# Ethical and Professional standards and quantitative methods

\[TOC]

## ethics and trusting the investment profession

> ethics: the study of moral principles or making good choices. Ethics encompasses a set of moral principles and rules of conduct that provide guidance for our behavior. stakeholders: individuals or groups of individuals who may be affected either directly or indirectly by a decision and thus have an interest, or stake, in the decision. code of ethics: an established guide that communicates an organization's values and overall expectations regarding member behavior. A code of ethics serves as a general guide for how community members should act. standards of conduct: behaviors required by a group; established **benchmarks** that clarify or enhance a group's code of ethics. a profession refers to a group of people with specialized skills and knowledge who serve others and agree to behave in accordance with a code of ethics.

### challenges to ethical behavior

* people tend to believe that they are ethical people and that their ethical standards are higher than average.
* decision makers often fail to recognize and/or significantly underestimate the effect of situational influences, such as what other people around them are doing.

> situational influences: external factors, such as environmental or cultural elements, that shape our behavior.

### the importance of ethical conduct in the investment industry

### Ethical VS. Legal standards

Not all unethical actions are illegal, and not all illegal actions unethical. In general, ethical decisions require more judgment and consideration of the impact of behavior on many stakeholders compared to legal decisions.

### ethical decision-making frameworks

the following ethical decision-making framework is presented in the Level 1 CFA curriculum:

* Identify: relevant facts, stakeholders and duties owed, ethical principles, conflicts of interest.
* Consider: situational influences, additional guidance, alternative actions
* Decide and act
* Reflect: Was the outcome as anticipated? Why or why not?

## code of ethics and standards of professional conduct

members are strongly urged to discuss with their supervisors and legal and compliance departments the content of the Code and Standards and the members' general obligations under the Code and Standards.

#### Mission

To lead the investment profession globally by promoting the highest standards of ethics, eduction, and professional excellence for the ultimate benefit of society.

Several circumstances can prompt such as inquiry: 1. self-disclosure by members or candidates on their annual professional conduct statements of involvement in civil litigation or a criminal investigation, or that the member or candidate is the subject of a written complaint. 2. written complaints about a member of candidate's professional conduct that are received by the Professional Conduct staff. 3. evidence of misconduct by a member or candidate that the Professional Conduct staff received through public sources, such as a media article or broadcast. 4. a report by a CFA exam proctor of a possible violation during the examination. 5. analysis of exam materials and monitoring of social media by CFA institute.

the Professional Conduct staff may decide: 1) that no disciplinary sanctions are appropriate, 2) to issue a cautionary letter, or 3) to discipline the member or candidate

## CFA institute code of ethics and standards of professional conduct

### the Code of Ethics

### Standards of Professional Conduct

1. Professionalism
   * relationship between the Code and Standards and Applicable Law
   * participant in or Association with Violations by Others
   * Investment Products and Applicable laws
   * knowledge of the law members must understand and comply with all applicable laws, rules and regulations of ant government, regulatory organization, licensing agency... in the event of conflict, members must comply with the more strict law, rule or regulation.
   * independence and objectivity

     &#x20; members must use reasonable care and judgment to achieve and maintain independence and objectivity in their professional activities. Members must not offer, solicit, or accept any gift, benefit, compensation or consideration that reasonably could be expected to compromise their own or another's independence and objectivity.
   * misrepresentation

     &#x20; members must not knowingly make any misrepresentations relating to investment analysis, recommendations, actions, or other professional activities.
   * misconduct

     &#x20; members must not engage in any professional conduct involving dishonesty, fraud, or deceit or commit any act that reflects adversely on their professional reputation, integrity or competence.
2. Integrity of Capital Markets
   * buy-side clients
   * fund manager and custodial(保管的) relationships
   * investment banking relationships
   * performance measurement and attribution
   * public companies
   * credit rating agency opinions
   * influence during the manager selection/procurement process
   * issuer-paid research
   * travel funding
   * material nonpublic information members who possess material nonpublic information that could affect the value of an investment must not act or cause others to act on the information

     > under so-called mosaic theory, reaching an investment conclusion through perceptive analysis of public information combined with non-material nonpublic information is not a violation of the Standard.
   * market manipulation

