STUDY SESSION

Code of ethicso Acting with integrity, competence, diligence, respect, and in

an ethical manner with the public, clients, prospective clients, employers, employees, colleagues, in the investment professional, and other participants in the global capital markets.

o Placing the integrity of the investment profession and the interests of clients above their own personal interests.

o Using reasonable care and exercise independent professional judgment when conducting investment analysis, making investment recommendations, taking investment actions, and engaging in other professional activities.

o Practicing and encouraging others to practice in a professional and ethical manner which reflects credit on themselves and their profession.

o Promoting the integrity of, and upholding the rules governing, capital markets.

o Maintaining and improving their professional competence and strive to maintain and improve the competence of other investment professionals

1. The Standards of Professional Conducta) Professionalism

Knowledge of the Law: Members and Candidates must understand and comply with all applicable laws, rules, and regulations of any government, regulatory organization, licensing agency etc. Members and Candidates must not knowingly participate or assist in any violation of laws, rules, or regulations and must disassociate themselves from any such violation.

Independence and Objectivity: Members and Candidates must use reasonable care and judgment to achieve and maintain independence and objectivity in their professional activities.

Misrepresentation: Members and Candidates must not knowingly make any misrepresentation relating to investment analysis, recommendations, actions, or other professional activities.

Misconduct: Members and Candidates 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.

b) Integrity of Capital MarketsMembers and Candidates having nonpublic information should not reveal the information to others. Also they should not artificially inflate trading volume with the intent to mislead market participations.

Material Non-public Information Market Manipulation

c) Duties to ClientsMembers and Candidates must act for the benefit of their clients and place their clients’ interests before their employer’s or their own interests. When they are managing a portfolio to a specific mandate the recommendations should be consistent with the stated objectives and constraints of the portfolio.

Loyalty, Prudence, and Care Fair Dealing Suitability

Performance Presentation Preservation of Confidentiality

d) Duties to employersMembers and Candidates must act for the benefit of their employers and not deprive their employer of the advantage of their skills and abilities. They must not accept gifts, benefits, compensation that competes with, or might reasonably be expected to create a conflict of interest with their employer’s interest unless they obtain written consent from all parties involved.

Loyalty Additional Compensation Arrangements Responsibilities of Supervisors

e) Investment analysis, recommendations, and actionsMembers and Candidates must have a reasonable and adequate basis, supported by appropriate research and investigations, making investment recommendations, and taking investment actions. They must also develop and maintain appropriate records to support their investment analysis, recommendations, actions, and other investment-related communications with clients and prospective clients.

Diligence and Reasonable Basis Communication with Clients and Prospective Clients Record Retention

f) Conflict of interestMembers and Candidates must disclose to their employer, clients, and prospective clients, as appropriate, any

compensation, consideration, or benefit received from, or paid to, others for the recommendations of products or services.

Disclosure of Conflicts Priority of Transactions Referral Fees

g) Responsibilities as a CFA institute member of a CFA candidateMembers and Candidates must not engage in any conduct that compromise the reputation of integrity of CFA Institute or the CFA designation or the integrity, validity, or security of the CFA examinations.

Conduct as Members and Candidates in the CFA Program

Reference to CFA Institute

2. Introduction To The Global Investment Performance Standards (GIPS)GIPS are a set of ethical principles based on a standardized, industry-wide approach. GIPS apply to investment management firms and are intended to serve prospective and existing clients of investment firms. GIPS allow clients to more easily compare investment performance among investment firms and more confidence in reported performance.

1. GIPS Objectives: To obtain global acceptance of calculation and presentation

standards in a fair, comparable format with full disclosure To ensure consistent, accurate investment performance data

in areas of reporting, records marketing, and presentations,

To promote fair competition among investment management firms in all markets without unnecessary entry barriers for new firms

To promote global “self-regulation”

2. Key Characteristics of GIPS To claim compliance, an investment management firm must

define its “firm.” This definition should reflect the “distinct business entity” that is held out to clients and prospects as the investment firm.

GIPS are ethical standards for performance presentation which ensure fair representation of results and full disclosure.

Firms are required to use certain calculation and presentation standards and make specific disclosures.

Input data must be accurate. GIPS contain both required and recommended provisions –

firms are encouraged to adopt the recommended provisions. Firms are encouraged to present all pertinent additional and

supplemental information. There will be no partial compliance and only full compliance

can be claimed Follow the local laws for cases in which a local or country

specific law or regulation conflict with GIPS, but disclose the conflict.

