Chapter 18 return on assets and risks
Investment rate of return = income / investment costs
Asset investment cost = number of assets monovalent ×
Investment income during the Closing Price = - Beginning Price + Other income
Investment income during the period yield = / Opening Price
During the net rate = (Closing Price - Opening Price + Other income during the - sell transaction costs) / (purchase price + the beginning of transaction costs)
1. Single-stage simple rate of return
The duration of each period of time in chronological order according to the asset price up and the resulting time series asset prices. The earliest a price indicated by P1, one after is P2, then you can get P1, P2, ..., Pt the time series. Investors to invest in an asset t-1 time, input price as P (t-1), holds a post to P (t) price to sell. If the asset has no other income in this period, do not consider transaction costs, then the single-phase simple investment rate of return (One Period Simple Return) R (t) is calculated as follows:
R(t) = (P(t) - P(t-1)) / P(t-1) = P(t) / P(t-1) - 1
2. Multi-period simple rate of return
If the investor t-2 in the second period at a price of P (t-2) to purchase the assets at a price of P (t) sold in period t. Two simple rate of return is calculated as follows:
R(t)2 = (P(t) - P(t-2)) / P(t-2) = P(t) / P(t-2) - 1
3. Single and Multi relationship of the simple rate of return
R & lt T (K) plurality of gains
R & lt T-J single return of
Multi-period rate of return another algorithm: a single sum of the yield on short-answer, as follows:
Different rates of return obtained by this method and multiplying the calculated, taking into account the effect of compound interest is calculated by multiplying the; and increase total investment considered after the principal, income obtained for each period not reinvested income assets.
Calculated by the single multi-period rate of return on the average rate of return involves the concept of computing a few of assets held in the past, the average income of each issue is how much. There are two ways, one is the arithmetic mean (Arithmetric Average), the other is the geometric mean (Geometric Average).
Consider the geometric average compound interest, a measure of past earnings each period k period the average investment return as the principal method of this investment in the case of assets, the arithmetic mean does not consider the effect of compound interest.
4. The annual yield
Calculation of earnings with compound interest, hypothetical time investors to hold assets for the period T, the gains rate R T , a total of m single period of one year, the annual rate of return of the asset:
Which 
is based on the arithmetic average yield of T earnings calculation, 
the geometric average rate of return, after the single-stage conversion yield of adult income is directly multiplied by the number of periods a year m, that is, the behavior of a single copy of m times the resulting rate of return.
5. Consider a simple Dividend yield
The cash dividend is the company's surplus cash is disbursed to shareholders, while the stock dividend is a way of bonus shares, the shares issued to shareholders.
Only before the record date (record date included this day) shares held by the shareholders have the right to share dividend.
a) ex-dividend price:
Closing price ex-dividend price = dividend record date - the amount of dividend per share in cash
b) ex Price:
Ex = monovalent bonus after closing price register ownership / (1 + bonus share or to increase the number of shares)
c) ex-dividend price:
Ex-dividend price = (record date of the closing price - the amount of cash dividends per share) / (1 + the number of bonus shares per share or to increase the number of shares)
Dividend yield = dividend / stock price × 100%
Earnings ratio = share price / earnings per share (EPS generally based on the company in the past year net profit divided by the total issued shares have been sold.)
6. measure of risk assets
(1) Variance
Risks of financial assets with the uncertainty of the return on assets is measured, namely variance risk measure:
Specific risk of individual assets can be expressed as:
Wherein R is a yield can happen, E (R) is the expected rate of return.
(2) downside risks
When calculating downward bias, one of the most important variable is the target rate of return, usually the minimum acceptable rate of return (Minimum Acceptable Rate of Return, MARR) representatives, MARR may be a risk-free rate of return, or 0, or return on assets average value.
Risk described with downlink deviation is called downside (Downside Risk).
(3) Value at Risk
VaR (Value at Risk, VaR) is expected at a given confidence level and the maximum loss target period. Under normal market conditions, namely fluctuations ,, at a certain level of probability α%, a financial asset or portfolio of financial VaR (α, Δt) is the maximum possible loss in the next specific period of time Δt, the mathematical formulas expressed as:
VaR risk to specific numbers shown, so that investors can clearly visually recognize the extent size of the risk; and investors can set up different confidence intervals and risk management evaluation interval.