     &#x20; members must not engage in practices that distort prices of artificially inflate trading volume with the intent to mislead market participant
3. Duties to Clients
   * loyalty, prudence and care
     * understanding the application of loyalty, prudence and care
     * identifying the actual investment client
     * developing the client's portfolio
     * soft commission policies
     * proxy voting policies

       members and candidates must:
     * manage pools of client assets in accordance with the terms of the governing documents
     * make investment decisions in the context of the total portfolio
     * inform clients of any limitations in an advisory relationship
     * vote proxies in an informed and responsible manner. Due to cost-benefit considerations, it may not be necessary to vote all proxies.
     * client brokerage, or soft dollars or soft commissions, must be used to **benefit** the client
     * the client may be the investing public as a whole rather than a specific entity or person
   * fair dealing
     * investment recommendations
     * investment action

       members and candidates must deal fairly and objectively with all clients when providing investment analysis, making investment recommendations, taking investment action, or engaging in other professional activities
     * do not discriminate against any clients when disseminating(传播) recommendations or taking investment action
     * difference service levels are acceptable, but they must not negatively affect any clients
     * give all clients a fair opportunity to act on every recommendation
     * treat clients fairly in light of their investment objectives and circumstances
   * suitability
     * when members are in an advisory relationship with a client, they must:
       * make a reasonable inquiry into a client's or prospective client's investment experience, risk and return objectives, and financial constraints prior to making any investment recommendation or taking investment action and must reassess and update this information regularly
       * determine that an investment is suitable to the client's financial situation and consistent with the client's written objectives, mandates and constraints before making an investment recommendation or taking investment action
       * judge the suitability of investments in the context of the client's total portfolio
     * when members are responsible for managing a portfolio to a specific mandate, strategy, or style, they must make only investment recommendations or take only investment actions that are consistent with the stated objectives and constraints of the portfolio.
   * performance presentation

     &#x20; when communicating investment performance information, members must take reasonable efforts to ensure that it is fair, accurate and complete
   * preservation of confidentiality

     &#x20; members must keep information about current former and prospective clients confidential unless:

     * the information concerns illegal activities on the part of the client
     * disclosure is required by law
     * the client or prospective client permits disclosure of the information
4. Duties to Employers
   * loyalty

     &#x20; in matters related to their employment, members must act for the benefit of their employer and not deprive their employer of the advantage of the skills and abilities, divulge confidential information, or otherwise cause harm to their employer.
   * responsibilities of supervisors

     &#x20; members  must make reasonable efforts to ensure that anyone subject to their supervision or authority complies with applicable laws, rules, regulations, and the Code and Standards.
   * additional compensation arrangements

     &#x20; members must not accept gifts, benefits, compensation, or consideration that competes with or might reasonably be expected to create a conflict of interest with their employers' interest unless they obtain written consent from all parties involved.
5. Investment Analysis, Recommendations, and Actions
   * diligence and reasonable basis

     &#x20; members must: 1) exercise diligence, independence, and thoroughness in analyzing investments, making investment recommendations and taking investment actions. 2) have a reasonable and adequate basis, supported by appropriate research and investigation, for any investment analysis, recommendation, or action.
   * communication with clients and prospective clients

     &#x20; members must:

     * disclose to clients the basic format and general principles of the investment process they use to analyze investment, select securities and construct portfolios and must promptly disclose any changes that might materially affect those processes.
     * disclose to clients and prospective clients significant limitations and risks associated with the investment process
     * use reasonable judgment in identifying which factors are important to their investment analysis, recommendations or actions and include those factors in communications with clients and prospective clients
     * distinguish between fact and opinion in the presentation of investment analysis and recommendations.
   * record retention

