02 Quantitative Methods - SwiftNotes

CFA Level I - SwiftNotes CFA Level I - Quantitative Methods – SwiftNotes Reading 6 – Time Value of Money Interest rate can be considered as: • Minimum required rate of return • Discount rate • Opportunity cost From a market perspective, 1 + Interest rate = (1 + Real risk-free interest rate)(1 + Inflation premium)(1 + Default risk premium) × (1 + Liquidity premium)(1 + Maturity premium) or Interest rate ≈ Real risk-free interest rate + Inflation premium + Default risk premium + Liquidity premium + Maturity premium 1 + Nominal risk-free interest rate = (1 + Real risk-free interest rate)(1 + Inflation premium) Single Cash Flow: • Remember to clear the stored values in TVM. [2ND] [FV] • Interest rate in percentage • [PV] Present Value, [I/Y] Interest rate, [N] number of periods, [FV] future value • Adjust [I/Y] and [N] when compounding frequency (m) is more than once a year. • Semiannual (m = 2), quarterly (m = 4), monthly (m = 12), daily (m = 365), continuous compounding (m = 1000) • If compounding period and payment frequency are different, use EAR instead of quoted rate. • Continuous Compounding: 𝐹𝐹𝐹𝐹 = 𝑃𝑃𝑃𝑃 × 𝑒𝑒 𝑟𝑟𝑐𝑐𝑇𝑇 Effective Annual Rate (EAR) • Use [2ND] [2]  ICONV • [NOM]  Nominal interest rate (per annum) [EFF]  Effective interest rate, [C/Y]  Compounding period per year Annuity • Remember to clear the stored values in TVM. [2ND] [FV] • [PV], [I/Y], [N], [FV], and [PMT] (Annuity amount) • Ordinary annuity: [2ND] [PMT]  END • Annuity due: [2ND] [PMT]  BGN (Press [2ND] [ENTER] to change mode) • END – Ordinary annuity; BGN – Annuity due 1 CFA Level I - SwiftNotes • • Amortization Schedule: [2ND] [PV] P1 = (Beginning Period) P2 = (Ending Period) Bal = (Balance as at P2) PRN = (Total principal between P1 and P2) INT = (Total interest between P1 and P2) PV of perpetuity = PMT/r (i.e. assumes that first cash flow occurs at the end of the period) Reading 7 – Discounted Cash Flow Applications Net Present Value • NPV > 0  Accept investment NPV < 0  Reject investment • [CF]  Cash Flow Worksheet [NPV]  Net Present Value [IRR]  Internal Rate of Return • [CF] [2ND] [CE|C] to clear values stored in [CF] • CFo  Initial outlay C01  Cash flow for period 1 F01  Frequency of cash flow … Internal Rate of Return (IRR) • Discount rate at which NPV = 0 • If IRR > Discount rate  Accept investment • If IRR < Discount rate  Reject investment When there is conflict between NPV and IRR • Choose project with highest NPV. Mutually exclusive projects (choose only one) • Choose project with highest NPV Independent projects • Choose project as long as NPV > 0 Portfolio Return Measurement • Money Weighted Rate of Return (MWRR) o Uses the concept of Internal Rate of Return (IRR) o Money invested: Cash outflow; Money received from selling/dividend: Cash inflow o Drawback: Return measurement is distorted by additions/withdrawals of funds by clients 2 CFA Level I - SwiftNotes • Time Weighted Rate of Return (TWRR) o Uses the concept of Holding Period Return (HPR) o Calculate HPR whenever there are additions/withdrawals o Advantage: Not influenced by additions/withdrawals of funds o Drawback: Tedious to calculate if there are many additions and withdrawals Pure Discount