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comm 308: introduction to corporate finance > chapter 8 book: valuing portfolios and stuff > Flashcards

chapter 8 book: valuing portfolios and stuff Flashcards

1
Q

Risk

A

the possibility of incurring harm

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2
Q

ex post returns

A

past or historical returns

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3
Q

ex ante returns

A

expected returns

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4
Q

the return on an investment consists of which two components

A

the income yield

the capital gain (or loss) yield

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5
Q

The income yield

A

the return earned in the form of a periodic cash flow received by the investors

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6
Q

the income yield formula

A

Income yield = CF1 / P0

CF1 = the expected cash flows to be received
 
P0 = the purchase price (or beginning market price)

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7
Q

The capital gain (or capital loss)

A

measures the appreciation (or depreciation) in the price of the asset from some starting price, usually the purchase price or the price at the start of the year

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8
Q

capital gain yield formula

A

Capital gain yield = (P1 - P0) / P0

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9
Q

capital gain

A

the appreciation in the price of an asset from some starting price

usually the purchase price or the price at the start of the year

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10
Q

capital loss

A

the depreciation in the price of an asset from some starting price

usually the purchase price or the price at the start of the year

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11
Q

total return formula

A

income yield plus the capital gain (or loss) yield

(CF1 + P1 - P0) / P0

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12
Q

paper losses

A

capital losses that people do not accept as losses until they actually sell and realize them

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13
Q

our decision to acknowledge paper gains and losses depends on what?

A

our investment horizon

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14
Q

A day trader

A

someone who buys and sells based on intraday price movements

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15
Q

what do we mean when we say that investors have to mark to market the prices of all financial securities over the relevant investment horizon?

A

investors always carry securities at the current market value regardless of whether they sell them

–> the total return includes the effect of paper gains and losses on securities not yet sold

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16
Q

How can we measure the ex post or historical returns?

A

The arithmetic mean or geometric average

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17
Q

The arithmetic mean or arithmetic average

A

the most commonly used value in statistics

the sum of all of the returns divided by the total number of observations

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18
Q

The arithmetic mean or arithmetic average formula

A

Arithmetic mean (AM) = (Eri / n)

ri = the individual returns

n = the total number of observations

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19
Q

The geometric mean

A

measures the compound growth rate over multiple periods

this is the growth rate in the value invested or, equivalently, the compound rate of return

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20
Q

The geometric mean formula

A

(1 + rn) ^(1/n) - 1

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21
Q

the standard deviation

A

a measure of risk over all the observations

A more accurate measure of risk

the square root of the variance, denoted as σ

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22
Q

The Arithmetic Mean is appropriate to use when?

A

when we are trying to estimate the typical return for a given period, such as a year

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23
Q

what do we use when we are interested in determining the “true” average rate of return over multiple periods?

A

the Geometric Mean

–> We use the GM because it measures the compound rate of growth in our investment value over multiple periods

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24
Q

the better way to estimate the average return when we are interested in the performance of an investment over time