     &#x20; members must develop and maintain appropriate records to support their investment analyses, recommendations, actions, and other investment-related communications with clients and prospective clients.
6. Conflicts of Interest
   * disclosure of conflict
     * disclosure of conflicts to employers
     * disclosure to clients
     * cross-departmental conflicts
     * conflicts with stock ownership
     * conflicts as director

       member and candidates must make full and fair disclosure of all matters that could reasonably be expected to impair their independence and objectivity or interfere with respective duties to their clients, prospective clients and employer. also must ensure that such disclosure are prominent, are delivered in plain language and communicate the relevant information effectively.
     * disclosure of broker-dealer market-making activities would be included. Board service as well.
     * **actual ownership of stock** in companies is the most common conflict
     * another is a member's compensation/bonus structure: immediate or long-term
     * must give employers enough information to judge the impact of a conflict, to avoid and report them.
   * priority of transactions

     &#x20; investment transactions for clients and employers must have priority over investment transactions in which a Member is the beneficial owner
   * referral fees

     &#x20; members must disclose to their employer, clients and prospective clients as appropriate any compensation, consideration or benefit received from or paid to others for the recommendation of products or services.
7. Responsibilities as a CFA Institute Member or CFA Candidate
   * conduct as participants in CFA institute program

     &#x20; members must not engage in any conduct that compromises (危及) the reputation or integrity of CFA institute or the CFA designation or the integrity, validity, or security of CFA institute programs.
   * reference to CFA institute, the CFA Designation and CFA program

     &#x20; when referring to CFA institute, CFA Institute membership... Members must not misrepresent or exaggerate the meaning or implications of membership in CFA institute, holding the CFA designation or candidacy in the CFA program.

## GIPS

## quantitative methods

### time lines

* discounting: moved to the beginning of the investment period to calculate the PV through a process called discounting
* compounding: to the end of the period to calculate the FV using a process called compounding.

$$NPV = \sum\_{t=0}^N \frac{CF\_t}{(1+r)^t}$$ where r=the discount rate (opportunity cost of capital)

* ordinary annuity: has a first cash flow that occurs one period from now (indexed at t=1)
* annuity due: has a first cash flow that occurs immediately (indexed at t=0)

nominal risk-free rate = real risk-free rate + expected inflation rate

required interest rate on a security = nominal risk-free rate + default risk premium + default risk premium + liquidity premium + maturity risk premium

### stated and effective rates

* effective annual rate (EAR) $$EAR = (1 + Periodic\ interest\ rate)^m - 1$$ where: periodic rate = stated annual rate/m m = the number of compounding periods per year

  with continuous compounding $$EAR = e^{r\_s} - 1$$

## discounted cash flow applications

Given that shareholder wealth maximization is the ultimate goal of the firm, always select the project with the **greatest NPV** when the IRR and NPV rules provide conflicting decisions.

* holding period return (HPR)

  &#x20; $HPR = (P\_1 - P\_0 + D\_1)/P\_0$
* money weighted return: applies the concept of IRR to investment portfolios. The  money weighted rate of return is defined as the internal rate of return on a portfolio, taking into account all cash inflows and outflows.
* time weighted rate of return: measures compound growth. It is the rate at which $1 compounds over a specified performance horizon. Time-weighting is the process of averaging a set of values over time. The annual time-weighted return for an investment may be computed by performing the following steps:
  1. value the portfolio immediately preceding significant additions or withdrawals. From subperiods over the evaluation period that correspond to the dates of deposits and withdrawals.
  2. compute the holding period return (HPR) of the portfolio for each subperiod.
  3. compute the product of (1+HPR) for each subperiod to obtain a total return for the entire measurement period $\prod\_{i=1}^N (1+HPR\_i)$. If the total investment period is greater than one year, you must take the geometric mean of the measurement period return to fins the annual time-weighted rate of return.
* in the investment management industry, the time-weighted rate of return is the preferred method of performance measurement, because it is not affected by the timing of cash inflow and outflow.

## money market yields

* bank discount basis: a quoting convention that annualizes, on a 360-day year, the discount as a percentage of face value.

