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Business Finance > Lecture 8 - Expected value and variance criterion > Flashcards

Lecture 8 - Expected value and variance criterion Flashcards

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1
Q

What is the expected value (mean) of a random variable?

A

The expected value (mean) of a random variable is the average outcome you would expect if you repeated a random process many times.

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2
Q

How do different investments or time periods affect returns?

A

Investments in different assets or over different time periods can yield different returns, which are treated as outcomes of a random variable.

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3
Q

When should you use a simple average to calculate expected return?

A

Use a simple average when all investments are equally important or when all outcomes are equally likely.

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4
Q

What is the formula for calculating the simple average of returns?

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5
Q

What is a weighted average in the context of expected returns?

A

A weighted average is used when some investments are more important or likely than others. Different weights are assigned to each return, reflecting their importance or likelihood.

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6
Q

What is the formula for calculating the weighted average of returns?

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7
Q

Why would you use a weighted average instead of a simple average?

A

You use a weighted average when some outcomes are more likely or more important than others, to reflect the true expected value more accurately.

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8
Q

What does the sum of the weights pip_ipi​ equal in a weighted average?

A
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9
Q

What does variance measure in the context of a random variable?

A

Variance measures how much a random variable deviates from its mean, indicating how spread out the returns are from their average.

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10
Q

How is variance denoted mathematically?

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11
Q

What is the formula for sample variance?

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12
Q

Why do we use 1n−1\frac{1}{n-1}n−11​ in the sample variance formula?

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13
Q

What is weighted variance and when is it used?

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14
Q

What is the standard deviation?

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15
Q

How is standard deviation interpreted in finance?

A

In finance, standard deviation is referred to as volatility and is used to measure the level of risk associated with investment returns. A higher standard deviation indicates more variability (risk) in returns.

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16
Q

What do the prices in the table represent?

A

The prices shown are adjusted prices (for shares) or index levels (for the FTSE 100), accounting for stock splits, dividends, and other corporate actions.

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17
Q

What is the formula to calculate the return from one period to the next?

A
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18
Q

How do you interpret the return calculated using the formula?

A

The return represents the percentage change in price from one year to the next, indicating the investment’s performance over that period.

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19
Q

What was the return for Tesco from April 1988 to April 1989?

A
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20
Q

What was the return for Tesco from April 1989 to April 1990?

A
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21
Q

Why are adjusted prices used in these calculations?

A

Adjusted prices are used because they account for stock splits, dividends, and other corporate actions, providing a more accurate reflection of the value.

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22
Q

What is the mean of the annual returns and how is it calculated?

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23
Q

What does the variance of returns measure?

A

Variance measures how much the returns deviate from the mean return, indicating the spread or volatility of the returns.

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24
Q

What is the formula for calculating variance?

