CFA Quantitative Methods III Updated

8/10/2019 CFA Quantitative Methods III Updated

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EduPristine CFA - Level I

Mapping to Curriculum

Reading 10: Sampling and Estimation

Reading 11: Hypothesis Testing

Reading 12: Technical Analysis


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Reading 10: Sampling and Estimation


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Coverage of the Reading 10

Central Limit Theorem

Sampling Distribution

Standard error of sample mean

Students t -distribution

Confidence Interval


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For a population with a mean and a variance 2 the sampling distribution of the means of all possiblesamples of size n generated from the population will be approximately normally distributed.

The mean of the sampling distribution equal to and the variance equal to 2/n.

How is variance related to standard error?

As sample size gets large (typically > 30)Sampling distribution becomes almost normal regardless of shape of population

X



Sampling Error

The sampling error is the difference between a sample statistic and its corresponding populationparameter. It is found by subtracting the value of a Parameter from the value of a Statistic.

For example, if a poll was conducted where the population included all students in that school and thesample was a class. If the sample had a mean GPA of 3.4, and the populations mean GPA was 3.2, then thesample error was 0.2.



Methods of Probability Sampling

Simple Random Sampling: A sample formulated so that each item or person in the population has thesame chance of being included. This requires that the entire population must be known and serialnumbered.

Systematic Random Sampling : The items or individuals of the population are arranged in some order. Arandom starting point is selected and then every kth member of the population is selected for the sample.Used in case the entire population cannot be identified.

Stratified Random Sampling: A population is first divided into subgroups called strata, and a sample isselected from each stratum. Ensures that all subgroups are represented in the sample. Has a smaller

variance than the estimates observed from simple random sampling. Example: Bond Indexing


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Developing Sampling Distributions

Suppose theres a population of 4 oldest scientists in a university: Jack, Andrew, Michelle and Tom

Random variable, X is the ages of the individuals

Values of X: 78, 76, 72, 74

Summary Measure for Population Distribution

236.2 N

X

754

74727678 N

X

AgeAverage

N

1i

2i

N

1i

i 6970

71

72

73

74

75

76

77

78

79

Andrew Jack Michelle Tom

Ages of Population

0

0.05

0.1

0.15

0.2

0.25

0.3

Andrew Jack Michelle Tom

Prob. Of selection

Optional Topic


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0

0.05

0.1

0.15

0.2

0.25

0.3

72 73 74 75 76 77 78

Sampling Distribution of SampleMeans

16 Sample Means

78 76 74 7278 78 77 76 7576 77 76 75 7474 76 75 74 7372 75 74 73 72

1stObserv

2nd Observation

16 Samples of size n=2 each

78 76 74 7278 78,78 76,78 74,78 72,7876 78,76 76,76 74,76 72,7674 78,74 76,74 74,74 72,7472 78,72 76,72 74,72 72,72

2nd Observation1stObs

All Possible Samples of Size n = 2

1

Optional Topic


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7516

787373721 N

X N

i

i

x

SizeSampleVariancePopulation

Error)(Standardmeanof ondistributisamplingof Variance

Summary Measures for the SamplingDistribution

The mean of the sample

The standard deviation of the sample means:

Two important points worth noting in population and sampling distributions:

Population mean and the sample mean is same which is equal to 76.

Variance of the population = 2.236 2=5 and Variance of the sample = 1.58 2=2.5 which is lower than thepopulation variance.

Also the

1

Optional Topic

58.1

16

757875737572 222

1

2

N

X N

i

xi

x


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Standard Error of sample mean

It is the standard deviation of the distribution of the sample means

When the standard deviation of the population is known, the standard error of the sample mean iscalculated as:

Standard error of sample mean = Standard deviation of population

Square root of the sample size (n)

Example : The mean hourly wage for Mumbai farm workers is $13.50 with a population standard deviationof $2.90. Calculate & interpret the standard error of the sample mean for a sample size of 30

Answer: Because the population standard deviation is known, the standard error of the sample mean isexpressed as = $2.90/ root of (30) = $0.53

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Desirable properties of an estimator

Unbiasedness: expected value of an estimator is equal to the parameter you are trying to estimate