Securities (e.g. T-Bills) 1) 𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷  Used to quote securities’ price  Not suitable as a return measure 2) 3) 4) 360 Bank discount yield = 𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉 × 𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 𝑡𝑡𝑡𝑡 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 Holding period yield, 𝐻𝐻𝐻𝐻𝐻𝐻 = 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃ℎ𝑎𝑎𝑎𝑎𝑎𝑎 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝  Measures the return over the holding period  Appropriate measure to discount a risk-free cash flow that occurs over the same period Effective Annual Yield, 𝐸𝐸𝐸𝐸𝐸𝐸 = (1 + 𝐻𝐻𝐻𝐻𝐻𝐻)365/𝑡𝑡 − 1  Measures return on discounted security if it is rolled over to 1 year. 𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 360 Money market yield, 𝑀𝑀𝑀𝑀𝑀𝑀 = 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃ℎ𝑎𝑎𝑎𝑎𝑎𝑎 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 × 𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 𝑡𝑡𝑡𝑡 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚  Allows comparison to add-on interest instruments. Bond-equivalent yield • YTM × 2 for semiannual-paying bond • YTM × 4 for quarterly-paying bond, etc… Reading 8 – Statistical Concepts and Market Returns Measurement Scales: • Nominal scale: Categorical (no ranking) • Ordinal scale: Categorical + Ranking • Interval scale: Differences between scales are equal • Ratio scale: Has a true zero point Arithmetic mean: • Simple average of data observations • Advantage: Uses all the data available • Disadvantage: - Influenced by extreme values Median: • Value in the middle of an ascending data • Position of median = (n + 1)/2 • Advantage: Not influenced by extreme values 3 CFA Level I - SwiftNotes Mode: • Find the value with the highest frequency/occurrence Weighted Mean • Takes the weightage of observations into account Geometric Mean • Used to calculate average return over time • Need to add 1 to each return before multiplying. Remember to subtract 1 at the end. • 𝑅𝑅�𝐺𝐺 = [(1 + 𝑅𝑅1 )(1 + 𝑅𝑅2 ) … (1 + 𝑅𝑅𝑁𝑁 )]1/𝑁𝑁 − 1 Harmonic Mean • Used to calculate average rates. • Application is minimal, e.g. cost averaging 𝑛𝑛 • 𝑅𝑅�𝐻𝐻 = 1 1 1 • + 𝑋𝑋1 𝑋𝑋2 +⋯+ 𝑋𝑋𝑁𝑁 Harmonic mean < Geometric mean < Arithmetic mean Quantiles: 𝑦𝑦 • Location of yth percentile, 𝐿𝐿𝑦𝑦 = (𝑛𝑛 + 1) 100 Range • Range = Maximum – Minimum • Advantage: Easy to compute and interpret • Drawback: Does not tell what happens in between Mean Absolute Deviation (MAD) • • • 𝑀𝑀𝑀𝑀𝑀𝑀 = � ∑𝑁𝑁 𝑖𝑖=1|𝑋𝑋−𝑋𝑋 | 𝑁𝑁 Higher MAD indicates higher dispersion Step 1: Calculate the arithmetic mean Step 2: Subtract the arithmetic mean from each data and take the absolute (i.e. positive values) Step 3: Sum up the absolute deviations Step 4: Divide by n Variance and Standard deviation • Standard deviation = √𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉 • Variance = (𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑)2 • Use [2ND] [7] to enter data in DATA worksheet • Use [2ND] [8] to see data summary (use 1-V or LIN) n = number of observations 𝑥𝑥̅ = arithmetic mean Sx = sample standard deviation 𝜎𝜎𝑥𝑥 = population standard deviation 4 CFA Level I - SwiftNotes Semivariance and