Department

FinanceCourse Code

MGFB10H3Professor

Derek ChauChapter

8This

**preview**shows half of the first page. to view the full**3 pages of the document.**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; (P1 – P0) / P0 where P1 the selling price or current market share

•total return 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

•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 = ∑ (ri – Probi)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 = √ [(∑ (ri – r-bar)2) / (n – 1)]

•variance the standard deviation squared; denoted as 2 and expressed in units of %2

•ex ante = √ [∑ (Probi) (ri – ERi)]

•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 (ERA – ERB)

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