Cfa Level 1 - 2012 - Quantitative Methods

Front 1

Descriptive Statistics:

Back 1

Describe the properties of a large data set.

Front 2

Inferential Statistics:

Back 2

Use a sample from a population to make probabilistic statements about the characteristics of a population.

Front 3

Population:

Back 3

A complete set of outcomes.

Front 4

Samples:

Back 4

A subset of outcomes drawn from a population.

Front 5

NOIR:

Back 5

Nominal, Ordinal, Interval, Ratio.

Front 6

Nominal:

Back 6

Only names (bird: robin, parrot, seagull)

Front 7

Ordinal:

Back 7

Ordered (large, mid, small).

Front 8

Interval:

Back 8

Go by intervals (0-40, 41-80, 81-120) .

Front 9

Ratio:

Back 9

Ratios make sense, absolute zero.

Front 10

Parameter:

Back 10

Describe a characteristics of a population.

Front 11

Sample statistic:

Back 11

Describes a characteristic of a sample.

Front 12

Frequency Distribution:

Back 12

a table that summarizes a large data set by assigning the observations to intervals (Histogram).

Front 13

Relative frequency distributions:

Back 13

A table ordered by percentage.

Front 14

Cumulative Frequency Distribution:

Back 14

Shows the percentage of observations less than the upper bound of each interval.

Front 15

Population Mean:

Back 15

Mew

Front 16

Samples Mean:

Back 16

Xbar

Front 17

Geometric Mean (Description and formula):

Back 17

Used to calculate compound growth rates.
If the returns are constant over time, geometric mean equals arithmetic mean.

The greater the variability of returns over time, the more the arithmetic mean will exceed the geometric mean.

Also known as Average Annual Compound Rate of Return

Periodic R = [(1+R1)(1+R2)...(1+Rn)^(1/n)] - 1

sqroot^n of (x1 * x2 * x3 * xn)
example:
2, 3, 4
G mean = sqroot^3 (2x3x4)
= 2.88

Front 18

Weighted Mean:

Back 18

Places a percentage weight on sections of a problem. A mean in which different observations have different proportional influence on the mean.

X= sum of Wi x Ri = W1R1 + W2R2 + …. Whereby W is the weight (%)

Front 19

Harmonic Mean:

Back 19

Used to find out the average cost per shares over time.

Xharmonic = N / sum(1/Xi)

T1 = 3,000 @ $20/share
T2 = 3,000 @ $25/share
Xharmonic = 6,000/270 shares = $22.2/share

Front 20

Arithmetic mean:

Back 20

= (x1+x2+x3+... + xn) / n

Example:
= (2+3+4+5+6+7) / 6

Front 21

Median:

Back 21

It is midpoint of a population of numbers. If there is an even number then you add 2 middle numbers and divide by 2.

Advantages: resistant to outliers.

Front 22

Mode:

Back 22

The most common observation.

Example:
1, 2, 3, 3, 4, 4, 4, 4, 4, 5, 5, 6, 7, 8, 8, 9.
Mode is 4 because it appeared the most.

There can be more than one mode (bimodal).

Front 23

Quantiles:

Back 23

Like from standardized tests.

Example:
"You are in the 75th percentile."

"60% of the data points are less than the 6th percentile."

Front 24

Range:

Back 24

Range of the data.

Front 25

Mean absolute Deviation:

Back 25

Average of the absolute values of deviations from the mean.

[I(X1-mean)I + I(X2-mean)I + … + I(Xn-mean)I] / n

Front 26

Standard Deviation and Variance:

Back 26

How spread out the data is. The bigger the standard deviation, the bigger the deviation from the mean.

Variance = sum [(Xi – mean)^2] / n
StdDiv = sqroot (Variance)

Example:
Mean = 2
X1 = 2, X2 = 3 X4 = 5
= [(2-2)^2 + (3-2)^2 + (4-2)^2] / 3
= 1.33

Std Div = sqroot (1.33)

Front 27

Sample Variance:

Back 27

Same equation as the mean except you add -1 to the n.
Variance = sum of [(Xi – mean)^2] /( n-1)

Front 28

Chebyshev’s Inequality:

Back 28

Specifies the minimum percentage of observations that lie within k standard deviation of the mean; applies to any distribution with k>1.

Min% = 1 – (1/k^2).

Example:
The minimum percentage of obeservations of any distribtuions of 2 standard deviations of the mean?
= 1- (1/2^2) = 75%

Remember, this is for ANY distribution.

Front 29

Coefficient of Variance.

Back 29

Risk per unit of measure. Therefore, the lower the better.
CV = StdDiv / Mean

Front 30

Sharpe Ratio:

Back 30

Excess return per unit of risk. More the better.

(Rp – Rf) / StdDivP

Rf = Average risk free rate
Rp = Mean Portfolio Risk
StdDivP = Portfolio Standard deviation

Front 31

Random Variable

Back 31

Uncertain Number

Front 32

Outcome

Back 32

Realization of random Variable

Front 33

Event

Back 33

Set of one or more outcomes

Front 34

Mutually exclusive

Back 34

Cannot both happen.