Certain recommendations may become requirement in the future.

3. Definitions:a. Firm: Include the broadest definition of the firm, including all

geographical offices marketed under the same brand name.

b. Document policies and procedure: Document, in writing, policies and procedures the firm uses to comply with GIPS.

4. Major Sections of GIPS Standards:

5. Fundamentals of compliance:Fundamental issues involved in complying with GIPS are Definition of firm Documentation of firm policies and procedures with respect

to GIPS compliance Complying with GIPS update Claiming compliance

Input Data

Input data should be consistent in order to establish full, fair, and comparable investment performance presentations.

Calculating Methodology

Uniformity in methods across firms is required so that their results are comparable.

Composite Construction

Composite performance is based on the performance of one or more portfolios that have the same investment strategy or investment objective. Composite returns are the asset-weighted average of the returns on the portfolios that are included in each composite

Disclosures

The firm must disclose information about the presentation and the policies adopted by the firm so that the raw numbers presented in the report are understandable to the user.

Presentation And Reporting

Investment performance must be presented according to GIPS requirements.

Real Estate

Certain provisions apply to all real estate investments regardless of the level of control the firm has over management of the investment.

Private Equity

Private equity investments must be valued according to the GIPS Private Equity Valuation Principles unless the investment is an open-end or evergreen fund.

Time Value of Money

When an investment is subjected to compound interest, the growth in the value of investment is not only because of the interest on principal, but also the interest on interest.

Future Value is the result of compound interest at the end of a certain period. Present value is an investment back to the beginning of an investment life.

Cash flows associated with an income flow is very well represented on a Time line. It should be noted that cash flow represented is taken to be that at the end of the year.

The real risk free rate of interest is the theoretical rate over the entire period of a loan that has no expectation of inflation on it.

Securities may have one or more types of risk. Future Value of a single sum: Future value is the amount to which a

current deposit will grow over time when it is placed in an account paying compound interest.

Present Value of a single sum: is the amount invested today at a given rate over a certain period of time in order to end up with a specified FV.

Annuities: are stream of equal cash flows that occur at equal intervals over a given period.

Future Value of an Annuity Due: an annuity where the annuity payments occur at the beginning of each compounding period.

Perpetuity: pays a fixed amount of money over an infinite period. It is perpetual annuity.

Loan amortization: is the process of paying off a loan with a series of periodic loan payments, whereby a portion of the outstanding loan amount is paid off with each payment.

Cash flow additivity principle states that present value of any stream of cash flows is equal to the sum of present cash flows.

Connection between present values , future values and series of cash flows: Present values of a series of cash flows is how much money should be put in the bank today to make future withdrawals such that the last withdrawal exhausts the account.

Discounted cash flow applications

Net Present Value: of an investment project is the present value of expected cash inflows associated with the project less the projected value of the project’s expected cash outflows , discounted at the appropriate cost of capital. The higher the NPV for a company, the better.

Internal rate of return

It equates PV of the investment’s expected benefits with the PV of its costs. If the Discount rate > IRR, then the investment should not be made.

If for a single method, the IRR and the NPV rules lead to exactly same accept/reject decision. If the IRR > Discount rate, the NPV is +ve and vice versa.

Problems associated with IRR method

When the acceptance/rejection of one project has no bearing on that of the other project, the projects are said to be independent.

NPV method assumes the reinvestment of funds at the opportunity cost of capital, while the IRR method assumes that the investment rate is the IRR. The discount rate denotes the market-based opportunity cost of capital and is the required rate of return for the shareholders of the firm

Higher NPV should be chosen over more favourable IRR.

Holding period return

Is simply the %age change in the value of an investment over the period it is held.

Money Weighted Return

This concept applied IRR to investment portfolios. It is defined as the internal rate of return on portfolio, taking into account all cash outflows and inflows.

Time Weighted Rate of return :

Measures compound growth. It is the rate at which 1$ compounds over a specified performance horizon.

Statistical concepts and market returns

Two key concepts to be focused on are measures of central tendency and measures of dispersion

Measures of central tendency:

1. Arithmetic Mean2. Geometric mean

3. Weighted mean4. Median5. Mode

Measures of dispersion:

1. Range2. Variance3. Mean absolute deviation

Descriptive statistics: summarizes important characteristics of huge sets of data.

Inferential Statistics: it pertains to the procedures used in making forecasts, estimates, or judgements about a large set of data.

A Population is defined as the sum of all possible members of a stated group.