  &#x20; $$r\_{BD} = \frac{D}{F} \frac{360}{t}$$

  &#x20; where

  &#x20; $r\_{BD}$ = the annualized yield on a bank discount basis

  &#x20; D = the dollar discount, which is equal to the difference between the face value of the bill, F, and its purchase price, $P\_0$

  &#x20; F = the face value of the T-bill

  &#x20; t = the actual number of days remaining to maturity

  &#x20; 360 = bank convention of the number of days in a year
* holding period return (HPR)

  &#x20; $HPR = (P\_1 - P\_0 + D\_1)/P\_0$
* effective annual yield (EAY)

  &#x20; $$EAY = (1 + HPY)^{365/t} - 1$$
* money market yield (also known as the CD equivalent yield)

  &#x20; $$r\_{MM} = \frac{360 r\_{BD}}{360 -  t \times r\_{BD} }$$

## statistical concepts and market returns

* descriptive statistics
* inferential(推理) statistics

### types of measurement scales

* nominal scales: no particular order
* ordinal scales
* interval scales: temperature
* ratio scales

### populations and samples

* population: is defined as all members of a specified group
* sample: a subset of a population
* parameter: any descriptive measure if a population characteristic is referred to as a parameter
* mode: is the value that occurs most frequently in a data set. When a set of data has two or three values that occur most frequently, it is said to be bimodal or trimodal, respectively.
* harmonic mean is used for certain computations, such as the average cost of shares purchased over time.

  &#x20; $$\frac{N}{\sum\_{i=1}^N \frac{1}{X\_i}}$$
* for the values that are not all equal: harmonic mean < geometric mean < arithmetic mean
* the geometric mean compounds the periodic returns of every period, giving the investor a more accurate measure of the terminal value of an investment.

### other measures of location: quantiles

* Quartile: 1/4
* quintiles: 1/5
* deciles: 1/10
* percentiles: 1/100

The formula for the position of a percentile in an array with n entries sorted in ascending order is $$L\_y = (n+1) \frac{y}{100}$$ where y is the percentage point at which we are dividing the distribution and $L*y$ is the location (L) of the percentile ($P\_y$) in the array sorted in ascending order. For a dataset sizing 50, we want first quintile, which is $P\_20$, $$L*{20} = (n+1) \frac{y}{100} = (50 + 1) (20/100) = 10.2$$ $$P\_{20} \approx X\_{10} + (10.2 - 10) (X\_{11} - X\_{10})$$

### calculate and interpret a range and a mean absolute deviation and the variance and standard deviation of a population and of a sample.

* coefficient of variation (CV):

  &#x20; $$CV = \frac{s\_X}{\bar{X}} = \frac{standard\ deviation\ of\ x}{average\ values\ of\ x}$$
* the Sharp ratio

  &#x20; $$sharpe\ ratio = \frac{\bar{r\_p} - r\_f}{\sigma\_p}$$

  &#x20; where:

  &#x20; $\bar{r\_p}$ = portfolio return

  &#x20; $r\_f$ = risk-free return

  &#x20; $\sigma\_p$ = standard deviation of portfolio returns

### relative locations of the mean, median, and mode for a unimodal, nonsymmetrical distribution

* for positive (right) skew: mode < median < mean
* for negative (left) skew: mode > median > mean

### measures of sample skewness and kurtosis

* Leptokurtic: a distribution that is more peaked than a normal distribution, and has fatter tails K>3
* Platykurtic: refers a distribution that is less peaked, or flatter than a normal distribution K<3
* mesokurtic: same kurtosis as a normal distribution K == 3

$$sample\ skewness (S\_K) =\frac{n}{(n-1)(n-2)} \frac{\sum\_{i=1}^n(X\_i - \bar{X})^3}{s^3} \approx \frac{1}{n} \frac{\sum\_{i=1}^n(X\_i - \bar{X})^3}{s^3}$$ $$sample\ kurtosis = \frac{1}{n} \frac{\sum\_{i=1}^n(X\_i - \bar{X})^4}{s^4}$$

excess kurtosis = sample kurtosis - 3

## probability concepts

* exhaustive events (完备事件)
* subjective probability: a probability drawing on personal or subjective judgment
* priori probability: a probability based on logical analysis rather than on observation or personal judgment
* odds for E: P(E)/(1 - P(E))