Efficiency: Variance of the sampling distribution is smaller than all the other unbaised estimators of the

parameter you are trying to estimateConsistency: accuracy of the parameter estimate increases as the sample size increases

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Point Estimate & Confidence Interval

Point estimates: These are the single (sample) values used to estimate population parameters

Confidence interval: It is a range of values in which the population parameter is expected to lie

Confidence interval takes on the following form where N 30

CI = m + Z*sxTrue for a population distribution

Where, m is the mean of the population

sx is the standard deviation of the population

For a sample mean,

Point estimate + (reliability factor * standard error )

CI = m + Z*(sx/n)

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Students t distribution (in cases where n < 30)

Students t -distribution, or simply the t-distribution, is a bell-shaped probability distribution that issymmetrical about its mean

It is appropriate distribution to use when constructing confidence intervals based on small samples (n


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Calculate & interpret a confidence interval for a sample distributiongiven population mean, and assuming a normal distribution

Population having normal distribution with a known variance : Confidence interval for population mean is

x(mean) + z /2 * standard deviation of population

square root of the sample size (n)

Population is normal with unknown variance: we can use t-distribution to construct a confidenceinterval as

Population with unknown variance given a large sample from any type of distribution

If the distribution is non-normal but the population variance is known, the z-statistic can be used as longas sample size is large (n>=30)

If the distribution is non-normal but the population variance is unknown, the t-statistic can be used aslong as sample size is large (n>=30)This means that while sampling from non-normal distribution, we cannot create a confidence interval ifthe sample size is less than 30

1

(n)sizesampletheof rootsquaredeviationstandardsample

*/2zx(mean)


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Selection of Sample Size

Factors affecting the width of a confidence interval and the Reliability Factor:

The choice of statistic (t or z values)

Choice of degree of confidence (90%, 95%, 99% levels of confidence)

Choice of the sample size

A larger sample size decreases the width of a confidence interval, all else equal

Considerations to be made while deciding to increase the sample size:

Risk of sampling from more than one population

Additional expense that outweigh the value of additional precision.

1

SizeSample

DeviationStandardSample MeanSampletheof ErrorStandard


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Sampling Related Issues

Data mining bias

It is the practice of determining a model by extensive searching through a dataset for statistically

significant patterns.It can be tested by using out-of-sample data

Two signs that may indicate the presence of data mining bias:

Low significance levels

No plausible economic rational behind the variable.

Sample Selection Bias

Arises when data availability leads to certain entities being excluded from the analysis.

This is a major issue in the hedge fund industry. Since performance disclosure is not mandatory, hedgefund returns are difficult to obtain.

This is also a problem in the mutual fund industry, as only funds that are currently exist are available inthe database. Funds that no longer exist, perhaps due to poor performance, are not available in thedatabase. This leads to survivorship bias .

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Sampling Related Issues

Look-ahead bias

Arises while using information that was not available on the test date.

For example, if using P/BV ratios, the BV may not be available till sometime in the following quarter.

Time-Period Bias

Arises when the analysis is based on a time period that may make the results time-period specific.

For example, a time period too short may give results that may not hold in the long run.

A time period too long has a potential for structural changes in which one segment cannot be comparedto the other segment. It could result in two different returns distribution.

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Question

1. As compared to normal distribution, the t-distribution has:

A. Similar tails

B. Fatter tailsC. Narrower tails

2. Which of the following is most likely to be a property of an estimator?

A. Correctness

B. ReliabilityC. Consistency

3. The mean age of all CFA candidates is 30 years. The mean age of random sample of 100 candidates isfound to be 27.5 years. The difference , 30-27.5=2.5, is called the:

A. Random error

B. Sampling error

C. Population error

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Questions (Cont)

4. Assume that a population has a mean of 14 with a standard deviation of 3. If a random sample of 64observations is drawn from this population, the standard error of the sample mean is closest to:

A. 0.575 B. 0.375 C. 0.575

5. The population mean is 30 & the mean of a sample of size 144 is 28.5. The variance of the sample is25. The standard error of the sample mean is closest to:

