chapter 8 book: valuing portfolios and stuff Flashcards
Risk
the possibility of incurring harm
ex post returns
past or historical returns
ex ante returns
expected returns
the return on an investment consists of which two components
the income yield
the capital gain (or loss) yield
The income yield
the return earned in the form of a periodic cash flow received by the investors
the income yield formula
Income yield = CF1 / P0
CF1 = the expected cash flows to be received
P0 = the purchase price (or beginning market price)
The capital gain (or capital loss)
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
capital gain yield formula
Capital gain yield = (P1 - P0) / P0
capital gain
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
capital loss
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
total return formula
income yield plus the capital gain (or loss) yield
(CF1 + P1 - P0) / P0
paper losses
capital losses that people do not accept as losses until they actually sell and realize them
our decision to acknowledge paper gains and losses depends on what?
our investment horizon
A day trader
someone who buys and sells based on intraday price movements
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?
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
How can we measure the ex post or historical returns?
The arithmetic mean or geometric average
The arithmetic mean or arithmetic average
the most commonly used value in statistics
the sum of all of the returns divided by the total number of observations
The arithmetic mean or arithmetic average formula
Arithmetic mean (AM) = (Eri / n)
ri = the individual returns
n = the total number of observations
The geometric mean
measures the compound growth rate over multiple periods
this is the growth rate in the value invested or, equivalently, the compound rate of return
The geometric mean formula
(1 + rn) ^(1/n) - 1
the standard deviation
a measure of risk over all the observations
A more accurate measure of risk
the square root of the variance, denoted as σ
The Arithmetic Mean is appropriate to use when?
when we are trying to estimate the typical return for a given period, such as a year
what do we use when we are interested in determining the “true” average rate of return over multiple periods?
the Geometric Mean
–> We use the GM because it measures the compound rate of growth in our investment value over multiple periods
the better way to estimate the average return when we are interested in the performance of an investment over time
the geometric mean
gives us a better insight
expected returns
estimated future returns
often estimated based on historical averages
problem with expected earnings
there is no guarantee the past will repeat itself
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
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
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
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