semideviation • Equivalent to variance and standard deviation but only values below the mean are considered (requires manual calculation) Chebyshev’s Inequality 1 • There is a proportion of at least (minimum) 1 − 𝑘𝑘 2 that the observations are • • between 𝜇𝜇 ± 𝑘𝑘𝑘𝑘 1 There is a proportion of at most (maximum) 𝑘𝑘 2 that the observations are outside 𝜇𝜇 ± 𝑘𝑘𝑘𝑘 Advantage: Generality. Can be applied on any distribution Coefficient of Variation • • • • 𝑆𝑆𝑆𝑆𝑆𝑆 𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 𝐶𝐶𝐶𝐶 = 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 Unitless, can be used to compare relative risk across different datasets The higher the CV, the higher the relative risk When the variable is the return, CV is the risk per unit of return. Sharpe ratio • • • • 𝑆𝑆ℎ = 𝑅𝑅�𝑝𝑝 −𝑅𝑅�𝑓𝑓 𝑠𝑠𝑝𝑝 Measures excess return over risk-free rate per unit of risk The higher the sharpe ratio, the better the performance (when Sharpe ratio is positive) Drawback: o When Sharpe ratio < 0, the higher it is doesn’t make it better o Does not capture the risk when options are used Skewness Symmetrical distribution (Normal distribution) Positively skewed distribution (Skewed to the right) Negatively skewed distribution (Skewed to the left) Mean = Median = Mode Skewness = 0 Mean > Median > Mode Skewness > 0 Mean < Median < Mode Skewness < 0 Kurtosis Leptokurtic • Contains fat tails (i.e. chances of extreme outcomes are more likely) • If equity returns is leptokurtic in nature but is modeled using normal distribution, then risk of extreme outcomes is underestimated Mesokurtic Normal distribution Platykurtic Flat and concentrated in the centre Note: Excess kurtosis = Kurtosis – 3 5 Kurtosis > 3 Excess kurtosis > 0 Kurtosis = 3 Excess kurtosis = 0 Kurtosis < 3 Excess kurtosis < 0 CFA Level I - SwiftNotes Reading 9: Probability • • Probability of an event always between 0 and 1, inclusive Three approaches to probability: o Empirical: Using historical data o Subjective: Opinion-based o A priori: Logical analysis, each outcome is equally likely (Random) Given a probability, P(E), 𝑃𝑃(𝐸𝐸) Odds for E = 1−𝑃𝑃(𝐸𝐸) Odds against E = Given the odds for an event E as a:b 𝑎𝑎 𝑏𝑏 𝑃𝑃(𝐸𝐸) = 𝑎𝑎+𝑏𝑏 𝑃𝑃(𝑛𝑛𝑛𝑛𝑛𝑛 𝐸𝐸) = 𝑎𝑎+𝑏𝑏 𝑃𝑃(𝐴𝐴|𝐵𝐵) = Conditional Probability: Multiplication Rule: 𝑃𝑃(𝐴𝐴𝐴𝐴) = 𝑃𝑃(𝐴𝐴|𝐵𝐵)𝑃𝑃(𝐵𝐵) 𝑃𝑃(𝐴𝐴𝐴𝐴) = 𝑃𝑃(𝐴𝐴)𝑃𝑃(𝐵𝐵) 𝑃𝑃(𝐴𝐴𝐴𝐴) = 0 Bayes’ Theorem: 𝑃𝑃(𝐸𝐸) 𝑃𝑃(𝐴𝐴𝐴𝐴) 𝑃𝑃(𝐵𝐵) (In general) (if A and B are independent) (if A and B are mutually exclusive) Addition Rule: 𝑃𝑃(𝐴𝐴 𝑜𝑜𝑜𝑜 𝐵𝐵) = 𝑃𝑃(𝐴𝐴) + 𝑃𝑃(𝐵𝐵) − 𝑃𝑃(𝐴𝐴𝐴𝐴) 𝑃𝑃(𝐴𝐴 𝑜𝑜𝑜𝑜 𝐵𝐵) = 𝑃𝑃(𝐴𝐴) + 𝑃𝑃(𝐵𝐵) − 𝑃𝑃(𝐴𝐴)𝑃𝑃(𝐵𝐵) 𝑃𝑃(𝐴𝐴 𝑜𝑜𝑜𝑜 𝐵𝐵) = 𝑃𝑃(𝐴𝐴) + 𝑃𝑃(𝐵𝐵) Total Probability Rule: 1−𝑃𝑃(𝐸𝐸) (In general) (if A and B are independent) (if A and B are mutually exclusive) 𝑃𝑃(𝐴𝐴 ) = 𝑃𝑃(𝐴𝐴|𝐵𝐵)𝑃𝑃(𝐵𝐵) + 𝑃𝑃(𝐴𝐴|𝐵𝐵 ′)𝑃𝑃(𝐵𝐵 ′ ) 𝑃𝑃(𝐵𝐵|𝐴𝐴) = 𝑃𝑃(𝐴𝐴𝐴𝐴) 𝑃𝑃(𝐴𝐴) = 𝑃𝑃�𝐴𝐴�𝐵𝐵 �𝑃𝑃(𝐵𝐵) 𝑃𝑃(𝐴𝐴) 6 CFA Level I - SwiftNotes Expected Value, 𝐸𝐸(𝑌𝑌) = ∑ 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 × 𝑌𝑌 Variance, 𝑉𝑉𝑉𝑉𝑉𝑉(𝑌𝑌) = ∑ 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 × (𝑌𝑌 − 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚)2 Correlation (𝜌𝜌) • • • • • • 𝜌𝜌 = 𝐶𝐶𝐶𝐶𝐶𝐶(𝑋𝑋,𝑌𝑌) 𝜎𝜎𝑋𝑋 𝜎𝜎𝑌𝑌 Unitless, measures the degree of linear relationship between X and Y Diversification if 𝜌𝜌 < 1 𝜌𝜌 = +1, perfectly positive correlation 𝜌𝜌 = −1, perfectly negative correlation 𝜌𝜌 = 0, no correlation (no straight line relationship) For a two-asset portfolio: Portfolio expected return, 𝐸𝐸�𝑅𝑅𝑝𝑝 � = 𝑤𝑤1 𝑅𝑅1 + 𝑤𝑤2 𝑅𝑅2 Portfolio variance, 𝜎𝜎𝑝𝑝2 = 𝑤𝑤12 𝜎𝜎12 + 𝑤𝑤22 𝜎𝜎22 + 2𝑤𝑤1 𝑤𝑤2 𝐶𝐶𝐶𝐶𝐶𝐶(𝑅𝑅1 , 𝑅𝑅2 ) Portfolio standard deviation, 𝜎𝜎𝑝𝑝 = �𝑤𝑤12 𝜎𝜎12 + 𝑤𝑤22 𝜎𝜎22 + 2𝑤𝑤1 𝑤𝑤2 𝐶𝐶𝐶𝐶𝐶𝐶(𝑅𝑅1 , 𝑅𝑅2 ) If the portfolio has n assets, then we require: • n means • n variances • n(n-1)/2 or nC2 covariances Combination  Order does not matter (nCr) Permutation  Order matters (nPr) Reading 10: Common Probability Distributions Binomial Distribution 𝑃𝑃(𝑋𝑋 = 𝑥𝑥) = 𝑛𝑛𝐶𝐶𝑥𝑥 × 𝑝𝑝 𝑥𝑥 × (1 − 𝑝𝑝)𝑛𝑛−𝑥𝑥 Mean, 𝜇𝜇 = 𝑛𝑛𝑛𝑛 Variance, 𝜎𝜎 2 = 𝑛𝑛𝑛𝑛(1 − 𝑝𝑝) Standard deviation, 𝜎𝜎 = �𝑛𝑛𝑛𝑛(1 − 𝑝𝑝) p < 0.5: Positive skew distribution p = 0.5: Symmetrical distribution p > 0.5: Negative skew distribution where: x = number of successes in n trials p = probability of success in a trial Continuous Uniform Distribution: 𝑥𝑥−𝑎𝑎 𝑃𝑃(𝑋𝑋 ≤ 𝑎𝑎) = 𝑏𝑏−𝑎𝑎 where 𝑎𝑎 < 𝑥𝑥 < 𝑏𝑏 =1 where x ≥ b 7 CFA Level I - SwiftNotes Normal Distribution 𝑋𝑋−𝜇𝜇 • 𝑍𝑍 = 𝜎𝜎 • • z 0.00 0.10 0.20 0.30 0.40 0.50 Used to model asset returns Statistical table used in CFA Exam is cumulative. 0.00 0.5000 0.5398 0.5793 0.6179 0.6554 0.6915 0.01 0.5040 0.5438 0.5832 0.6217 0.6591 0.6950 0.02 0.5080 0.5478 0.5871 0.6255 0.6628 0.6985 0.03 0.5120 0.5517 0.5910 0.6293 0.6664 0.7019 0.04 0.5160 0.5557 0.5948 0.6331 0.6700 0.7054 0.05 0.5199 0.5596 0.5987 0.6368 0.6736 0.7088 0.06 0.5239 0.5636 0.6026 0.6406 0.6772 0.7123 0.07 0.5279 0.5675 0.6064 0.6443 0.6808 0.7157 0.08 0.5319 0.5714 0.6103 0.6480 0.6844 0.7190 0.09 0.5359 0.5753 0.6141 0.6517 0.6879 0.7224 Safety-First Optimal Portfolio Roy’s Safety-First Ratio = 𝐸𝐸�𝑅𝑅𝑝𝑝 �−𝑅𝑅𝐿𝐿 𝜎𝜎𝑝𝑝 (RL is the minimum acceptable level of return) Shortfall risk = 𝑃𝑃𝑃𝑃(𝑍𝑍 < −𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆) • • Safety-first optimal portfolio: The portfolio with the highest Safety-First ratio and lowest shortfall risk. Shortfall risk: The probability that the portfolio return will be lower than the minimum acceptable level of return. Lognormal Distribution • Used to model asset prices • Scaling Return and Standard Deviation: Before After Scaling E(R)  E(R) × T 2 𝜎𝜎  𝜎𝜎 2 𝑇𝑇 𝜎𝜎  𝜎𝜎√𝑇𝑇 Monte Carlo Simulation • Simulates scenarios based on random numbers • Advantage: Forward looking, allows simulation of variables • Drawback: Complex, hard to interpret Historical Simulation • Simulates scenarios based on historical data • Advantage: Simple to compute • Drawback: Assumption that past will repeat in the future, can’t do simulation (Whatif) 8 CFA Level I - SwiftNotes Reading 11: Sampling and Estimation • • • • Sampling Error = Population mean – Sample mean Sampling methods o Simple random sampling o Systematic random sampling o Stratified random sampling Central Limit Theorem: In general, when sample size n is greater than or equal to 30 (n ≥ 30), we can assume that the distribution of sample mean is approximately normally distributed. Desirable properties of estimation: o Unbiasedness – An unbiased estimator is one whose expected value equals the parameter it is intended to estimate. o Efficiency – An unbiased estimator is efficient