Quantitative Flashcards Preview

CFA Level I (Joeker) > Quantitative > Flashcards

Flashcards in Quantitative Deck (35):
1

P(AB)

P(A|B) * P(B)

2

P(A or B)

P(A) + P(B) - P(AB)

3

Probability

to

Odds

P(E)

—————

1 - P(E)

4

Expected Value

E(X)

ΣX*P(X)

 

 

Weighted average of the possible outcomes of a random variable, where the weights are the probabilities that the outcomes will occur.

5

Degrees of Freedom

n - 1

6

Combination

n!

——————

(n - r)! r!

7

Permutation

n!

——————

(n - r)!

8

Percentile

(n + 1)*(y/100)

9

Money-Weighted

Rate of Return

The internal rate of return (IRR)

The rate of return where NPV = 0

10

Time-Weighted

Rate of Return

For periods less than one year

Σ(1 + HPRn) - 1

 

For periods greater than one year (geometric mean)

Σ(1 + HPRn)1/n - 1

 

The rate at which $1 compounds over time.

11

HPR

(P1 + D)

       ————   - 1

 P

12

Harmonic Mean

1

———————

Σ(1/Pn)

Average cost of shares purchased over time.

(Dollar cost averaging)

13

Population Variance

Σ(x - µ)2

—————

n

14

Sample Variance

Σ(x - µ)2

—————

(n - 1)

15

MAD

Σ|x - µ|

—————

n

16

Z or T

(x - µ)

————

σ

17

Standard Deviation

σ

SQRT of the Variance (σ2)

SQRTσ2

18

Standard Error

σ

————

SQRTn

The deviation between the sample mean and the population mean.

19

Z Score for 90%

1.65

µ (+/-) 1.65σ

20

Z Score for 95%

1.96

µ (+/-) 1.96σ

21

Z Score for 99%

2.58

µ (+/-) 2.58σ

22

Confidence Interval

X(+/-) Zσ

or

X(+/-) Z(Standard Error)

23

7 Steps in

Hypothesis Testing

  1. State hypothesis
  2. Select test statistic
  3. Specify level of significance
  4. State decision rule
     
  5. Collect sample, calculate sample statistic
     
  6. Make a decision based on hypothesis
  7. Make a decision based on results

24

Hypothesis Test Statistic

(x - H0)

————————

Standard Error

25

Coefficient of Variation

CV

S

———

X

Excess risk per unit of return.

(Lower is better)

26

Sharpe Ratio

E(Rp) - Rrf

——————

σp

Excess return per unit of risk.

(Higher is Better)

27

Chebyshev's Inequality

The percentage of observations that lie within k standard deviations of the mean is at least

1 - 1/k2

for all k > 1 regardless of the shape of the distribution.

28

Roy's Safety First Criterion

E(Rp​) - RL

——————

σp

Probability that the portfolio expected return E(Rp) will be greater than the threshold RL.

(Higher is Better)

29

APR to EAR

(1 + APR/n)n - 1

30

EAR to APR

[(1 + EAR)1/n- 1]n

31

EAR to HPR

(1 + EAR)n/365 - 1

32

HPR to EAR

(1 + HPR)365/n - 1

33

HPR to rmm

HPR(360/n)

34

EAR with

Continuous Compounding

er - 1

or

(rex - 1)

35

Perpetuity

         PMT

P  =   ———

         r