
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What benefits are visible through portfolio diversification?
What benefits are visible through portfolio diversification?
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The set of frontier portfolios represents those with the lowest risk for their particular level of expected ______.
The set of frontier portfolios represents those with the lowest risk for their particular level of expected ______.
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What does the variable $e_j$ represent in the return equation?
What does the variable $e_j$ represent in the return equation?
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The mean return of the MSCI EM is higher than that of the FTSE-100.
The mean return of the MSCI EM is higher than that of the FTSE-100.
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What is the maximum return of EXXON?
What is the maximum return of EXXON?
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The __________ value of an asset is represented by $P_j$ in the return on stock formula.
The __________ value of an asset is represented by $P_j$ in the return on stock formula.
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Match the following stock indices with their mean returns:
Match the following stock indices with their mean returns:
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Which stock has the highest kurtosis value?
Which stock has the highest kurtosis value?
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A higher skewness value indicates that the distribution is more negatively skewed.
A higher skewness value indicates that the distribution is more negatively skewed.
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What does σ stand for in stock market data?
What does σ stand for in stock market data?
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To calculate the expected return of stock j, you need to know the future price ($P_j$) and the future __________ ($D_j$).
To calculate the expected return of stock j, you need to know the future price ($P_j$) and the future __________ ($D_j$).
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Which stock has the lowest minimum return recorded?
Which stock has the lowest minimum return recorded?
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What is the formula for the expected return of a two-stock portfolio?
What is the formula for the expected return of a two-stock portfolio?
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The variance of a portfolio return does not take into account the correlation between the stocks.
The variance of a portfolio return does not take into account the correlation between the stocks.
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In a portfolio consisting of N stocks, what does σj2 represent?
In a portfolio consisting of N stocks, what does σj2 represent?
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If the correlation between two stocks is 1.0, the portfolio return standard deviation is given by σP = [______].
If the correlation between two stocks is 1.0, the portfolio return standard deviation is given by σP = [______].
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What happens to the expected return of a portfolio if the weights of the stocks are changed?
What happens to the expected return of a portfolio if the weights of the stocks are changed?
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Diversification reduces portfolio risk by decreasing the effect of individual stock variances.
Diversification reduces portfolio risk by decreasing the effect of individual stock variances.
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What effect does a correlation of less than 1.0 have on the portfolio variance formula?
What effect does a correlation of less than 1.0 have on the portfolio variance formula?
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As the number of stocks in a portfolio increases, what happens to the first term in the variance formula for a well-diversified portfolio?
As the number of stocks in a portfolio increases, what happens to the first term in the variance formula for a well-diversified portfolio?
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The risk of a well-diversified portfolio is entirely eliminated as the number of stocks increases.
The risk of a well-diversified portfolio is entirely eliminated as the number of stocks increases.
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What is the relationship between the average covariance of stock returns and the risk of a well-diversified portfolio?
What is the relationship between the average covariance of stock returns and the risk of a well-diversified portfolio?
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As N approaches infinity, the limit of the variance of a well-diversified portfolio is __________.
As N approaches infinity, the limit of the variance of a well-diversified portfolio is __________.
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If the average return standard deviation is 40%, what is the average variance?
If the average return standard deviation is 40%, what is the average variance?
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Diversifying a portfolio can eliminate half of the average standard deviation if the average return correlation is 0.25.
Diversifying a portfolio can eliminate half of the average standard deviation if the average return correlation is 0.25.
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What is the primary effect of diversifying a portfolio with stocks that have a positive covariance?
What is the primary effect of diversifying a portfolio with stocks that have a positive covariance?
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Study Notes
Equity Securities and Markets - SMM940
- Course taught by Joe Gong
- Course offered in Autumn 2024
- Covers financial markets and financial intermediation
- Module outline includes:
- Part 1: Financial markets (risk & returns, asset pricing, CAPM, other security classes)
- Part 2: Financial intermediaries (why banks?, types of banking, fintech, bank regulation)
Assessment
- Group coursework (25%):
- Weeks 1-5
- Portfolio optimization
- Deadline: 4 PM Monday, December 2nd
- Final exam (75%):
- 40% of the exam questions from weeks 1-5
- 60% of the exam questions from weeks 6-10
- Qualitative and quantitative questions
- Choice of questions
- Date: To be determined (probably in January)
About the Instructor
- Experience: Five years teaching undergraduate and postgraduate finance and banking modules
- Contact information:
- Office hours (in person or virtually): Wednesday afternoons 3-4 PM
- Office: Location TBD (under construction)
- Email: [email protected]
- Recommendations:
- Ask questions
- Review tutorial questions before solutions and videos are released
Today's Topic (Example)
- Basics (e.g., diversification)
- Summary
Roadmap
- Stock and portfolio returns: definitions and data
- Portfolio analysis for risk-averse investors
- Application to real-world data
Stock Returns
- Realized return on stock j over a historical period is:
- Rj = [(Pj + Dj) - P0,j] / P0,j
- Where:
- P0,j = Beginning of period price
- Pj = End of period price
- Dj = Dividend on stock
- When looking forward in time, the return on stock j is:
- Rj = (Pj + Dj) / Pj
- Where:
- Pj = Future price
- Dj = Future dividend
Recent Stock Market Data
- Various stock market indices (FTSE 100, SP500, MSCI World, MSCI EM, Lloyds, Exxon, Microsoft)
- Data presented in charts showing historical trends and returns.