A. 0.450 B. 0.317 C. 0.417

6. A random sample of 100 mobile store customers spent an average of $150 at the store. Assuming thedistribution is normal & the population standard deviation is $10, the 95% confidence interval for thepopulation mean is closest to:

A. $148.04 to $151.96

B. $144.08 to $159.96

C. $149.04 to $152.96

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Questions (Cont)

7. The Central Limit Theorem is best described as stating that the sampling distribution of the samplemean will be approximately normal for large-size samples:

A. if the population distribution is normal.

B. if the population distribution is symmetric.

C. for populations described by any probability distribution.

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Solution

1. B. The t-distribution has fatter tails compared to normal distribution

2. C. Consistency, Efficiency & unbaisedness are desirable properties of an estimator

3. B. It is the correct definition of the sampling error

4. B. = 3/8 = 0.375

5. C. = 5/12 = 0.417

6. A. Confidence interval is 150+ 1.96(10/10) = 150+ 1.96 = 148.04 to 151.96

7. C.

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64

3

144

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Reading 11: Hypothesis Testing

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Hypothesis Test

Type-1,2 error

P-Value

T-test

F-test, Chi-square test

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Hypothesis Testing

A statistical hypothesis test is a method of making statistical decisions from and about experimental data.

Null-hypothesis testing answers the question:

How well the findings fit the possibility that chance factors alone might be responsible."

Example: Does your score of 6/10 imply that I am a good teacher???

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Key steps in Hypothesis Testing

Null Hypothesis (H 0): The hypothesis that the researcher wants to reject

Alternate Hypothesis(H a): The hypothesis which is concluded if there is sufficient evidence to reject nullhypothesis

Test Statistic

Rejection/Critical Region

Conclusion

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Launching a niche course for MBA students?

Christos, a brand manager for a leading financial training center, wants to introduce a new niche financecourse for MBA students. He met some industry stalwarts and found that with the skills acquired byattending such a course, the students would be able to land up in a good job.

He meets a random sample of 100 students and discovers the following characteristics of the marketMean household income to $20,000Interest level in students = highCurrent knowledge of students for the niche concepts = low

Christos strongly believes the course would adequately profitable in students if they have the buyingpower for the course. They would be able to afford the course only if the mean household income isgreater than $19,000.

Would you advice Christos to introduce the course?What should be the hypothesis? Hint: What is the point at which the decision changes (19,000 or 20,000)? What about the alternate hypothesis?What other information do you need to ensure that the right decision is arrived at? Hint: confidence intervals/ significance levels? Hint: Is there any other factor apart from mean, which is important? How do I move from population

parameters to standard errors?

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f


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Criterion for Decision Making

What is the risk still remaining, when you take this decision?

Hint: Type-I/II errors?

Hint: P-valueTo reach a final decision, Christos has to make a general inference (about the population) from the sampledata.

Criterion: Mean income across all households in the market area under consideration.

If the mean population household income is greater than $19,000, then PD should introduce theproduct line into the new market.

Christoss decision making is equivalent to either accepting or rejecting the hypothesis:

The population mean household income in the new market area is greater than $19,000

The term one-tailed signifies that all z-values that would cause Christos to reject H 0, are in just one tailof the sampling distribution

-> Population Mean

H0: $19,000 Ha: $19,000

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Identifying the Critical Sample Mean Value S li Di ib i


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Sampling Distribution

Sample mean values greater than $19,000--that is x-values on the right-hand side of the samplingdistribution centered on = $19,000--suggest that H 0 may be false.

More important the farther to the right x is , the stronger is the evidence against H 0

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0

0.05

0.1

0.15

0.2

0.25

-10 -5 0 5 10$19,000

Critical Value(Xc)

Reject H 0 if the sample mean exceeds X c

C ti th C it i V l


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Computing the Criterion Value

Standard deviation for the sample of 100 households is $4,000. The standard error of the mean (s x) isgiven by:

Critical mean household income x c through the following two steps:

Determine the critical z-value, z c. For =0.05: zc = 1.645.

Substitute the values of z c, s, and (under the assumption that H 0 is "just" true )

Critical Value x c xc = + zcs = $19,658.