A
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25
What does the standard deviation represent in finance?
The standard deviation represents the average deviation of returns from the mean and is a measure of risk or volatility. It is the square root of the variance.
26
What is the formula for standard deviation and its value for Tesco?
27
What does a mean return of 13.09% indicate for Tesco shareholders?
A mean return of 13.09% indicates that, on average, Tesco shareholders earned 13% per year on their investment over the period from 1988 to 2004.
28
Why is standard deviation important in finance?
Standard deviation is important because it provides a measure of the risk associated with an investment, indicating how much the returns typically fluctuate around the mean.
29
What are the two forms of returns that shareholders receive?
Shareholders receive returns in the form of capital growth (change in share price) and cash dividends (cash paid out per share).
30
How is the total receipt of wealth for a shareholder calculated?
31
What is the formula for calculating total return RtR_tRt​?
32
What are adjusted prices and why are they used?
Adjusted prices account for dividends by assuming they are reinvested to buy more shares, allowing for a simplified calculation of returns by focusing on capital growth.
33
How do adjusted prices affect the calculation of returns?
Adjusted prices integrate dividends into the share price, so the focus is on capital appreciation, and dividends are not separately accounted for in return calculations.
34
Why is it important to consider total returns rather than just capital growth?
Total returns provide a complete picture of the shareholder’s returns, including both the change in share price and the dividends received.
35
What does the use of adjusted prices imply about the value of dividends?
Using adjusted prices implies that dividends are reinvested into the share price, preserving their value in a different form as part of the capital growth.
36
What is the Expected Value/Variance Criterion (EVC)?
The EVC is a decision-making tool used by investors to choose between investments by comparing their expected return and volatility (risk).
37
How does the EVC help in choosing between two investments with the same expected return?
When two investments have the same expected return, the EVC suggests choosing the one with lower volatility (risk).
38
How does the EVC help in choosing between two investments with the same volatility?
When two investments have the same volatility, the EVC suggests choosing the one with the higher expected return.
39
In Scenario 1, why is Investment A preferred over Investment B?
Investment A is preferred over Investment B because both have the same expected return (20%), but Investment A has lower volatility (10% vs. 12%).
40
In Scenario 2, why is Investment Y preferred over Investment X?
Investment Y is preferred over Investment X because both have the same volatility (15%), but Investment Y has a higher expected return (21% vs. 17%).
41
What is volatility in the context of the EVC?
Volatility is a measure of risk, representing how much the returns on an investment are expected to fluctuate.
42
Why would an investor use the EVC when evaluating investments?
An investor uses the EVC to balance the potential rewards (expected returns) against the risks (volatility) when comparing different investments.
43
What is the expected return and volatility for Tesco and Morrison?
Tesco: Expected return of 13.09%, Volatility of 22.10%. Morrison: Expected return of 19.53%, Volatility of 25.86%.
44
Can we choose between investing in Tesco or Morrison based on these figures?
No, because although Morrison has a higher expected return, it also comes with higher risk (volatility).
45
What is the relationship between risk and return?
The riskier the investment, the greater the expected return. This is known as a positive trade-off between return and risk.
46
What does portfolio theory suggest about choosing investments?
Portfolio theory suggests that instead of choosing between investments, investors should diversify their portfolio to reduce risk.
47
What is diversification?
Diversification is the practice of spreading investments across different types of assets (e.g., shares and bonds) or different stocks to reduce overall risk.
48
Why is diversification important in investment?
Diversification is important because it helps manage risk by reducing the impact of any single investment’s poor performance on the overall portfolio.
49
What is the benefit of a positive trade-off between return and risk?
A positive trade-off between return and risk means investors can achieve higher returns, but they must be willing to accept higher risk.
50
What is total risk composed of in an investment portfolio?
Total risk is composed of specific risk (unsystematic risk) and systematic risk (market risk).
51
What is specific risk?
Specific risk, also known as unsystematic or diversifiable risk, is the risk unique to a particular company or industry. It can be reduced by diversification.
52
What is systematic risk?
Systematic risk, also known as market or non-diversifiable risk, is the risk that affects the entire market or a large segment of it. It cannot be eliminated by diversification.
53
How does diversification affect specific risk?
Diversification reduces specific risk by spreading investments across multiple securities, thereby offsetting the negative performance of some with the positive performance of others.
54
Can systematic risk be reduced through diversification?
No, systematic risk cannot be reduced through diversification; it remains constant regardless of the size of the portfolio.
55
What does the graph in the slide illustrate about risk and diversification?
The graph shows that as the number of securities in a portfolio increases, total risk decreases due to the reduction of specific risk, but systematic risk remains.
56
Why does adding more securities to a portfolio eventually stop reducing total risk?
Adding more securities eventually stops reducing total risk because specific risk is minimized, and only systematic risk, which cannot be diversified away, remains.
57
What is specific risk?
Specific risk, also known as unsystematic risk, is the risk unique to a particular company or project and is independent of market risk.
58
Can specific risk be reduced? If so, how?
Yes, specific risk can be reduced through diversification, which involves spreading investments across multiple assets or companies.
59
What is an example of specific risk?
An example of specific risk is a company specializing in skiing holidays. If there is no snow, the company earns no income—this risk is specific to that company.
60
What is systematic risk?
Systematic risk, also known as market risk, is the risk that arises from broader market conditions and affects all participants in the market.
61
Can systematic risk be reduced through diversification?
No, systematic risk cannot be reduced through diversification. It affects the entire market, and all companies are subject to it.
62
What is an example of systematic risk?
An example of systematic risk is an increase in the cost of borrowing across the market, which leads to reduced returns for all companies.
63
How does diversification affect specific and systematic risks?
Diversification can reduce specific risk but has no effect on systematic risk. Specific risk decreases as a portfolio becomes more diversified, while systematic risk remains constant.
64
What is the key strategy for effective diversification?
Diversify across assets that are less perfectly correlated or don’t move in the same direction to reduce overall portfolio risk.
65
Why might investing in both Tesco and Morrison not offer significant diversification benefits?
If Tesco and Morrison are highly correlated, meaning they tend to move in the same direction, investing in both may not significantly reduce risk.
66
What is covariance?
Covariance is a measure of how two assets move together. It indicates the degree to which the returns on two assets are correlated.
67
What does a positive covariance between two assets indicate?
A positive covariance indicates that the two assets tend to move in the same direction at the same time.
68
What does a negative covariance between two assets indicate?
A negative covariance indicates that the two assets tend to move in opposite directions.
69
What is the formula for calculating covariance?
70
What is the estimator for covariance based on sample data?
71
What is correlation?
Correlation is a normalized form of covariance that measures the strength and direction of a linear relationship between two variables.
72
73
What does a positive correlation coefficient indicate?
74
What does a correlation coefficient of zero mean?
75
What does a negative correlation coefficient indicate?
76
What is the range of possible values for the correlation coefficient?
77
What is the formula for estimating the sample correlation coefficient?
78
What does covariance measure?
Covariance measures how two variables (e.g., returns of two companies) move together. Positive covariance indicates that when one variable is above its mean, so is the other.
79
What does a positive covariance between Tesco and Morrison indicate?
It indicates that when Tesco's returns are above its mean, Morrison's returns are also likely to be above its mean, and vice versa.
80
How is covariance calculated?
81
What does the diagonal of a variance-covariance matrix represent?
The diagonal of a variance-covariance matrix represents the variances of the individual assets (covariance of a variable with itself).
82
What do the off-diagonal elements of a variance-covariance matrix represent?
The off-diagonal elements represent the covariance between two different assets.
83
How do you calculate correlation from covariance?
84
What does a correlation coefficient of 0.584 between Tesco and Morrison indicate?
It indicates a moderate positive relationship between Tesco and Morrison’s returns, meaning they tend to move in the same direction but are not perfectly correlated.
85
What is the purpose of calculating covariance and correlation in finance?
Covariance and correlation help investors understand the co-movement of asset returns, which is crucial for diversification and managing portfolio risk.
86
How does diversification benefit from covariance and correlation analysis?
Diversification benefits when assets have low or negative covariance or correlation, reducing specific risk and stabilizing portfolio returns.
87
What is a portfolio?
A portfolio is a collection of investments in different areas or assets.
88
How do you calculate the return of a portfolio with different weights for assets?
89
What is the variance of a two-asset portfolio with equal weights?
90
What is the formula for the variance of a two-asset portfolio with different weights?
91
How is the expected return of a portfolio consisting of Tesco and Morrison shares calculated?
92
How is the variance of a portfolio consisting of Tesco and Morrison shares calculated?
93
How is the standard deviation of a portfolio calculated?
94
What is the expected return and variance for a portfolio with 30% in Tesco and 70% in Morrison?

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