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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?

A
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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?

A
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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?

A
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11
Q

What is the formula for sample variance?

A
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12
Q

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

A
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13
Q

What is weighted variance and when is it used?

A
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14
Q

What is the standard deviation?

A
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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?

A
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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
Q

What does the standard deviation represent in finance?

A

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.

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26
Q

What is the formula for standard deviation and its value for Tesco?

A
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27
Q

What does a mean return of 13.09% indicate for Tesco shareholders?

A

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.

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28
Q

Why is standard deviation important in finance?

A

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.

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29
Q

What are the two forms of returns that shareholders receive?

A

Shareholders receive returns in the form of capital growth (change in share price) and cash dividends (cash paid out per share).

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30
Q

How is the total receipt of wealth for a shareholder calculated?

A
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31
Q

What is the formula for calculating total return RtR_tRt​?

A
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32
Q

What are adjusted prices and why are they used?

A

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.

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33
Q

How do adjusted prices affect the calculation of returns?

A

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.

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34
Q

Why is it important to consider total returns rather than just capital growth?

A

Total returns provide a complete picture of the shareholder’s returns, including both the change in share price and the dividends received.

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35
Q

What does the use of adjusted prices imply about the value of dividends?

A

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.

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36
Q

What is the Expected Value/Variance Criterion (EVC)?

A

The EVC is a decision-making tool used by investors to choose between investments by comparing their expected return and volatility (risk).

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37
Q

How does the EVC help in choosing between two investments with the same expected return?

A

When two investments have the same expected return, the EVC suggests choosing the one with lower volatility (risk).

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38
Q

How does the EVC help in choosing between two investments with the same volatility?

A

When two investments have the same volatility, the EVC suggests choosing the one with the higher expected return.

39
Q

In Scenario 1, why is Investment A preferred over Investment B?

A

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
Q

In Scenario 2, why is Investment Y preferred over Investment X?

A

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
Q

What is volatility in the context of the EVC?

A

Volatility is a measure of risk, representing how much the returns on an investment are expected to fluctuate.

42
Q

Why would an investor use the EVC when evaluating investments?

A

An investor uses the EVC to balance the potential rewards (expected returns) against the risks (volatility) when comparing different investments.

43
Q

What is the expected return and volatility for Tesco and Morrison?

A

Tesco: Expected return of 13.09%, Volatility of 22.10%. Morrison: Expected return of 19.53%, Volatility of 25.86%.

44
Q

Can we choose between investing in Tesco or Morrison based on these figures?

A

No, because although Morrison has a higher expected return, it also comes with higher risk (volatility).

45
Q

What is the relationship between risk and return?

A

The riskier the investment, the greater the expected return. This is known as a positive trade-off between return and risk.

46
Q

What does portfolio theory suggest about choosing investments?

A

Portfolio theory suggests that instead of choosing between investments, investors should diversify their portfolio to reduce risk.

47
Q

What is diversification?

A

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
Q

Why is diversification important in investment?

A

Diversification is important because it helps manage risk by reducing the impact of any single investment’s poor performance on the overall portfolio.

49
Q

What is the benefit of a positive trade-off between return and risk?

A

A positive trade-off between return and risk means investors can achieve higher returns, but they must be willing to accept higher risk.

50
Q

What is total risk composed of in an investment portfolio?

A

Total risk is composed of specific risk (unsystematic risk) and systematic risk (market risk).

51
Q

What is specific risk?

A

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
Q

What is systematic risk?

A

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
Q

How does diversification affect specific risk?

A

Diversification reduces specific risk by spreading investments across multiple securities, thereby offsetting the negative performance of some with the positive performance of others.

54
Q

Can systematic risk be reduced through diversification?

A

No, systematic risk cannot be reduced through diversification; it remains constant regardless of the size of the portfolio.

55
Q

What does the graph in the slide illustrate about risk and diversification?

A

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
Q

Why does adding more securities to a portfolio eventually stop reducing total risk?

A

Adding more securities eventually stops reducing total risk because specific risk is minimized, and only systematic risk, which cannot be diversified away, remains.

57
Q

What is specific risk?

A

Specific risk, also known as unsystematic risk, is the risk unique to a particular company or project and is independent of market risk.

58
Q

Can specific risk be reduced? If so, how?

A

Yes, specific risk can be reduced through diversification, which involves spreading investments across multiple assets or companies.

59
Q

What is an example of specific risk?

A

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
Q

What is systematic risk?

A

Systematic risk, also known as market risk, is the risk that arises from broader market conditions and affects all participants in the market.

61
Q

Can systematic risk be reduced through diversification?

A

No, systematic risk cannot be reduced through diversification. It affects the entire market, and all companies are subject to it.

62
Q

What is an example of systematic risk?

A

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
Q

How does diversification affect specific and systematic risks?

A

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
Q

What is the key strategy for effective diversification?

A

Diversify across assets that are less perfectly correlated or don’t move in the same direction to reduce overall portfolio risk.

65
Q

Why might investing in both Tesco and Morrison not offer significant diversification benefits?

A

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
Q

What is covariance?

A

Covariance is a measure of how two assets move together. It indicates the degree to which the returns on two assets are correlated.

67
Q

What does a positive covariance between two assets indicate?

A

A positive covariance indicates that the two assets tend to move in the same direction at the same time.

68
Q

What does a negative covariance between two assets indicate?

A

A negative covariance indicates that the two assets tend to move in opposite directions.

69
Q

What is the formula for calculating covariance?

A
70
Q

What is the estimator for covariance based on sample data?

A
71
Q

What is correlation?

A

Correlation is a normalized form of covariance that measures the strength and direction of a linear relationship between two variables.

72
Q
A
73
Q

What does a positive correlation coefficient indicate?

A
74
Q

What does a correlation coefficient of zero mean?

A
75
Q

What does a negative correlation coefficient indicate?

A
76
Q

What is the range of possible values for the correlation coefficient?

A
77
Q

What is the formula for estimating the sample correlation coefficient?

A
78
Q

What does covariance measure?

A

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
Q

What does a positive covariance between Tesco and Morrison indicate?

A

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
Q

How is covariance calculated?

A
81
Q

What does the diagonal of a variance-covariance matrix represent?

A

The diagonal of a variance-covariance matrix represents the variances of the individual assets (covariance of a variable with itself).

82
Q

What do the off-diagonal elements of a variance-covariance matrix represent?

A

The off-diagonal elements represent the covariance between two different assets.

83
Q

How do you calculate correlation from covariance?

A
84
Q

What does a correlation coefficient of 0.584 between Tesco and Morrison indicate?

A

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
Q

What is the purpose of calculating covariance and correlation in finance?

A

Covariance and correlation help investors understand the co-movement of asset returns, which is crucial for diversification and managing portfolio risk.

86
Q

How does diversification benefit from covariance and correlation analysis?

A

Diversification benefits when assets have low or negative covariance or correlation, reducing specific risk and stabilizing portfolio returns.

87
Q

What is a portfolio?

A

A portfolio is a collection of investments in different areas or assets.

88
Q

How do you calculate the return of a portfolio with different weights for assets?

A
89
Q

What is the variance of a two-asset portfolio with equal weights?

A
90
Q

What is the formula for the variance of a two-asset portfolio with different weights?

A
91
Q

How is the expected return of a portfolio consisting of Tesco and Morrison shares calculated?

A
92
Q

How is the variance of a portfolio consisting of Tesco and Morrison shares calculated?

A
93
Q

How is the standard deviation of a portfolio calculated?

A
94
Q

What is the expected return and variance for a portfolio with 30% in Tesco and 70% in Morrison?

A

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