- Detailed data (mean, standard deviation, skewness, kurtosis, minimum, maximum values also shown in Table form) for FTSE-100, S&P-500, MSCI World, MSCI EM, LLOYD, XOM (Exxon) and MSFT (Microsoft).
Portfolio Weights
- Investor spreads wealth across N assets.
- Allocates a fraction wj of wealth to asset j (where Σwj = 1)
- Call wj portfolio weight on stock j.
- Positive wj: Stock purchased (long position)
- Zero wj: Stock ignored
- Negative wj: Stock sold short
Short Sales
- Borrow a stock from a lender
- Sell the stock receiving cash today
- Pay cash to buy the stock in the market later and return it to the lender
- Profit if stock price falls while you're short
- Loss if stock price rises while you're short
Portfolio Returns
- Realized portfolio return given an investment strategy
- Rp = ΣwjRj
- Future portfolio return:
- Rp = ΣwjRj
Risk and Return: 2 Stock Portfolios
- Investor's expected portfolio return and portfolio risk:
- E(Rp) = wE(RA) + (1 - w)E(RB)
- Var(Rp) = w2σA2 + (1 - w)2σB2 + 2w(1 - w)σA,BρA,B
- Expected portfolio returns are derived linearly from expected stock returns
- Portfolio return variance depends on stock return variances and stock return correlation.
Portfolio Return and Risk: N Stock Portfolios
- When the investor builds a portfolio of N stocks, we have:
- E(Rp) = Σj=1N wjE(Rj)
- Var(Rp) = Σi=1N Σj=1N wiwjσi,j
Diversification
- Limits of diversification: Portfolio variance is unlikely to reach zero due to positive correlations between stocks.
- Total risk = Non-diversifiable risk + Diversifiable risk = Systematic risk + Specific/Idiosyncratic risk = Market risk + Idiosyncratic risk
- Diversification eliminates idiosyncratic risk; but cannot eliminate systematic risk (market risk)
Limits to Diversification: Maths
- The risk of well diversified portfolios is controlled by the average covariance between stock returns. As stocks positively correlate on average, diversification will have less impact
- This risk converges (when the # of stocks is large) to the average covariance term
Note diversification in a large portfolio reduces portfolio risk
Portfolio Analysis: Data
- Data: 10 years of monthly returns on 3 stocks (UU, GSK, RIO) from the London Stock Exchange,
- Stocks represented in GBP
Stock-Level Descriptive Statistics
- Table of descriptive statistics for UU, GSK, RIO (mean, standard deviation, percentiles, median, monthly).
- Annualization method discussed.
Stock-Level Correlations
- Correlation matrix for UU, GSK, RIO returns.
- High correlation suggests potential for diversification.
Some Simple 3 Stock Portfolios
- Equally Weighted Portfolios: (weight of each stock = 1/3) and empirical correlation between returns were used.
- Non-Equally Weighted Portfolios were selected, weights 0.25, 0.30, 0.45 to demonstrate portfolio diversificaiton in action.
The Feasible Set of Portfolios
- Method to generate a portfolio consisting of the three stocks.
- Calculating weights for each stock
- Plotting these portfolios on a graph (x-axis is portfolio variance/standard deviation, y-axis is average/expected return)
Feasible Set: Interpretation
- Individual stock locations and diversification benefits are visible
- Identifying frontier portfolios: lowest risk portfolios for a specified return.
- Identification of inefficient portfolios
- Identifying efficient portfolios
Summary
- Demonstrating portfolio risk calculation
- Showing the effects of diversification and its limits
- Applying concepts to a practical example of stock portfolios.
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Description
Test your understanding of portfolio risk, diversification, and the concepts related to stock correlations. This quiz covers key components of total risk, the effects of increasing stock numbers on diversifiable risk, and the implications of portfolio weights. Perfect for finance students looking to deepen their knowledge.