In this case, since the observed sample statistic (20,000) is greater than the critical value (19,658), sothe null hypothesis is rejected =>

3

400$n

s s x

Decision RuleIf the sample mean household income is greater than $19,658, reject the null hypothesis and introduce the new course

T t St ti ti


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Test Statistic

The value of the test statistic is simply the z-value corresponding to = $20,000.

Here, s x is the standard error

3

5.2 x s

x Z

0

0.05

0.1

0.15

0.2

0.25

-10 -5 0 5 10=$19,000Z=0

x= $ 20,000Z=2.5

Do not Reject H 0 Reject H 0

645.1658,19$

c

c

Z

X

= 0.05

There is a significantdifference in thehypothesized populationparameter and the observedsample statistic =>

Mean income > 19,000 =>

Launch the course

Errors in Estimation


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Errors in Estimation

Please note: You are inferring for a population, based only on a sample

This is no proof that your decision is correct & Its just a hypothesis

There is still a chance that your inference is wrong. How do I quantify the prob. of error in inference?Type I and Type II Errors:

Type I error occurs if the null hypothesis is rejected when it is true

Type II error occurs if the null hypothesis is not rejected when it is false

Significance Level:

-> Significance level : The upper-boundprobability of a Type I error

1 - ->confidence level : The complementof significance level

The power of a test is the probabilityof correctly rejecting the null.

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Actual

Inference

H0 is True H 0 is False

H0 is TrueCorrect DecisionConfidenceLevel=1-

Type-II ErrorP(Type-IIError)=

H0 is FalseType-I ErrorSignificanceLevel=

Power=1-

P Value Actual Significance Level


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P - Value Actual Significance Level

The p-value is the smallest level of significance atwhich the null hypothesis can be rejected.

P-value

The probability of obtaining an observed value ofx (From the sample) as high as $20,000 or morewhen actual populations mean ( ) is only$19,000 = 0.00621

Calculated probability of rejecting the nullhypothesis (H 0) when that hypothesis (H 0) is true(Type I error)

The actual significance level of 0.00621 in this casemeans that the odds are less than 62 out of 10,000that the sample mean income of $20,000 wouldhave occurred entirely due to chance (when thepopulation mean income is $19,000)

3

=$19,000Z=0

p-value= 0.00621

Do not Reject H 0 Reject H 0

= 0.05

0

0.05

0.1

0.15

0.2

0.25

Some variations in the Z Test I


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Some variations in the Z-Test - I

What if Christos surveyed the market and found that the student behavior is estimated to be:

They would found the training too expensive if their household income is < US$ 19,000 and hencewould not have the buying power for the course?

They would perceive the training to be of inferior quality, if their household income is > US$19,000 andhence not buy the training?

How would the decision criteria change? What should be the testing strategy?

Hint: From the question wording infer: Two tailed testing

Appropriately modify the significance value and other parameters

Use the Z-test

Appropriate change in the decision making and testing process process:

Students will not attend the course if:

The household income >$19,000 and the students perceive the course to be inferior

The household income is


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216,18$400*95.1000,19*2/ Z

784,19$400*95.1000,19*2/ Z

Two- Tailed Test

Now the test is modified to two-tailed test,which signifies that all z-values that would causePD to reject H0, are in both the tails of the

sampling distribution -> Population Mean

H0: = $19,000

Ha: $19,000

Since we are checking for significance differenceon both the ends, so its a two tailed test

The lower boundary =

Conclusion: If the household income lies

between $18,216 and $19,784 then the studentwill attend the course at 95% confidence

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=$19,000Z=0

Do notReject H 0

Reject H 0

= 0.025

0

0.05

0.1

0.15

0.2

0.25

- 10 - 5 10

= 0.025

Reject H 0

t-test


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t test

The t-distribution is a probability distribution defined by a single parameter known as degrees offreedom (df).

Like the standard normal distribution, a t-distribution has a mean of zero.

However, unlike a standard normal distribution that has a variance of one, a t-distribution has a variancegreater than one.

The t-distribution also has fatter tails than a normal distribution.

The t-distribution approaches a normal distribution as the degrees of freedom increases.

A sample size greater or equal to 30 is treated as a large sample and a sample less than 30 is treated as a

small sample.

The test statistic for a sample size n (and degrees of freedom n-1) is given by.