Types of Measurement Scale

Nominal Scale Ordinal Scale Interval scale Ratio scales

A measure used to describe the characteristics of a population is referred to as a parameter

A measure used to describe the characteristics of a sample is referred to as a sample characteristic

Frequency Distributionfrequency distribution describes large data sets by doing the following:

(1) Establish series of intervals, as categories, (2) Assign every data point in the population to one of the categories, (3) Counting the number of observations within each category and

(4)Present the data with assigned category, also the frequency of observations in every category. 

Frequency distribution is indeed one of the simplest methods employed in describing populations of data and is used for all four measurement scales -, it is often the best way to describe data measured on a nominal, interval or ordinal scale.

Measures of central Tendency

Identifies center, or average, of a data set. This central point can then be used to express the expected value of the data point.

To calculate the population mean, all the values are added and divided by the number of observations. (µ)

Sample mean is the all the values are added and divided by the number of observations in a sample of a population.

MedianMedian is the middle value in a series which is sorted in either descending or ascending order. ModeMode is the particular value which is most frequently observed. In some applications, the mode is often the most meaningful description. Weighted MeanWeighted mean is often seen in portfolio problems wherein various assets classes are to be weighted within the portfolio.

Harmonic mean is computed by the following steps:

1. Take the reciprocal of each observation

2. Add these terms together, 

3. Average the sum by dividing by n( #of observations) 

4. Take the reciprocal of this

Quartiles, Quintiles, Deciles, Percentiles.By the same process, quartiles are the result of a distribution being divided into

four parts; quintiles refer to five parts; deciles, 10 parts; and percentiles, 100 parts.

Quantiles and measures of central tendency are known as measures of location.

Dispersion is defined as the variability around the central tendency. Range= Maximum Value-minimum value Mean absolute deviation

Variance is defined as the mean of the squared deviations from the arithmetic mean of the expected value of a distribution

Population Variance

Sample Variance

Standard deviation is the positive square root of variance is often used as a quantitative measure of risk

Chebyshev’s inequality: States that the proportion of population within K standard deviations of the mean is atleast 1-1/K2

The coefficient of variation of sample data is the ratio of standard deviation of the sample to its mean

The Sharpe ratio measures excess return per unit of risk Skewness describes a degree to which a distribution is not symmetric

about its mean. A right skewed distribution has a positive skewness. A left skewed distribution has negative skewness.

For a positively skewed, unimodal distribution, the mean is greater than the median, which is greater than the mode.

For a negatively skewed unimodal distribution, the mean is less than the median, which is greater than the mode

Kurtosis measures peakness of a distribution and probability of extreme outcomes :

o Excess Kurtosis is measured relative to the normal distribution, which has a K of 3

o +vevalues of K indicate a distribution which is leptokurtic so that the probability of extreme outcomes is greater than a normal distribution

o –vevalues of excess kurtosis indicate a platykurtic distribution o Excess kurtosis with an absolute value greater than 1 is

significant The Arithmenticmean return is appropriate for forecasting single

period returns in the future periods, while the GM is appropriate for forecasting future compound returns over multiple periods.

Probability Concepts

Definitions:

Random Variable: RV is an uncertain number and an outcome is an observed value of a random variable.

MutualExclusive: Events that can’t both happen at the same time.

ExhaustiveEvents: Those events that include all possible outcomes.

Odds: If an event has a probability of occurring as ‘p’, the odds of the event occurring are p/(1-p)

Unconditional Probability: P(A) or P(B) is the probability of an event happening regardless of the occurrence of other events. Unconditional probability is also called marginal probability

Conditional Probability: P(A/B) or P(B/A) is one where occurrence of one event affects the probability of occurrence of other events.

Joint Probability: P(AB) of two events is the probability that they will occur both. The relationship between these: P(A/B) = P(AB) / P(B)

Independent Event: The events whose probability is unaffected by the occurrence of other events.

Expected Values: It is the probability weighed average of the conditional expected values:

E(X) =∑ pi (si )xE ( XiSi

)

a. Expected Value of a random variable: E(X) = ∑[Pi(xi)Xi

b. Variance of a random variable: Var(X) = ∑[Pi(xi) [Xi – E(X)]2

Correlation: It is a standardized measure of association between two random variables. The value of correlation ranges from -1 to 1 and is equal to Cov(A,B)/α AαB

Theories:

Properties of probability:

a. The sum probabilities of all the possible mutually exclusive events is 1.

b. Probability ranges from 0 ≤P ≤ 1

Multiplication Rule of Probability:

P (AB) = P(A|B) x P(B)

Additional Rule of Probability: This gives the probability that at least one of two events will occur:

P(A or B) = P(A) + P(B) – P(AB)

Total probability rule is often used to determine the unconditional probability of an event, given conditional probabilities:

P(A) = P(A |B1) P(B1) + P(A | B2) P(B2) +…+P(A|BN)P(BN)

Where B1, B2,…BN is mutually exclusive and exhaustive set of outcomes.