if no other unbiased estimator of the same parameter has a sampling distribution with smaller variance. o Consistency – A consistent estimator is one for which the probability of estimates close to the value of the population parameter increases as sample size increases. Sampling From Population with: Normal distribution; known variance (𝜎𝜎 2 ) Normal distribution; unknown variance (𝜎𝜎 2 ) Nonnormal distribution; known variance (𝜎𝜎 2 ) Nonnormal distribution; unknown variance (𝜎𝜎 2 ) Statistics for small sample size (n < 30) Z T Not available Not available Statistics for large sample size (n ≥ 30) z t z t (1 – α)100% confidence interval for the population mean 𝜎𝜎 𝑥𝑥̅ ± 𝑧𝑧𝛼𝛼/2 � � if 𝜎𝜎 is known √𝑛𝑛 𝑠𝑠 𝑥𝑥̅ ± 𝑡𝑡𝛼𝛼/2 � � √𝑛𝑛 if 𝜎𝜎 is unknown (Degrees of freedom, df = n – 1) where: α = level of significance 𝜎𝜎 𝑠𝑠 and = standard error of the mean √𝑛𝑛 √𝑛𝑛 What makes the confidence interval wider? • Higher confidence level • High standard deviation • Small number of observations Biases: • Data mining bias - Cherry-picking data • Sample selection bias - Omitting certain data • Self-selection bias - Report only when performance is good (hedge funds) 9 CFA Level I - SwiftNotes • • • Survivorship bias - Mutual funds & hedge funds that have been closed Look ahead bias - Using data that was not available yet at that time (P/E ratio) Time period bias - Using short period of data Reading 12: Hypothesis Testing • • Type I error: Rejecting the null hypothesis when it is true Type II error: Not rejecting the null hypothesis when it is false Test Null hypothesis, H0 Alternative hypothesis, Ha Two-tailed test = ≠ Right-tailed test ≤ or = > Left-tailed test ≥ or = < Probability of Type I error = α (Significance level) Probability of Type II error = β Power of the test = 1 – β (i.e. The probability of rejecting the null hypothesis when it is false) • p-value: The smallest significant level at which the null hypothesis can be rejected o If p-value < significance level, reject null hypothesis (H0) o If p-value > significance level, do not reject null hypothesis (H0) Test statistic: Single mean: Single mean: Single variance: Two variances: 𝑍𝑍 = 𝑋𝑋� − 𝜇𝜇 𝜎𝜎⁄√𝑛𝑛 𝑋𝑋�−𝜇𝜇 𝑡𝑡 = 𝑠𝑠⁄ 𝑛𝑛 𝜒𝜒 2 = √ (𝑛𝑛−1)𝑠𝑠2 𝜎𝜎2 𝑠𝑠12 𝐹𝐹 = 𝑠𝑠2 Note: For the F test, 𝑠𝑠12 ≥ 𝑠𝑠22 . • • 2 (df = n – 1) (df = n – 1) (df for numerator = n1 – 1; df for denominator = n2 - 1) If you rejected the null hypothesis, base your conclusion on the alternative hypothesis. If you did not reject the null hypothesis, base your conclusion on the null hypothesis. 10 CFA Level I - SwiftNotes Reading 13: Technical Analysis Technical Analysis Tools Charts: • Line Chart: Shows closing price • Bar Chart: Open/Close, High/Low • Candlestick charts: Open/Close, High/Low, White body (Up), Shaded body (Down), doji • Point and Figure chart: Changes in price, no time horizon • Relative strength analysis: Measure outperformance/underperformance/neutral Scale: • Linear scale: For small price range • Logarithmic scale: For large price range (e.g. DJIA) Support and Resistance • Support – A low price range in which buying activity is sufficient to stop a decline in price • Resistance – A high price range in which selling activity is sufficient to stop a rise in