$$\sigma^2(R\_p) = \sum\_{i=1}^n \sum\_{j=1}^n w\_i w\_j Cov(R\_i, R\_j)$$

## common probability distribution

* A cumulative distribution function (CDF), defines the probability that a random variable, X, takes on a value equal to or less than a specific value, x.
* tracking error: the standard deviation of the differences between a portfolio's return and benchmark's returns; a synonym of active risk.
* the limit of a exercise, as the compounding will produce still larger and shorter, is called continuous compounding. The effective annual rate, based on continuous compounding for a stated annual of $R\_{cc}$, cane be calculated from the formula:

  $$effective\ annual\ rate = e^{R\_{cc}} - 1$$

## distribution of the sample man

* tge central limit theorem states that for a population which a mean $\mu$ and a finite variance $\sigma^2$, the sampling distribution of the sample mean of all possible samples of size n (for n $\geq$ 30) will be approximately normally distributed with a mean equal to $\mu$ and a variance equal to $\sigma^2/n$
* confidence interval $$confidence\ interval = point\ estimate \pm (reliability\ factor \times standard\ error)$$
* confidence intervals for the population mean (Normally distributed population with known variance) $$\bar{X} \pm z\_{\alpha/2} \frac{\sigma}{\sqrt{n}}$$
* reliability factors for confidence intervals based on the standard normal distribution
  * 90% confidence intervals: $z\_{0.05} = 1.65$
  * 95% confidence intervals: $z\_{0.025} = 1.96$
  * 99% confidence intervals: $z\_{0.005} = 2.58$
* confidence intervals for the population mean (Large sample, population variance unknown) $$\bar{X} \pm z\_{\alpha/2} \frac{s}{\sqrt{n}}$$
* confidence intervals for the population mean (population variance unknown) $$\bar{X} \pm t\_{\alpha/2} \frac{s}{\sqrt{n}}$$ where the number of degrees of freedom for $t\_{\alpha/2}$ is n-1 and n is the sample size

| sampling from                                | statistic for small sample size | statistic for large sample size |
| -------------------------------------------- | ------------------------------- | ------------------------------- |
| normal distribution with known variance      | z                               | z                               |
| normal distribution with unknown variance    | t                               | t\*                             |
| nonnormal distribution with known variance   | not available                   | z                               |
| nonnormal distribution with unknown variance | not available                   | t\*                             |

\*use of z also acceptable

* a consistent estimator's sampling distribution become concentrated on the value of parameter it is intended to estimate as the sample size approaches infinity.
* a standard normal distribution has tails that approach zero faster than the t-distribution. as degree of freedom increase, the tail of the t-distribution become less fat and the t-distribution begins to look more like a standard normal distribution.
* potential mistakes in the sampling method can bias results. These bias include data mining (significant relationship that have occurred by chance), sample selection bias (selection is non-random), look-ahead bias, survivorship bias (using only surviving mutual funds, hedge funds, etc.) and time-period bias (the relation does not hold over other time periods).
* out-of-sample test: is used to investigate the presence of data mining bias. Such a test uses a sample that does not overlap the time period of the sample on which a variable, strategy, or model was developed.

## hypothesis testing

### hypothesis testing procedure

state the hypothesis -> select the appropriate test statistic -> specify the decision rule regarding the hypothesis -> collect the sample and calculate the sample statistics -> make a decision regarding the hypothesis -> make a decision based on the results of the test

> null hypothesis $H\_0$: is the hypothesis that the researcher wants to reject alternative hypothesis $H\_a$: is what is concluded if there is sufficient evidence to reject the null hypothesis. It is usually the alternative hypothesis that you are really trying to assess.

* the general decision rule for a two-tailed test is:

  &#x20; reject $H\_0$ if test statistic > upper critical value or test statistic < lower critical value

  &#x20; test statistic = (sample statistic - hypothesized value)/(standard error of the sample statistic)
* type of error:
  * type I error: the rejection of the null hypothesis when it is actually true
  * type II error: the failure to reject the null hypothesis when it is actually false.
* $(1 - \alpha)$ confidence interval represents the range of values of the test statistic for which the null hypothesis will not be rejected at an $\alpha$ significance level.
* the p-value is the smallest level of significance at which the null hypothesis can be rejected. the smaller the p-value, the stronger the evidence against the null hypothesis and in favor of the alternative hypothesis.