A

the geometric mean

gives us a better insight

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25
expected returns
estimated future returns often estimated based on historical averages
26
problem with expected earnings
there is no guarantee the past will repeat itself
27
expected returns formula
ER = E(ri · Probi) ER = the expected return on an investment ri = the estimated return in scenario i Probi = the probability of state i occurring
28
difference between arithmetic mean and expected returns
they both look at past data the difference is that expected returns consider different probabilities while arithmetic mean weights the probabilities equally
29
which is better between the scenario based and historic approach in the short term future? why?
scenario based approach because where we are today has a huge bearing on what is likely to happen over a short period
30
which is better between the scenario based and historic approach in the long term future? why?
historic based approach tends to be better because it reflects what actually happens, even if it was not expected
31
the range
the difference between the maximum and minimum values
32
why is the standard deviation a more accurate measure of risk than the range?
because the range uses only two observations, the maximum and minimum, whereas the standard deviation uses all the observations
33
The formula of the standard deviation for a series of historical or ex post returns is historical approach
ex post σ = ((E(ri - r_)^2) / (n - 1))^(1/2) ri = the return in year i r_ = the average return n = number of observations basically, whats inside the square root is the variance
34
the variance
denoted as σ^2 square of the standard deviation expressed in units of %2
35
The formula of the standard deviation for a scenario based ex ante returns scenario based approach
ex ante σ = (E(Probi)(ri - ER)^2)^(1/2)
36
ex ante is scenario based or historic approach
scenario based approach
37
ex post is scenario based or historic approach
historic approach
38
The coefficient of variation (CV)
an alternative measure of risk compared to the variance or standard deviation a standardized measure of dispersion that can be used to compare the risks of two investments with different arithmetic means not expressed as a percentage
39
The coefficient of variation (CV) formula
Standard deviation of returns / Arithmetic mean return
40
a higher risk is a higher or lower coefficient of variation (CV)?
a lower coefficient of variation (CV)
41
A portfolio
a collection of securities, such as stocks and bonds, that are combined and considered a single asset may refer to the holdings of a single investor or to holdings that are managed as a unit by one or more portfolio managers on behalf of their clients
42
modern portfolio theory (MPT)
The study of portfolios and the potential gains related to them the theory that securities should be managed within a portfolio, rather than individually, to create risk-reduction gains also stipulates that investors should diversify their investments so as not to be unnecessarily exposed to a single negative event
43
why investors should diversify their investments?
so that they are not unnecessarily exposed to a single negative event
44
The expected return on a portfolio
the weighted average of the expected returns on the individual securities in the portfolio The “portfolio weight” of a particular security is the percentage of the portfolio’s total value that is invested in that security
45
The expected return on a portfolio formula
ERp = E(wi · ERi) ERp = the expected return on the portfolio ERi = the expected return on security i wi = the portfolio weight of security i
46
The standard deviation of a two-security portfolio (first formula excluding the correlation coefficient)
σp = (((WA)^2)((σA)^2) + (WB)^2)((σB)^2) + 2(WA)(WB)(COVAB))^(1/2) σp = the portfolio standard deviation COVAB = the covariance of the returns on security A and security B
47
covariance
a statistical measure of the correlation of the fluctuations of the annual rates of return of different investments related to the correlation coefficient
48
covariance first formula formula (excluding the correlation coefficient)
COVAB = EProbi · (rA,i - r_A)(rB,i - r_B) rA,i = the ith return on security A rB,i = the ith return on security B
49
the correlation coefficient
ρAB related to covariance and individual standard deviations a statistical measure that identifies how security returns move in relation to one another has a maximum value of +1.0, which denotes perfect positive correlation, and a minimum value of −1.0, which denotes perfect negative correlation
50
the correlation coefficient formula
ρAB = COVAB / (σA · σB)
51
covariance new formula with the correlation coefficient
COVAB = ρAB · σA · σB
52
the formula to calculate the portfolio standard deviation with the correlation coefficient
σp = (((wA)^2)((σA)^2) + (wB)^2)((σB)^2) + 2(wA)(wB)(ρAB · σA · σB))^(1/2)
53
what does a positive correlation coefficients imply?
that the returns on security A tend to move in the same direction as those on security B
54
what does a negative correlation coefficients imply?
the returns on security A tend to move in the opposite direction to those on security B
55
what does the covariance measure when we compare it to the correlation coefficient? (it always measures it anyways)
measures the strength, or magnitude, of the relationship between two variables
56
the lower the correlation coefficient, the lower or higher the standard deviation involved?
the lower
57
the secret of MPT
by combining securities in a portfolio, we can reduce risk risk reduction increases as we combine securities that are less than perfectly correlated
58
what does it mean when we say that the relationship between the correlation coefficient and the standard deviation of our pertfolio is bowed?
because, as it decreases towards -1, it directly touches the horizontal line perpendiculairement on the other hand, as it is at 1, it becomes on straight line (does not curve anymore)
59
how to calculate the standard deviation of a portfolio that removes all risk?
σp = wσA - (1 - w) · σB when p = -1 where, the singular w = σB / (σA + σB)
60
the basis of hedging
The perfect negative correlation case taking an offsetting position so as to minimize risk
61
three securities portfolios standard deviation
just write it on your cheat sheet if you need it bro
62
the father of modern portfolio theory
Harry Markowitz
63
Harry Markowitz's three main assumptions for investors
1. Investors are rational decision-makers. 2. Investors are risk averse 3. Investor preferences are based on a portfolio’s expected return and risk (as measured by variance or standard deviation)
64
risk averse
to dislike risk and require compensation to assume additional risk
65
efficient portfolios
those that offer the highest expected return for a given level of risk or offer the lowest risk for a given expected return
66
The first step in the Markowitz analysis
to determine the expected return-risk combinations available to investors from a given set of securities we allow the portfolio weights to vary
67
the minimum variance frontier
the curve produced when determining the expected return-risk combinations available to investors from a given set of securities by allowing the portfolio weights to vary
68
the attainable portfolios
portfolios that may be constructed by combining the underlying securities those that lie on the minimum variance frontier
69
the minimum variance portfolio (MVP)
a portfolio that lies on the efficient frontier and has the minimum amount of portfolio risk available from any possible combination of available securities
70
The importance of the minimum variance portfolio MVP
portfolios lying below it, on the bottom segment of the minimum variance frontier, are dominated by portfolios on the upper segment
71
the efficient frontier
the segment above the inefficient frontier in the minimum variance frontier Rational, risk-averse investors will be interested in holding only those portfolios (which offer the highest expected return for their given level of risk)
72
diversification
the process of investing funds across several securities, which results in reduced risk
73
Random diversification or naïve diversification
the act of randomly diversifying without regard to relevant investment characteristics, such as company size, industry classification, and so on basically, what I've been doing for 90% of the time
74
unique (non-systematic) risk or diversifiable risk
The part of the total risk that is eliminated by diversification
75
the market (systematic) risk or non-diversifiable risk
The part that is not eliminated by diversification This portion of the risk cannot be eliminated because all the securities in the portfolio will be directly influenced by overall movements in the general market or economy
76
formula for total risk
market (systematic) risk + unique (non-systematic) risk non-diversifiable risk + diversifiable risk
77
why evidence suggests the benefits of international diversification have been declining?
because global equity markets become more integrated

comm 308: introduction to corporate finance (13 decks)

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