CFA L1V1 - Probability Concepts - Reading 8 PDF

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04.01.20 CFA Level 1: Probability Concepts Commonly referred to concepts, terms, or definitions I’m not familiar with, which aren’t the core concepts presented in the reading: Options Pairs arbitrage trade: A trade in two closely related stocks involving the short sale of one and purchase of the other. Dutch Book Theorem: Inconsistent probabilities create profit opportunities. Definitions: Random variable: A quantity whose outcomes, i.e. the possible values, are uncertain. An example is the return on a risky asset. Event: A specified set of outcomes. Probability: (1) All probabilities are between 0 and 1, inclusive; (2) The sum of probabilities of any set of mutually exclusive and exhaustive events equals 1. Mutually exclusive: Only one event can occur at a time. Exhaustive: Events cover all possible outcomes. The probability of any event is the sum of the probabilities of the distinct outcomes included in the definition of the event. Estimating probabilities in investments: Probabilities are often estimated as a relative frequency of occurrence based on historical data. Empirical probability: Estimating relative frequency of occurrence using historical data. This is an empirical insight, i.e. it is based on observation and past experience. Subjective probability: Whenever personal or subjective judgment is introduced into the calculation of probability, i.e. the calculation is not empirical, then the type of probability is subjective probability. A priori probability: Using deduction and logical reasoning to arrive at the probability of an event. Objective probabilities: Empirical probability and a priori probability are both objective probabilities. They will not vary from person to person. Probability to Odds (For): If P(E) is given, then odds for E are calculated using the formula E = P(E)/[1-P(E)].

Probability to Odds (Against): If P(E) is given, the odds against E are the reciprocal of odds for E, i.e. E = [1P(E)]/P(E). Odds (For) to Probability: If the odds for E are given as a to b, then P(E) can be calculated using the formula a/ (a+b). Odds (Against) to Probability: If odds against E are given as a to b, then P(E) is b/(a+b). Unconditional probability (a.k.a Marginal Probability): Probability of an event without any restriction, i.e. a stand-alone probability. Conditional probability: Probability of an event given that another event has occurred. Represented as P(A | B), i.e. “Probability of A given B”. Joint probability: The probability of both A and B happening. Represented as P(AB). It is the sum of the probabilities which both A and B have in common. Calculating conditional probability: P(A | B) = (Joint Probability of A and B)/[P(B)] = P(AB)/P(B) Multiplication rule (derived from conditional probability equation): P(AB) = P(A | B) x P(B) Addition rule for probabilities: Given events A and B, we often want to know the probability that either Event A or Event B will occur. Put simply, we want to know the probability of at least one of the two events occurring. To calculate such probabilities, we use the addition rule. It is stated as follows: P(A or B) = P(A) + P(B) – P(AB) Remember this: P(AB) = P(BA) Independent events: Events that are not related to one another. Events are independent when P(A | B) = P(A) or, equivalently, P(B | A) = P(B). Multiplication rule for independent events: P(AB) = P(A) x P(B), P(ABC)= P(A) x P(B) x P(C) Total probability rule: When events are mutually exclusive and exhaustive, we can analyze the event using the total probability rule. The rule is stated as follows: P(A) = P(AS) + P(ASC) P(A) = P(A | S) x P(S) + P(A | SC) x P(SC)...