- Book measures of returns use book value inputs from accounting-based financial statements. Market returns use cash flow inputs. The ex-ante return is the expected return of an investment. The ex-post facto return is the realized, or actual, return on an investment. The ex-ante return is calculated by: R = (forecasted dividend) + (forecasted change in price)/investment. The ex-post facto is calculated by: R = (actual dividend) + (actual change in stock price)/investment.
- Ex-ante and ex-post returns differ because of uncertainty. To the extent that actual returns differ from expected returns, the ex-post return will not equal the ex-ante return.
- A probability distribution is a graphical depiction of the expected returns on an investment and the probability of achieving those returns. Discreet distributions are created with bar charts because it is assumed that the returns can take only certain discreet values. Continuous distributions are plotted as curves because it is assumed that the returns can take on any value within a certain range.
- The arithmetic mean of a distribution is the expected return of the investment. It is what on average the investment is expected to return. The variance and standard deviation of a distribution are measures of the “spread” of possible returns around the average return and are indicators of the riskiness of the investment.
- Risk is defined in finance as the potential for variability of returns.
- The assumption of a normal distributions allows for the calculation of an estimate of the likelihood that an ex post observation will be within a certain range of returns (+/- 1,2,3 standard deviations).
- Investors are rewarded for risk, but risk does not guarantee higher returns. Higher risk guarantees a higher likelihood of a greater return, but it also guarantees a higher likelihood of a greater loss. The shorter the period a risky stock is held, the less the likelihood that the investor will be rewarded for taking the risk. This relates to the uncertainty resolution principle, whereby over time the ex-post and ex-ante returns merge.
- Imperfect correlation means that two or more stocks in a portfolio are not directly correlated with one another. That is, when one stock does well, the other does not do as well or does poorly, and vice versa. This concept is important because building a portfolio of imperfectly correlated stocks reduces the overall risk of the portfolio.
- The expected return of a portfolio is determined by summing the expected returns of each stock in the portfolio times their relative weights in the portfolio. The variance of a portfolio is determined by multiplying the weight of each asset in the portfolio (squared) by the variance of each asset in the portfolio and adding (N)(Wa*Wb*Va*Vb*Ccab).
- Diversification reduces risk intuitively because in a portfolio with stocks of different risks (variability), a gain or loss in one security would be offset by a different gain or loss in another security, and the overall risk would be less. Mathematically, if a portfolio only contained a single stock, risk would be defined as the standard deviation of the expected returns. However, with multiple stock portfolios that are imperfectly correlated, the overall standard deviation is a function of the weighted average of each of the stocks’ variances, plus a correlation coefficient.
- Because the future is uncertain and because statistically trends over time generally continue through the long run, historical stock information is the best available for estimating the future performance of a particular stock.

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