3

n s

X

/ -t 01-n

Question


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Question

1. A researcher has a sample of 400 observations from a population whose standard deviation is knownto be 136. The mean of the sample is calculated to be 17.2. The null hypothesis is stated as Ho: mean =4. The p-value under the alternative hypothesis H1: mean > 4 equals

A. 3.92% B. 2.6% C. 5.2%

2. Buchanan thinks that KKR is unable to perform because of Ganguly. He sees the statistics and conductsleadership survey, which reveals that Ganguly scores low on Leadership qualities. BuchananHypothesizeHo: Ganguly Not a Leader,HA: Ganguly a LeaderBuchanan removes Ganguly as KKR captain, but KKR keeps losing. Subsequent analysis shows thatShahRukh Khan was causing the problem. By Removing Ganguly, Buchanan:

A. Made a Type II error.

B. Is correct.

C. Made a Type I error.

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Solution


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1. B. 2.6%.The z-statistic under the null is calculated to be (17.2 - 4)/(136/(400^.5)) = 1.94.The right-tailed probability of observing a z-statistic at least as big as 1.94 equals 1.0 - 0.9738 = 0.026 =

2.6%. This is the p-value of the right-tailed test in this sample.

2. C. Made a Type II error.Type II error is an which occurs when you fail to reject a hypothesis when it is actually false (alsoknown as the power of the test). A Type I error is the rejection of a hypothesis when it is actually true(also known as the significance level of the test). P(Type II) = P(Accepting H 0| H 0 false).

3. C. 12.5

4. C. Rejecting the null when it is true is a Type I error. A Type II error I failing to reject the null hypothesiswhen it is false

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5.128

10064

100n

X

X

Hypothesis Tests for Variances


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yp

4

Test for Single PopulationVariance

Hypothesis Test ofVariances

Test for Two PopulationVariances

Chi-SquareTest Statistic

F-test Statistic

20

22

)1(,

)1(

sn

n 22

21

,, s s

F dd f ndf

ExampleHypothesis

ExampleHypothesis

H 0: 12 22 = 0H A: 12 22 0

H 0: 2 = 02 H A: 2 02

In testing for variances, there are two different tests,because sum of two chi-squares is not a chi-square


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Appendix: The Chi-square Distribution


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The chi-square distribution is a family of distributions, depending on degrees of freedom:d.f. = n - 1

4

0 4 8 12 16 20 24 28

d.f. = 15

20 4 8 12 16 20 24 28

d.f. = 5

20 4 8 12 16 20 24 28

d.f. = 1

2

Example : F-test


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Q : William Waugh is examining the earnings for two different industries. He suspects that the earnings for chemicalindustry are more divergent than those of petroleum industry. To confirm, he took a sample of 35 chemical manufacturers& a sample of 45 petroleum companies. He measured the sample standard deviation of earnings across the chemicalindustry to be $3.5 & that of petroleum industry to be $3.00. Determine if the earnings of the chemical industry have

greater standard deviation than those of the petroleum industry.A: 1) State the hypothesis:

where variance of earnings for the chemical industry =

variance of earnings for the petroleum industry =

Note:

2) Select the appropriate test statistic:

3) Specify the level of significance: Take it 5% here

4) State the decision rule regarding the hypothesis:

5) Collect the sample & calculate the sample statistics:

Using the information provided, the F-statistic can be computed as:

4

022

a022

0 :Hverses:H

21

22

22

21

22

21

S

S F

1165.1002.3$502.3$

22

21

S

S F

1.74Fif HReject 0

Example : F-square Test


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Question: You are a financial analyst for a brokerage firm. You want to compare dividend yields betweenstocks listed on the BSE & NSE. You collect the following data:

BSE NSE Number 30 50Mean 3.27 2.53

Std dev 1.5 1.4

Is there a difference in the variances between the BSE & NSE at the = 0.05 level?

