(8) Quantitative Methods: Probability Concepts (kyle created) Flashcards Preview

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Flashcards in (8) Quantitative Methods: Probability Concepts (kyle created) Deck (34)
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1
Q

Random Variable

A

A quantity whose outcomes are unknown

2
Q

Outcome

A

Possible values

3
Q

Event

A

A specified set of outcomes (point or range); denoted by capital letters

4
Q

The two defining properties of a probability are as follows:

A

= P (A)

  1. P (A) is less than or equal to 1 or greater than or equal to zero
  2. The sum of all probabilities sums up to 1
5
Q

Mutually exclusive events

A

If one event happens, another event can’t

6
Q

Exhaustive events

A

Covers all possible outcomes

7
Q

The two elements needed to solve a probability problem are:

A
  1. Set of all distinct possible outcomes

2. The probability distribution

8
Q

Empirical Probability

A
  • Based on historical observations
  • Past is assumed to be representative of the future
  • Historical period must include occurrences of the event
9
Q

Subjective probability

A
  • Adjust an empirical probability based on intuition or experience
  • This occurs when there is a complete lack of empirical observations or
  • to make a personal assessment
10
Q

A priori probability

A

arrived at based on deductive reasoning

11
Q

Odds for E. What is the formula and meaning?

A

P (E) / 1 - P(E);

Ex: P(E) = 10%
Odds for E = .1 / (1 - .10)
Odds for E = .1/.9 or 1 to 9
This is saying for each occurrence of event E, we should expect 9 events of non-occurrence

If Odds for E = 1 to 9 then to get the probability you take 1 / (1+9)

12
Q

Odds against E. What is the formula and meaning?

A

1 - P (E) / P(E);

Ex: P(E) = 10%
Odds against E = .9 / .1 or 9 to 1
This is saying for every 9 non-occurrence of event E, we should expect 1 occurrence of the event

If Odds against E = 9 to 1 then to get the probability you take 1 / (9+1)

13
Q

Probability: Terminology (5)

A
  1. Random Variable: Uncertain number
  2. Outcome: Realization of random variables
  3. Event: Set of one or more outcomes
  4. Mutually exclusive: cannot both happen
    5: Exhaustive: Set of events includes all possible outcomes
14
Q

Probability: Types (3)

A
  1. Empirical: Based on analysis of data
    1. Subjective: Based on personal perception
    2. A priori: Based on reasoning, not experience
15
Q

Probability: Odds for or Against (2)

A

Odd happening/ odds not happening.

Given probability that a horse will win a race= 20%

Odds for: .20/ (1-.2)= .2/.8= 1/4 or 1 to 4
Odds against: (1-.2) .2= .8/.2= 4 or 4 to 1
16
Q

Probability: Conditional vs Unconditional (2)

A

Two types of probability:

  • Unconditional P (A), the probability of an event regardless of the outcomes of other events
  • Conditional P (A|B), the probability of A given that B has occurred (e.g. The probability that Marley will be up, given the red raises interests rates)
17
Q

Joint Probability (Multiplication rule of probability)

A

Notation is P (AB) which means the probability of A and B

The probability that both events will occur is their joint probability
Examples using conditional probability:
P (interest rates will increase) = P (A) = 40%
P (recession given a rate increase) = P (B|A) = 70%

Probability of a recession and an increase in rates,

P (BA) =P(B|A) x P(A) =.7 x .4 = 28%
18
Q

Addition Rule for Probabilities

A
  • P (A or B) = P(A) + P(B) - P(AB)
  • We must subtract the joint probability P (AB)
  • At least one of two events will occur
19
Q

Formula for the probability of A given B; P (A|B) =

A

P(AB) / P(B)

20
Q

Multiplication rule for independent events

A

When two events are independent of each other, the joint probability of A and B = P(A) x P(B)

21
Q

Total probability rule formula is

A

P(A) = P(A|S1)xP(S1) + P(A|S2)xP(S2)….+ P(A|Sn)xP(Sn)

A is the event
S1 is scenario 1
S2 is scenario 2

22
Q

Portfolio expected return

A

Weighted average of the expected returns on the different securities

23
Q

Covariance of returns is negative if these two conditions are met

A
  1. The return on one asset is above its expected value
  2. The return on the other asset tends to be below its expected value
    This is an inverse relationship
24
Q

Covariance of returns is equal to 0 when

A

The return on the assets are unrelated

25
Q

Covariance of returns is positive the following is met

A

The returns on both assets tend to be on the same side (above or below) their expected values at the same time
This is a positive relationship

26
Q

Bayes’ formula

A

Rational method for adjusting our viewpoints as we confront new information

P (event | information) = [P (Information | event) / P (information) ] x P (event)

27
Q

4 Principles of counting

A
  1. Multiplication rule
  2. Multinomials
  3. Combinations
  4. Permutations
28
Q

Calculate the correlation of returns using a covariance matrix

A

= covariance / [square root of variance 1 x square root of variance 2]

29
Q

What is permutation used for?

A

Is a listing in which the order of the listed items does matter

30
Q

What is combination used for?

A

Is a listing in which the order of the listed items does not matter

31
Q

Another way to calculate covariance if given standard deviation and correlation

A

= standard deviation of one bond x standard deviation of second bond x the correlation between two bonds

32
Q

Which of the following has the weakest linear relationship? - .85, -.15, or .43

A

-.15 because its closest to zero

33
Q

A correlation will always be between what two numbers?

A

-1 and 1

the closer the value is to 1 or -1, the stronger the linear relationship

34
Q

Given a portfolio of 5 stocks, how many unique covariance terms, excluding variances, are required to calculate the portfolio return variance?

A

Formula: N^2 - n / 2

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