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Chapter 8

Chapter 8 Notes

Course Code
Derek Chau

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Chapter 8 Risk, Return, and Portfolio Theory Notes
8.1 Measuring Returns
Ex Post versus Ex Ante Returns
ex post returns past or historical returns
ex ante returns future or expected returns
the return on investment consists of 2 components: the income yield and the capital gain (or loss) yield
income yield the return earned by investors as a periodic cash flow; CF1 / P0 where CF1 is expected cash flows to be received
capital gain (or loss) the appreciation (or depreciation) in the price of an asset from some starting price, usually the purchase
price or the price at the start of the year; (P1P0) / P0 where P1 the selling price or current market share
total return income yield plus the capital gain (or loss) yield; (CF1 + P1P0) / P0
paper losses capital losses that people do not accept as losses until they actually sell and realize them
day trader someone who buys and sells based on intraday price movements
mark to market carrying securities at the current market value regardless of whether they are sold
Measuring Average Returns
arithmetic mean or average the sum of all returns divided by the total number of observations; ri / n
geometric mean the average or compound growth rate over multiple time periods; [(1 + r1) (1 + r2)…(1 + rn)]1/n – 1
the geometric mean is always less than the arithmetic mean, unless the values are all identical
standard deviation a measure of risk over all the observations; the square root of the variance, denoted as
the difference between the AM and GM returns is approximately half the variance
the more variable the annual returns, the bigger the difference between the AM and GM measures of return
the AM is appropriate when we are trying to estimate the typical return for a given period, such as a year
we use the GM when we are interested in determining the “true” average rate of return over multiple periods
Estimating Expected Returns
expected returns estimated future returns
expected returns are estimated based on historical averages, but the problem is that there is no guarantee the past will repeat itself
an alternative approach is to use all available information to assess the most likely returns under various future scenarios and
then attach probabilities to the likelihood of each occurring
using this approach, the expected return is estimated as the weighted average of the expected returns under each scenario; the
weights correspond to the probability actually occurring ER = (riProbi)where ER = the expected return
on an investment, ri = the estimated return in scenario i, Probi = the probability of state i occurring
8.2 Measuring Risk
range the difference between the maximum and minimum values
a more accurate measure of risk is the standard deviation, because the range only uses two observations, the maximum and
minimum, whereas the standard deviation uses all the observations
ex post = [( (rir-bar)2) / (n 1)]
variance the standard deviation squared; denoted as 2 and expressed in units of %2
ex ante = [ (Probi) (riERi)]
another commonly used measure of risk is “value at risk” (VaR); probability-based measure of loss potential to a firm
technically, it represents estimated loss (in money terms) that could be exceeded (minimum loss) at a given level of probability
a lower probability translates into a higher potential loss, all else being equal
8.3 Expected Return and Risk for Portfolios
portfolio a collection of securities, such as stocks and bonds, that are combined and considered a single asset
it is a basic proposition in finance that securities should be managed within a portfolio, rather than individually, because it is
possible to realize risk-reduction gains by combining securities into a portfolio
modern portfolio theory (MPT) theory that securities should be managed within portfolio, rather than individually, to create
risk-reduction gains; stipulates that investors should diversify investments so as not to be needlessly exposed to negative event
ERp = (wi × ERi)where ERp = expected return on portfolio, ERi = expected return on security i, and wi = portfolio weight
ERp = ERB + w (ERAERB)
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