The probability of an independent event is unaffected by the occurrence of other events, but the probability of a dependent event is changed by the occurrence of another event.

Events A and B are independent if and only if:

P(A|B) = P(A), or equivalently, P(B | A) = P(B)

According to the total probability rule, the unconditional probability of A is the probability weighted sum of the conditional probabilities:

P(A) = ∑i=1

n

(Pi (Bi )) x P ( A|Bi )

Where Bi is a set of mutually exclusive and exhaustive events.

Conditional expected values depend on the outcome of some other event. Hence, for forecasts of expected values of a stock return or earning, conditional expected values are used.

Covariance measures the extent to which two random variables tend to be above and below their respective means for each joint realization.

Cov(A,B) = ∑i=1

n

Pi ( A i−A ) (Bi−B )

Correlation is a standardized measure of association between two random variables; it ranges from -1 to 1.

The variance of a random variable, Var(X) equals ∑i=1

n

P (x i ) (X i−E (X )2 )=σ x2

and Standard deviation is σ x=√σ x2

Bayes’ formula for updating probabilities based on the occurrence of an event O is:

P ( I|0 )=P (0|I )P (0 )

xP ( I )

P (A|C) = P ( AC )P ( AL )P (BC )

The number of ways to order n objects in n factorial, n! = n x (n-1) x (n-2) x … x 1

There are N!n1! x n2! x… xnk !

ways to assign k different labels to n items, where

niis the number of items with the labeli.

Common Probability Distributions

Probability distributions describe the probability of all possible outcomes for a random variable.

A discrete random variable Is one for which the possible outcomes are finite and measurable

Probability function, denoted by p(x), specifies the probability that a RV is equal to a specific value.

The set of specific outcomes of specific discreet RV are a finite set of values

The cumulative distribution function gives the probability that a RV will be less than or equal to a specified value.

Given the CDF of a RV, the probability that an outcome will be less than or equal to a specific value is represented by the area under the probability distribution to the left of that value

A discrete uniform distribution is one where there are n discreet, equally likely outcomes.

The binomial distribution is a probability distribution for a binomial RV that has two possible outcomes

For a discreet uniform distribution with n possible outcomes, the probability of each outcome equals 1/n

For a binomial distribution, if the probability of success is ‘p’, the probability of x successes in n trials is:

A binomial tree illustrates the probabilities of all possible values that a variable can take on, given a couple of ( up move and magnitude of up move) probabilities.

Tracking Error is calculated as the total return on a portfolio minus the total return on a benchmark or index portfolio

A continous uniform Distribution is one where the probability of X occuring in a possible range is the length of the range relative to the total of all possible values. If a and b are the lower and uppier limit of the distribution:

The normal probability distribution and the normal curve :

o Is symmetrical, bell shaped, with a single peak at the exact centre of distribution

o Mean=median=modeo A normal Distribution can be completely defined by its mean and

standard deviation because skewness is always 0 and kurtosis=3 Multivariate distributions describe the probabilities for more than 1 RV A confidence level is the range within which we have a given level of

confidence of finding a point estimate A normally distributed RV X can be standardized by Z=(X-µ)/σ A standard normal distribution has a mean of 0 and a standard

deviation of 1 Shortfall Risk is the probability that a portfolio’s value will fall below a

specific value over a certain given period of time. If x is normally distributed, e^xfollows a lognormal distribution. A

lognormal distribtution is often used to model asset prices. As we decrease the length of discreet compounding periods, the

effective annual rate increases. For a holding period return ( HPR ), over any period, the

equivalent continuously compounded rate over the period is ln(1+HPR) Monte Carlo Simulation uses randomly generated values for risk

factors, based on their assumed distributions, to produce a distribution of possible security values.

Historical simulation uses randomly selected past changes in risk factors to generate a distribution of possible security values.

Sampling and Estimation

Some basic definitions:Parameter: A parameter is a quantity used to describe a populationStatistic: Statistic is a quantity computed from a sample and is used to estimate a population:We typically use statistics to estimate parameters because

1. It isn’t possible to examine the entire population.2. It will be too expensive to go through every individual.

Random Sample: A simple random sample is a subset of the population drawn in such a way that each element of the population has an equal probability of being selected.