### hypothesis tests concerning the mean

* test statistic for hypothesis tests of the population mean (practical case population variance unknown)

  &#x20; $$t\_{n-1} = \frac{\bar{X} - \mu\_0}{s/ \sqrt{n}}$$
* the z-Test alternative

  &#x20; $$z = \frac{\bar{X} - \mu\_0}{\sigma / \sqrt{n}}$$

  &#x20; $$z = \frac{\bar{X} - \mu\_0}{s / \sqrt{n}}$$
* test statistic for a test of the different between two population means (normally distributed populations, population variances unknown but assumed equal)

  &#x20; $$t = \frac{(\bar{X\_1} - \bar{X\_2}) - (\mu\_1 - \mu\_2)}{(\frac{s\_p^2}{n\_1} + \frac{s\_p^2}{n\_2})^{1/2}}$$

  &#x20; where $s\_p^2 = \frac{(n\_1 - 1) s\_1^2 + (n\_2 - 1) s\_2^2}{n\_1 + n\_2 - 2}$
* test statistic for a test of the different between two population means (normally distribution populations, unequal and unknown population variances)

  &#x20; $$t = \frac{(\bar{X\_1} - \bar{X\_2}) - (\mu\_1 - \mu\_2)}{(\frac{s\_1^2}{n\_1} + \frac{s\_2^2}{n\_2})^{1/2}}$$

  &#x20; where the degree of freedom df is

  &#x20; $$df = \frac{(\frac{s\_1^2}{n\_1} + \frac{s\_2^2}{n\_2})^{1/2}}{(\frac{(s\_1^2/n\_1)^2}{n\_1} + \frac{(s\_2^2/n\_2)^2}{n\_2})^{1/2}}$$

### tests concerning mean differences

* test statistic for a test of mean differences (normally distributed populations, unknown population variances)

  &#x20; $$t = \frac{\bar{d} - \mu\_{d0}}{s\_{\bar{d}}}$$

  &#x20; where the sample mean difference is:

  &#x20; $$\bar{d} = \frac{1}{n} \sum\_{i=1}^n d\_i$$

  &#x20; and the sample variance is

  &#x20; $$s\_d^2 = \frac{\sum\_{i=1}^n (d\_i - \bar{d})^2}{n - 1}$$

  &#x20; and the stand error of the mean differences as follows:

  &#x20; $$s\_{\bar{d}} = \frac{s\_d}{\sqrt{n}}$$

### hypothesis tests concerning variance

* test statistic for tests concerning the value of a population variance (normal population)

  &#x20; $$\chi^2 = \frac{(n-1)s^2}{\sigma\_0^2}$$

  &#x20; with n-1 degree of freedom. In the numerator of the expression is the sample variance, calculated as

  &#x20; $$s^2 = \frac{\sum\_{i=1}^n (X\_i - \bar{X})^2}{n - 1}$$
* test concerning the equity (inequity) of two variances

  &#x20; $$F = \frac{s\_1^2}{s\_2^2}$$

  &#x20; with $df\_1 = n\_1 - 1$ numerator degrees of freedom and $df\_2 = n\_2 - 1$ denominator degrees of freedom.

## other issues: nonparametric inference

* parametric test: any test (or procedure) concerned with parameters or whose validity depends on assumptions concerning the population generating the sample
* nonparametric test: a test that is not concerned with a parameter, or that makes minimal assumptions about the population from which a sample comes

### tests concerning correlation: the Spearman Rank correlation coefficient

1. rank the observations on X from largest to smallest. Perform same thing on Y
2. calculate the difference, $d\_i$, between the ranks of each pair of observations on X and Y
3. with n the sample size, the Spearman rank correlation is given by：

   &#x20;$$r\_s = 1 - \frac{6 \sum\_{i=1}^n d\_i^2}{n (n^2 - 1)}$$

## test statistic methods conclusion

* test the mean of a normally distributed population with
  * unknown variance: t test
  * known variance: z test
* test whether observed difference between two means is statistically significant:
  * independent: test differences between means, t test
  * dependent: paired comparison tests
* test the difference between two population means from normally distributed populations with unknown variance, if we assume the variance:
  * equal: t test based on pooling the observations of the two samples $s\_p$
  * not equal: t test $s\_1$ and $s\_2$
* test concerning the variance of a single, normally distributed population: $\chi$ with n-1 degrees of freedom
* test concerning differences between the variances of two normally distributed populations based on two random, independent samples: F-test

