CFA Level 1 - 101 Must Knows Addition Rule of Probability - Answer: ADDITION: P (A or B) = P(A) + P(B) - P(AB) Roy's Safety-First Criterion - Answer: Safety First Ratio = (E(R) - Rₜ) / σ Larger ratio is better If (Rₜ) is risk free rate, then it becomes Sharpe Ratio Sharpe Ratio - Answer: Sharpe Ratio = (E(R) - RFR) / σ Larger ratio is better If (Rt) is higher than RFR, then it becomes Safety First Ratio Central Limit Theorem - Answer: If we take samples of a population, with a large enough sample size, the distribution of all sample means is normal with: - A mean equal to the population mean CFA Level 1 - 101 Must Knows - A variance equal to the population variance divided by sample size (σ² / n) Standard Error of Sample Mean - Answer: σ / n^½ Binomial Probability - Answer: One of two possible outcomes (i.e. success/failure) Possible outcomes can be demonstrated in binomial tree Use "nCr" on calculator to solve: nCr = P(success)^x * P(failure)^(n-x) P - Value - Answer: Based on a calculated test statistic, rather than a significance level (which is chosen) p-value = smallest significance level at which an analyst can reject the null hypothesis one-tailed test - "less than or equal to" two-tailed test - "equal to" CFA Level 1 - 101 Must Knows Cumulative Distribution Function - Answer: Gives the probability that a random variable will have an outcome less than or equal to a specific value (represented by F(x)) F(x) = probability of an outcome less than or equal to x Standard normal table (z) shows cumulative probabilities Effective Annual Yield - Answer: EAY = (1 + (i/n))^n - 1 Stated Rate = (EAY^(1/n) - 1) * n Continuous Compounding - Answer: ln(EAY) = continuously compounded stated rate e^(continuously compounded stated rate) = EAY Type I Error - Answer: Incorrectly rejecting a true null hypothesis (convicting an innocent person is Type I) Type II Error - Answer: Failure to reject a false null hypothesis CFA Level 1 - 101 Must Knows (failure to convict a guilty person is Type II) Significance Level / Power of a Test - Answer: Significance Level = Probability of Type I Power of a Test = (1 - Probability of Type I) Covariance (Probability Model) - Answer: Covariance of random variables A and B from probability model On the calculator: 1) Enter returns for set A and joint probabilities for AB; find mean A 2) Enter returns for set B and joint probabilities for AB; find mean B 3) Multiply each joint probability AB by each set's returns minus means (ex: P(AB1)(A1 - Mean A)(B1 - Mean B) + P(AB2)(A2 - Mean A)(B2 - Mean B) + ... + P(ABn)(An - Mean A)(Bn - Mean B)) 4) The summed total is your covariance Covariance (Sample) - Answer: Covariance of random variables A and B from sample with historical data with n observations