price • Change in polarity – Once a resistance (support) level is breached, it becomes a support (resistance) level Reversal patterns: Head and Shoulders Inverse Head and Shoulders Double Tops, Triple Tops Double Bottom, Triple Bottom Uptrend  Downtrend Downtrend  Uptrend Uptrend  Downtrend Downtrend  Uptrend Target price for: Head and Shoulders: Inverse Head and Shoulders: Double Top: Double Bottom: Neck – (Head – Neck) Neck + (Neck – Head) Valley low – (Valley high – Valley low) Valley high + (Valley high – Valley bottom) Continuation Patterns: • Triangles • Rectangle • Flags and pennants (Shorter-term compared to triangles and rectangle) Price-based indicators: • Moving average o Rolling averages to remove noise/smoothening o Buy at golden cross (ST > LT), sell at dead cross (ST < LT) o Note: ST denotes short term, and LT denotes Long term 11 CFA Level I - SwiftNotes • • • • • Bollinger bands o Mean +/- 2 standard deviations o Strategy: Buy (sell) when price breaks above upper (below lower) band o Contrarian strategy: Buy (sell) when price reaches lower (upper) band Momentum oscillators: o Determine strength of trend or detect reversals or overbought/oversold Relative Strength Index (RSI) o Compared gains over losses over a set period o Strategy: Buy at oversold level (20), sell at overbought level (80) Stochastic Oscillator: o has two lines, %K and %D; o prices tend to stay at high end during uptrend, stay at low end during downtrend; o Buy at oversold level, sell at overbought level Moving-Average Convergence/Divergence Oscillator (MACD) o MACD line and Signal Line (Crossovers indicate change in trend) Sentiment Indicators: • Opinion Polls o Based on expert opinion • Put/Call ratio o If ratio > 1 (more puts than calls, bearish) o If ratio < 1 (more calls then puts, bullish) • CBOE Volatility Index o Volatility implied from option prices o High index reflects high volatility in the market • Margin debt o When margin debt is too high (bubble), market may reverse • Short Interest ratio o High ratio indicates bearish sentiment Flow-of-Funds Indicators: • Arms Index (TRIN) o TRIN > 1, more volume in declining stocks o TRIN = 1, market is in balance o TRIN < 1, more volume in rising stocks • Mutual Fund Cash Position o Analyst: Low cash position, managers bullish, anticipate rising prices High cash position, managers bearish, anticipate lower prices o Contrarian: Low cash position, effect of purchases reflected in price High cash position, buying power for manager, bullish • New equity issuance o When too many IPOs have been done, upward price trend may be about to turn down • Secondary Offerings: Same as IPO • Margin debt 12 CFA Level I - SwiftNotes Cycles • Kondratieff Wave: Western economies have a 54-year cycle • 18-Year Cycle (Real Estate) • Decennial Pattern (for DJIA): o Years ending with 0 – Worst performance o Years ending with 5 – Best performance • Presidential Cycle (DJIA): o Year prior to election shows the best performance (due to stimulus) Elliott Wave Theory • Consists of five impulse waves, followed by three corrective waves • Price projection base on Fibonacci ratio • Fibonacci sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34,… • Golden ratio: 1.618 13