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Example : F- square Test (Cont)


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The test statistic is:

F = 1.148 is not greater than the critical F value of 1.881, so we do not reject H 0

Conclusion: There is no evidence of a difference in variances at = 0.05

4

148.140.1

50.12

2

2

2

2

1

s

s

F

0 /2 = .025

F /2 =1.881Reject H 0Do not

reject H 0

H0: 12 22 = 0HA: 12 22 0

Parametric & Non parametric tests


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Parametric tests: They rely on assumptions regarding the distribution of the population & are specific topopulation parameters

Example : z-test

Nonparametric tests: They either do not consider a particular parameter or have few assumptions aboutthe population that is sampled

These are used when there is concern about quantities other than the parameters of a distribution orwhen the assumptions of parametric tests cant be supported

Example: ranked observations

Spearman rank correlation test: It can be used when the data are not normally distributed

Example : The performance ranks of 20 mutual funds for two years which are not normally distributed

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Questions


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1. An analyst is testing a hypothesis about stock returns. He would like to minimise the chances of rejecting thenull hypothesis when it is true. Which of the following is most likely to be the level of significance?

A. 0.05 B. 0.95 C. 0.01

2. An analyst would like to compare the returns of two sample portfolios derived from the S&P 500 index. If heperforms a two sample test to test the hypothesis with a 5% level of significance, which of the following ismost likely?

A. The probability of Type I error is 95%

B. The probability that the null hypothesis would not be rejected when it is true is 5%C. The probability of Type I error is 5%

3. What is the power of the test if the significance level of the test is 0.05 & the probability of the Type II error is0.25?

A. 0.250

B. 0.750

C. C. 0.850

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Questions


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7. The F Statistic is:

A. Always +ve and is +ve skewed

B. Always -ve and is -ve skewedC. Can be +ve or Negative and is symmetric

8. Which of the following statements about the F-distribution & chi-square distribution is least accurate?Both distributions:

A. Are asymmetricalB. Are bound by zero on the left

C. Have means that are less than their standard deviations

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Solutions


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1. C. As here the analysts want to minimize the chances of rejecting the null hypothesis when it is truethen he will use the least possible level of significance 0.01

2. C. The probability of Type I error is 5%

3. B. Power of the test = 1 P(Type II error) = 1 - 0.25 0.750

4. A. For large n if the population distribution is uniform, the sample distribution is always normal

5. A. In this case, the investment options will follow Binomial Distribution

6. C. The z value is used for hypothesis testing when the sample variance is known.

7. A. F Statistic is ratio of 2 variances and hence always +ve. F Distribution is also +vely skewed.

8. C. There is no consistent relationship between the mean & the standard deviation of the chi-squaredistribution or F-distribution

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Technical Analysis vs. Fundamental Analysis

Advantages & Challenges of Technical Analysis

Line Charts, Bar Charts & Candlestick charts

Point and Figure Charts

Trend, support, resistance lines & change in polarity

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Technical Analysis vs. Fundamental Analysis


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Technical vs. Fundamental Analysis : The main difference between technical analysis and fundamentalanalysis is the use of financial statements to value equities.

Technical analysis is the practice of valuing stocks on past volume and pricing information. Technicalanalysis combines both the use of past information (how stocks have reacted previously) and "feeling"(how the market is moving the name) to value a security.

Fundamental analysis , however, takes a more formal approach. Fundamental analysts review thefinancial statements of a company and generate metrics, such as price-to-book value and enterprisevalue-to-EBITDA to value a security.

Assumptions of Technical Analysis :

Prices are determined by investor supply and demand for assets.

Supply and demand are driven by both rational and irrational behaviour.

While the causes of changes in supply and demand are difficult to determine, the actual shifts in supplyand demand can be observed in market prices.

Prices move in trends and exhibit patterns that can be identified and tend to repeat themselves overtime.

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Bar Charts & Candlestick charts


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OHLC Bar Charts

Bar charts consist of bars, which are vertical lines with the bottomrepresenting the low price (L) of the time-frame and the toprepresenting the high price (H). The bars also have a horizontal dashon the right side of the bar to indicate the close price (C) for thetime frame and some have a horizontal dash on the left side toindicate the open price (O)

Japanese candlestick charts form the basis of the oldest form oftechnical analysis. Candlestick charts provide the same informationas OHLC bar charts.