- Finite and limited populations can be sampled by assigning random numbers to all of the elements in the population, and then selecting the sample elements by using a random number generator and matching the generated numbers to the assigned numbers.

Sampling Error: The difference between the observed value of a statistic and the value of the parameter is known as the sampling error.

- Random sampling should reflect the characteristics of the underlying population in such a way that the sample statistics computed from the sample are valid estimates of the population parameter.

Sampling Distribution: Sample statistics, calculated from multiple samples from the same population, will then have a distribution of differing values that is known as the sampling distribution.

We generally refer to a sampling distribution by indicating the statistic to which the distribution applies:“the sampling distribution of the sample mean.”

Stratified random sampling: A set of simple random samples drawn from an overall population in such a way that subpopulations are accurately represented in the overall sample.

- In a large population, we may have subpopulations, known as strata, for which we want to ensure inclusion in a representative way in the sample.

- To do so, we can use stratified sampling, wherein we draw simple random samples from each strata and then combine those samples to form the overall sample on which we perform our analysis.

Time-Series and Cross-sectional data

• Time Series Data: Time-series samples are constructed by collecting the data of interest at regularly spaced intervals of time and are known as time-series data.

• Cross-Sectional Data: Cross-sectional samples are constructed by collecting the data of interest across observational units (firms, people, precincts) at a single point in time and are known as cross-sectional data

• The combination of the two is known as panel data

Central limit theorem

The central limit theorem (CLT) allows us to make precise probability statements about the population mean using the sample mean, regardless of the underlying distribution.

The standard error of the sample mean

• The standard deviation of the distribution of the sample mean is known as the standard error of the sample mean.

• When the sample size is large (generally n > 30 or so), the distribution of the sample mean will be approximately normal when the sample is randomly generated (collected).

• The standard error of the mean can then be shown to take the value of

Point estimates & confidence intervals

Estimators are the generalized mathematical expressions for the calculation of sample statistics, and an estimate is a specific outcome of one estimation.

Estimates take on a single numerical value and are, therefore, referred to as point estimates.

• It is a fixed number specific to that sample.

• It has no sampling distribution.

In contrast, a confidence interval(CI) specifies a range that contains the parameter in which we are interested (1 – a)% at the time.

• The (1 – a)% is known as the degree of confidence.

• Confidence intervals are generally expressed as lower confidence limit or upper confidence limit.

Estimator Properties:

Unbiasedness

o Occurs when the estimator expected value is equal to the value of the parameter being estimated.

Efficiency

o Occurs when no other estimator has a smaller variance.

Consistency

o Asymptotic in nature, thereby requiring a large number of observations.

o Occurs when the probability of obtaining estimates close to the value of the population parameter increases as sample size increases.

Confidence intervals

Constructing Confidence Intervals = Point estimate ± Reliability factor × Standard error

1. Point estimate: A point estimate of the parameter (a value of a sample statistic), such as the sample mean.

2. Reliability factor: A number based on the assumed distribution of the point estimate and the degree of confidence (1 − α) for the confidence interval.

3. Standard error: The standard error of the sample statistic providing the point estimate.

Student’s t-distribution

When the population variance is unknown and the sample is random, the distribution that correctly describes the sample mean is known as the t-distribution.

The t-distribution has larger reliability (cutoff) values for a given level of alpha than the normal distribution, but as the sample size increases, the cutoff values approach those of the normal distribution.

The t-distribution is a symmetrical distribution whose probability density function is defined by a single parameter known as the degrees of freedom (df).

Degrees of freedom

The degrees of freedom for a given t-distribution are equal to the sample size minus 1.

• For a sample size of 45, the degrees of freedom are 44.

• Consider that our calculation of the sample standard deviation isand that the sample mean is measured with error because it is not the true population mean, m.

Data-mining bias

Data-mining bias results from the overuse and/or repeated use of the same data to repeatedly search for patterns in the data.

If we were to test 1,000 different variables, 50 of them would be significant at the 5% level even though the significance is just an artefact of the testing error rate.

This approach is sometimes called a “kitchen sink” problem.

Look-ahead bias and time-period bias

Look-ahead bias occurs when researchers use data not available at the test date to test a model and use it for predictions.

Time-period bias ( TPB ) occurs when the model uses data from a time period when the data is not representative of all possible values of the data across all times.