Front 35

Exhaustive

Back 35

Set of events includes all possible outcomes.

Front 36

Empirical:

Back 36

Based on analysis of data.
Using past information to make a prediction about a future outcome.

Front 37

Subjective:

Back 37

Personal opinion.

Front 38

A Priori:

Back 38

Based on reasoning, not experience.

Front 39

Odds for:

Back 39

Example: 20% of the time a horse will win.

Front 40

Odds against:

Back 40

Example: 80% of the time a horse will lose.

Front 41

Unconditional:

Back 41

Probability of an event that is independent of other events.
P(A).

Front 42

Conditional:

Back 42

A probability that is dependent on other events.
P(A|B): Probability of A given B.

Front 43

What are the probability rules?

Back 43

Addition rule:
P (A or B) = P(A) + P(B) - P(AB).

Multiplication (Joint Probability):
P(AB) = P(A|B) x P(B)

Multiplication (Independent Pr.):
P(AB) = P(A) x P(B)

Front 44

Total Probability Rule:

Back 44

P(A) = P(A|B) x P(B) + P(A|Bc) x P(Bc)

P(A) = P(AIS1) x P(S1) + P(AIS2) x P(S2) + ...

Front 45

Give example of a joint probability:

Back 45

P(Interest rate increased) =
P(I) = 0.4
P(Recession given at a rate increase) = P(R|I)

The probability of a recession and an increase in rates =
P(R|I) x P(I) = 0.7 x 0.4 = 28%

Front 46

Give equation for joint probability events and explain it.
How is this different from mutually exclusive?

Back 46

P(A or B) = P(A) + P(B) - P(A|B).

You must subtract P(A|B) because if you look at a Venn diagram you will notice that you have counted the overlapping section of two circles more than once.
Mutually exclusive events do not require the final subtraction.

Front 47

Dependent Events:

Back 47

Knowing the outcome of one tells you something about the probability of the other event.

Front 48

Independent Events:

Back 48

Occurrence of one event does not influence the occurrence of the other.

Front 49

Covariance:

Back 49

A measure of how two variables move together.
The value range from + infinity, to - infinity.

∑[(x-mean) / (Sx)]

Front 50

Correlation:

Back 50

p(Ri, Rj) = (Cov(Ri,Rj) / σ(Ri)σ(Rj)

Small p represents correlation.

Front 51

Expected Value:

Back 51

∑P*x

Example:
75% chance that you will receive $125,000.
The expected value is 93,750.

Front 52

Portfolio Expected Value:

Back 52

Weighted Average basically.

Front 53

Portfolio Variance and Standard Deviation.

Back 53

Var(Rp) = σ²₁w²₁+ σ₂²w₂² + 2w₁w₂p₁₂σ₁σ₂

note: p is correlation. Derived from correlation formula.

Front 54

Factorial:

Back 54

Example:
3! = 3 x 2 x 1
6! = 6 x 5 x 4 x 3 x 2 x1

Front 55

When should you use nCr and when should use nPr?

Back 55

nCr when order does not matter.
nPr when order does matter.

Front 56

Sign for sample mean?
Sign for population mean?

Back 56

Sample mean = x bar
Population mean = μ

Front 57

Explain the geometric mean formula:

Back 57

Simply multiply all the numbers given; X1 x X2 x Xn... then take the root to the power of however many observations there are (n).

Since you can not take the root of a negative number you must instead add each return by 1 then multiply;
(X1+1) x (X2+1) x (Xn+1)...
then take the root of that to the power of n.

Front 58

What is MAD and how is it different from variance?

Back 58

MAD uses an absolute and is not squared.

MAD =
[|X1-mean| + |X2-mean| + |Xn-mean|] / n

Variance =
[(X1-mean)^2 + (X2-mean)^2 + (Xn-mean)^2] / n

So, basically instead of absolutes you have squares.

Front 59

Standard deviation =

Back 59

Square root of the variance.

Front 60

What's the difference between the sample variance formula and the variance formula?

Back 60

the -1 at the divisor.

Front 61

Coefficient of Variation?

Back 61

StDiv / Mean.
Not bloody hard.

Front 62

Sharpe Ratio?

Back 62

The sharpe ratio is simply the mean return from an investment minus a risk free rate (like a t-bill) all divided by the standard deviation of that investment.

The investment can be a portfolio.

Front 63

Kurtosis?
Leptokurtic?
Platykurtic?
Mesokurtic?

Back 63

Kurtosis is a measure of the peek like q in a frequency filter.

Leptokurtic = more peek.
Platykurtic = less peek.
Mesokurtic = normal peek.

Front 64

Sample Skewness?

Back 64

How skewed the sample is.
(1/n)[(X - μ)^3 / (σ^3)]

Front 65

Sample Kurtosis?

Back 65

Same as sample skewness but replace the 3s with 4s.