CFA 2018 smart summary, study session 02, reading 09 1

2017, Study Session # 2, Reading # “PROBABILITY CONCEPTS” Random Variable Quantity with uncertain possible value(s) Outcome An observed value of a random variable Event A single outcome or a set of outcomes Mutually Exclusive Events Both cannot happen at the same time P(A|B) = & P(AB) = P(A|B) × P(B) = Probability Two Defining Properties of Probability ≤ P(E) ≤ i.e., Probability of an event lies b/w & ΣP( E i ) = i.e., Total probability is equal to Probability in terms of Odds for the event Probability of occurrence divided by probability of nonoccurrence Multiplication Rule (Joint Probability) Probability that both events will occur P(AB) = P(A|B) × P(B) ⇒ For mutually exclusive events; P(A|B) = 0, hence, P(AB) = Exhaustive Events Include all possible outcomes Empirical Probability Based on historical facts or data No judgments involved Historical + non random A Priori Probability Based on logical analysis Random + historical Subjective Probability An informal guess Involves personal judgment Objective Probability Odds against the event Probability of nonoccurrence divided by probability of occurrence Addition Rule Probability that at least one event will occur P(A or B) = P(A) + P(B) - P(AB) ⇒ For mutually exclusive events P(A or B) = P(A) + P(B) Unconditional Probability Marginal probability Probability of occurrence of an event-regardless of the past or future occurrence Conditional Probability; P(A|B) Probability of the occurrence of an event is affected by the occurrence of another event It is also known as likelihood of an occurrence ‘|’ denotes ‘given’ or ‘conditional’ upon P(A|B) = P (AB) P(B) Mutually exclusive events P(A|B) = For independent events, P(A|B) = P(A) Total Probability Rule It highlights the relationship b/w unconditional & conditional probabilities of mutually exclusive & exhaustive events P(R) = P(RI) + P(RIc) = P(R|I) × P(I) + P(R|Ic) ì P(Ic) Copyright â FinQuiz.com All rights reserved Independent Events Events for which occurrence of one has no effect on occurrence of the other P(A|B) = P(A) P(B|A) = P(B) 2017, Study Session # 2, Reading # Covariance Measure of how two assets move together It measures only direction -∝ ≤ Cov(x, y) ≤ +∝ (property) It is measured in squared units Cov(Ri,Rj) = E {[Ri - E(Ri)] [Rj – E(Rj)]} = Σ P(S) [Ri – E(Ri)] [Rj – E(Rj) Cov (RA,RA ) = variance (RA) (property) Covariance Expected Value Conditional Expected Value Probability weighted outcomes of a random variable It is the best guess of the outcome of a random variable Calculated using conditional probabilities Are contingent upon the occurrence of some other event Variables tend to Correlation + ve ⇒ Move in same direction - ve ⇒ Move in opposite direction ‘0’ ⇒ Asset returns are unrelated Measures the direction as well as the magnitude It is a standardized measure of co-movement It has no units -1 ≤ corr (Ri,Rj) ≤ + Value Correlation Variables tend to +1 ⇒ Perfectly positive ⇒ Move proportionally in the same direction -1 ⇒ Perfectly negative ⇒ Move proportionally in the opposite direction ⇒ Uncorrelated ⇒ No linear relationship Corr (Ri,Rj) = Cov (Ri,Rj) σ (Ri) σ (Rj) Baye’s Formula Portfolio Expected Value Variance ே ே ‫ܧ‬൫ܴ௣ ൯ = ෍ ‫)ܴ݅(ܧ ݅ݓ‬ = ෍ ‫ݓ‬௜ଶ ௜ୀଵ ⇒ Used to update a given set of prior probabilities in response to the arrival of new information ܸܽ‫ݎ‬൫ܴ௣ ൯ ே ߪ௜ଶ ௜ୀଵ ⇒ Where wi = market value of investment in asset ‘i’ market value of the portfolio ே + ෍ ෍ ‫ݓ‬௜ ‫ݓ‬௝ ‫ݒ݋ܥ‬௜௝ ௜ୀଵ ௝ୀଵ Updated probability prior Probability = of new info × probability of the unconditional event probability of new info Copyright © FinQuiz.com All rights reserved 2017, Study Session # 2, Reading # Counting Methods Labeling Formula ݊! ݊ଵ ! … ݊௞ ! The number of ways ‘n’ objects can be labeled with k different labels Factorial [!] Permutation [nPr] Combination [nCr] Multiplication Rule Arranging a given set of ‘n’ items No subgroups There are n! ways of arranging ‘n’ items Number of ways of choosing r objects from a total of n objects when order matters Choosing ‘r’ items from a set of ‘n’ items when order does not matter The number of ways k tasks can be done is (n1)(n2)(n3)…(ni) Copyright © FinQuiz.com All rights reserved  ...2 017 , Study Session # 2, Reading # Covariance Measure of how two assets move together It measures only direction... unconditional event probability of new info Copyright © FinQuiz.com All rights reserved 2 017 , Study Session # 2, Reading # Counting Methods Labeling Formula ݊! ݊ଵ ! … ݊௞ ! The number of ways ‘n’ objects... of co-movement It has no units -1 ≤ corr (Ri,Rj) ≤ + Value Correlation Variables tend to +1 ⇒ Perfectly positive ⇒ Move proportionally in the same direction -1 ⇒ Perfectly negative ⇒ Move proportionally