## technical analysis

> technical analysis: a form of security analysis that uses price and volume data, which is often displayed graphically, in decision making.

assumption of technical analysis:

* security markets are NOT efficient

the underlying logic of technical analysis is simple:

* supply and demand determine prices
* changes in supply and demand cause changes in prices
* prices can be projected with charts and other technical tools

### technical analysis tools

* charts
  * line chart: has one data per time interval
  * bar chart: has four bits of data in each entry: high/low/open/close
  * candlestick chart
  * point and figure chart
  * scale: linear/logarithmic
  * volume
  * time interval
  * relative strength analysis

### trend

> trend: a long-term pattern of movement in a particular direction.

uptrend line: the lows of the price chart downtrend line: the highs of the price chart support: a price range in which buying activity is sufficient to stop the decline in the price of a security. resistance: a price range in which selling activity is sufficient to stop the rise in the price of a security. change in polarity principle: a tenet of technical analysis that once a support level is breached, it becomes a resistance level. The same holds true for resistance levels; once breached, they become support levels.

### chart patterns

* reversal patterns
  * head and shoulders
    * setting price targets with head and shoulders pattern

      &#x20; price target = neckline - (head - neckline) = 2\*headline - head
  * inverse head and shoulders
    * setting price targets with inverse head and shoulders pattern

      &#x20; price target = neckline + (neckline - head) = 2\*headline - head
  * double tops and bottoms
  * triples tops and bottoms: three peaks/bottoms at toughly the same price level
* continuation patterns
  * triangles
  * rectangle pattern
  * flags and pennants

### technical indicator

* price based indicators
  * moving average lines
  * Bollinger Band: the more volatile the security being analyzed becomes, the wider the range becomes between the two outer lines or bands.
* momentum oscillators:
  * momentum or rate of change oscillator (ROC)

    &#x20; $$M = (V - V\_x) \times 100$$

    &#x20; where

    &#x20; M =momentum oscillator value

    &#x20; V = last closing price

    &#x20; $V\_x$ = closing price x days ago, typically 10 days
  * relative strength index

    &#x20; $$RSI = 100 - \frac{100}{1 + RS}$$

    &#x20; where $RS = \frac{\sum (up changes for the period under consideration)}{\sum (|down changes for the period under consdieration|)}$

    &#x20; the index construction forces the RSI to lie within 0 and 100. A value above 70 presents an overbought situation; values below 30 suggest the asset is oversold.
  * stochastic oscillator

    &#x20; $$% K = 100 (\frac{C - L14}{H14 - L14})$$
  * moving average convergence/divergence oscillator (MACD)
* sentiment indicators
  * opinion polls
  * calculated statistical indices
* flow-of-funds indicators
  * arms index or TRIN (for "short-term trading index")

    &#x20; arms index = \[(numbers of advancing issues)/(number of declining issues)]/\[(volume of advancing issues)/(volume of declining issues)]
  * margin debt
  * new equity issuance

### cycles

* Kondratieff Wave (K Wave): A 54-year long economic cycle postulated by Nikolai Kondratieff
* 18-Year Cycle: is most often mentioned in connection with real estate prices, but it can also be found in equities and other markets
* decennial pattern: is the pattern of average stock market returns (based on the DJIA) broken down on the basis of the last digit in the year. Years ending with a 0 have had the worst performance, and years ending with a 5 have been by far the best.
* presidential cycle: refers to a superior performance in the third year

### Elliott Wave Theory: the relationship among wave heights are frequently Fibonacci ratios.

* grand supercycle
* supercycle
* cycle
* primary
* intermediate
* minor
* minute
* minuette
* subminuette

### intermarket analysis

use relative strength analysis

### miscellaneous

* valuation models cannot be used to determine fundamental intrinsic value for commodities and currencies which do not have underlying financial statements or an income stream.