Candlesticks indicate a bullish up bar, when the closing price ishigher than the opening price, using a light color such as white orgreen, and a bearish down bar, when the closing price is lower thanthe opening price, using a darker color such as black or red forthe real body of the candlestick

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Point and Figure Charts


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Point and Figure (P&F) charts differ from other stock charts as itdoes not plot price movement from left to right within fixed timeintervals. It also does not plot the volume traded.

Instead it plots unidirectional price movements in one verticalcolumn and moves to the next column when the price changesdirection.

It represent increases in price by plotting X's in the column anddecreases in price by plotting O's. Each X and O represents a box of aset size or price amount.

This box size determines how far the price must move beforeanother X or O is added to the chart, depending on the direction ofthe price movement.

Thus if the box sixe is set at 15, the price must move 15 points abovethe previous box before the next X or O is plotted. Any movement

below 15 is ignored.

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Trend, support, resistance lines & change in polarity


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In an uptrend , prices are reaching higher highs and higher lows. An uptrend line is drawn below theprices on a chart by connecting the increasing lows with a straight line.

In a downtrend , prices are reaching lower lows and lower highs. A downtrend line is drawn above the

prices on a chart by connecting the decreasing highs with a straight line. Support and resistance are price levels or ranges at which buying or selling pressure is expected to limitprice movement. Commonly identified support and resistance levels include trend lines and previoushigh and low prices.

The change in polarity principle is the idea that breached resistance levels become support levels andbreached support levels become resistance levels.

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Technical Analysis Indicators


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Price-based indicators include moving averages, Bollinger bands, and momentum oscillators such as theRelative Strength Index, moving average convergence/divergence lines, rate-of-change oscillators, andstochastic oscillators.

These indicators are commonly used to identify changes in price trends, as well as overbought marketsthat are likely to decrease in the near term and oversold markets that are likely to increase in the nearterm.

Sentiment indicators include opinion polls, the put/call ratio, the volatility index, margin debt, and theshort interest ratio. Margin debt, the Arms index, the mutual fund cash position, new equity issuance, andsecondary offerings are flow-of-funds indicators.

Technical analysts often interpret these indicators from a contrarian perspective, becoming bearishwhen investor sentiment is too positive and bullish when investor sentiment is too negative

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Cycles in Technical Analysis

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Some technical analysts believe market prices move in cycles. Examples include the Kondratieff wave ,which is a 54-year cycle, decennial patterns or 10-year cycles & a 4-year cycle related to U.S. presidentialelections.

Elliott wave theory suggests that prices exhibit a pattern of five waves in the direction of a trend andthree waves counter to the trend.

Technical analysts who employ Elliott wave theory frequently use ratios of the numbers in the Fibonaccisequence to estimate price targets and identify potential support and resistance levels

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Terms & Definitions

Terms Definitions


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EduPristine CFA - Level I6

Terms Definitions

What does relative weakness mean? a trend that indicates the asset is underperforming the benchmark

What is an uptrend? if prices are consistently reaching higher highs and retracing to higher lows;demand is increasing relative to supply

What is a downtrend? if prices are consistently declining to lower lows and retracing to lower highs;supply is increasing relative to demand

What is a breakout? when price crosses the trendline from a downtrend by what the analystconsiders a significant amount

What is a breakdown? when price crosses the trendline from an uptrend by what the analystconsiders a significant amount

What is a support level? buying which is expected to emerge that prevents further price decreases

What is a resistance level? selling which is expected to emerge that prevents further price increases

What is a change in polarity? belief that breached resistance levels become support levels and thatbreached support levels become resistance levels

Terms & Definitions

Terms Definitions


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Terms Definitions

What is a head-and-shoulders pattern? a reversal pattern that suggests the demand that has been driving the uptrendis fading, especially if each of the highs in the pattern occurs on declining

volumeWhat are three reversal patterns fordowntrends?

1) inverse head-and-shoulders2) double bottom3) triple bottom

What is a continuation pattern? suggests a pause in a trend rather than a reversal

What are triangles? Form when prices reach lower highs and higher lows over a period of time.Trendlines on the highs and on the lows thus converge when they areprojected forward. they can be symmetrical, ascending or descending;suggests buying and selling pressure have become roughly equal temporarilybut they do not imply a change in direction of a trend

What are rectangles? when trading temporarily forms a range between a support level and aresistance level; suggests the prevailing trend will resume and can be used to

set a price target; they do not imply a change in direction of a trend

What is a moving average? mean of the last 'x' closing prices; often viewed as support or resistance levels

Terms & Definitions

Terms Definitions


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Terms Definitions

In an uptrend where is price in relationto the moving average?

price is higher than the moving average

In a downtrend where is price inrelation to the moving average?

price is lower than the moving average

What is a golden cross? when short-term average crosses the long-term average from below; 'buy'signal; emerging uptrend

What is a dead cross? when a short-term average crosses the long-term average from above, 'sellsignal'; emerging downtrend

What are bollinger bands? constructed based on the standard deviation of closing prices over the last 'n'periods; move away from each other when volatility increases and move closertogether when prices are less volatile

What do contrarians believe? markets get overbought or oversold because most investors tend to buy andsell at the wrong times, and thus it can be profitable to trade in the oppositedirection

Terms & Definitions

Terms Definitions


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Terms Definitions

What is an oscillator? group of technical tools TAs use to identify overbought/oversold markets;based on market prices but scaled so that they "oscillate" around a given value

such as zero or between two values such as zero and 100; extremely highvalues indicate overbought condition whereas extremely low values indicateoversold condition; can be used to identify convergence or divergence.

What does convergence indicate? price trend is likely to continue

What does divergence indicate? potential change in price trend

What are four examples of oscillators? 1) ROC (rate of change)2) RSI (relative strength index)3) MACD (moving average convergence/divergence)4) stochastic oscillator

What is the ROC oscillator? 100 x latest closing price - closing price from n period earlier; buy when ROCchanges from negative to positive during an uptrend and sell when ROCchanges from positive to negative during downtrend

Questions

1. Which of the following is most likely to be considered a momentum indicator?


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. W c o t e o ow g s ost e y to be co s de ed a o e tu d cato ?

A. Put-call ratio

B. Breadth of market

C. Mutual fund cash position

2. A low price range in which buying activity is sufficient to stop a price decline is best described as:

A. Support

B. Resistance

C. Change in polarity

3. A technical analyst has detected a price chart pattern with three segments. The left segment shows adecline followed by a reversal to the starting price level. The middle segment shows a morepronounced decline than in the first segment and again a reversal to near the starting price level. Thethird segment is roughly a mirror image of the first segment. This chart pattern is most accuratelydescribed as:

A. A triple bottom

B. A head and shouldersC. An inverse head and shoulders

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Solution

1. B. List and describe examples of each major category of technical trading rules and indicators.


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1. B. List and describe examples of each major category of technical trading rules and indicators.Breadth of market is a momentum indicator. Put-call ratio and mutual fund cash position are contrary-opinion rules.

2. A. Support is defined as a low price range in which buying activity is sufficient to stop the decline inprice.

3. C. An inverse head and shoulders pattern consists of a left segment that shows a decline followed by areversal to the starting price level, a middle segment that shows a more pronounced decline than inthe first segment and again a reversal to near the starting price level, and a third segment that isroughly a mirror image of the first segment.

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Five Minute Recap

Methods of Sampling Desirable Properties of an Estimator0.25


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All possible samples of size n generated from a population will beapproximately normally distributed.The mean of the sampling distribution equal to P and the standarddeviation is equal to P/n . This is know as standard error.

Methods of SamplingSimple Random SamplingSystematic Random SamplingStratified Random Sampling

Desirable Properties of an EstimatorUnbiasednessEfficiencyConsistency

Sampling Biases:Data mining biasSample Selection BiasLook-ahead biasTime-Period Bias

Actual

InferenceH0 is True H 0 is False

H0 is TrueCorrect DecisionConfidence Level=1-

Type-II ErrorP(Type-II Error)=

H0 is FalseType-I ErrorSignificance Level= Power=1-

Chi Square Test : Used for testinghypothesis concerning variance ofa populationF Test : Used to test hypothesisabout difference in variance of twodifferent population

t-Distribution

00.05

0.1

0.15

0.2

0

0.1

0.15

0.2

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0.05


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