https://www.fintreeindia.com/ The Time Value of Money © 2017 FinTree Education Pvt Ltd LOS a Interest rate can be interpreted as - Required rate of return, Discount rate or Opportunity cost LOS b International Fischer Relationship (approx.) 100 @ 10% p.a 110 Consumption cost 107 True saving Inflation Real rate of return e Nominal risk-free rate = Real risk-free rate + Expected inflation Treasury bonds = Real RFR + Expected inflation re Corporate bonds = Real RFR + Expected inflation + Risk premium Return on Non-investment grade bond > Return on Investment grade bond, because risk of Non-investment grade bond > risk of Investment grade bond Types of risks nT Liquidity risk Maturity risk Risk that borrower will not make promised payments in a timely manner Risk of receiving less than FV for an investment if it must be sold for cash quickly Risk of volatility of price of a bond because of its longer maturity Default risk premium Liquidity risk premium Maturity risk premium Low default rate = Low DRP Less liquidity = High LRP Shorter maturity = Low MRP Fi Default risk https://www.fintreeindia.com/ LOS c © 2017 FinTree Education Pvt Ltd Calculation and interpretation of effective annual rate The rate of interest that an investor actually earns as a result of compounding is known as EAR + (Int rate/m)m - Effective Annual Rate = m = compounding frequencies per year EAR on TI BA II Plus Professional - 2nd LOS d TVM with different compounding frequencies Annual Quarterly Semiannual N=1 I/Y = 13.25 PV = -100 FV = 113.25 N=1X2=2 I/Y = 13.25/2 = 6.625 PV = -100 FV = 113.68 LOS e Monthly N=1X4=4 I/Y = 13.25/4 = 3.3125 PV = -100 FV = 113.92 N = X 12 = 12 I/Y = 13.25/12 = 1.104 PV = -100 FV = 114.08 Annuity e It is a stream of equal cash flows occurring at equal intervals Annuity due re Ordinary annuity End mode 100 100 100 100 100 100 100 PV of perpetuity = LOS f nT Beginning mode Amortization schedule Loan - 100,000 Fi CF Disc rate Int rate - 10% Tenure - yrs Year Opening loan Instalment Interest (Op loan X rate of int.) Principal repayment (Inst - Int.) Closing loan (Op loan Princ repayment) 100,000 31,547 10,000 21,547 78,452 78,452 31,547 7,845 23,701 54,751 54,751 31,547 5,475 26,071 28,679 28,679 31,547 2,868 28,679 - https://www.fintreeindia.com/ © 2017 FinTree Education Pvt Ltd Using amort function in TI BA II plus professional Ÿ Ÿ Ÿ Ÿ Ÿ Ÿ Ÿ Ÿ Ÿ Ÿ Ÿ 2nd CLR TVM (FV) PV = -100,000 N = I/Y = 10 CPT PMT = 31,547 2nd AMORT (PV) 2nd CLR WORK (CE|C) P1 = P2 = BAL = 78,452 PRN = 21,547 INT = 10,000 P1 = P2 = Eg CFs: PV and FV of uneven CFs Discount rate = 10% N = years Year = −1,000 Year = −500 Year = Year = 4,000 Year = 3,500 Year = 2,000 re CF 2nd CLR WORK (CE|C) CF0 = CF1 = −1,000 CF2 = −500 CF3 = CF4 = 4,000 CF5 = 3,500 CF6 = 2,000 I = 10 → Enter → ↓ (down key) CPT NPV = 4711.91 Fi nT Ÿ Ÿ Ÿ Ÿ Ÿ Ÿ Ÿ Ÿ Ÿ Ÿ Ÿ e Using CF function in TI BA II plus professional https://www.fintreeindia.com/ © 2017 FinTree Education Pvt Ltd Discounted Cash Flow Applications LOS a NPV PV of inflows − PV of outflows IRR Rate at which PV of inflows = PV of outflows At IRR, NPV = LOS b Decision rule IRR NPV +ve = Accept If IRR > WACC = Accept −ve = Reject If IRR < WACC = Reject Mutually exclusive projects Accept project with highest NPV For a single project NPV and IRR rules lead to same accept/reject decision e If IRR > WACC, NPV =+ve If IRR < WACC, NPV =−ve LOS c re Holding period return (HPR) Ending value − beginning value Beginning value Or Ending value − Beginning value Total return Ending value + CF received − Beginning value Time-weighted rate of return (TWRR) IRR Geometric mean of HPR Appropriate if manager has complete control over inflows and outflows ! Or Money-weighted rate of return (MWRR) Fi LOS d nT Ending value - beginning value + CF received Beginning value Provides better measure of manager’s ability to select investments TWRR is not affected by timing of the cash flows, therefore it is more preferred method of performance measurement ! If funds are contributed to a portfolio just prior to a period of relatively poor performance, MWRR < TWRR ! If funds are contributed to a portfolio just prior to a period of relatively high returns, https://www.fintreeindia.com/ © 2017 FinTree Education Pvt Ltd LOS e & f Effective earning yield (1+3.09%)365/90- = 13.13% j k l Or mistakes analogy to remember the formulas (indicated in red) Compounding 365 days Investment value as base 90 3.09% 365 12.53% 3.09 + 3.09% 1000 90 days 30 = 3.09% 970 Bank discount yield 12% j k l Money market yield No Compounding 360 days Face value as base − 3% 90 3.09% 360 12.36% Fi nT re e 360 No Compounding 365 days Investment value as base T - bill 970 30/1000 =3% j k l Holding period yield N = 90/365 PV = -970 FV = 1000 I/Y = 13.14 % 90 Bond equivalent yield j k l No Compounding 360 days Investment value as base Statistical Concepts and Market Returns https://www.fintreeindia.com/ © 2017 FinTree Education Pvt Ltd LOS a Descriptive statistics Inferential statistics Used to summarize important characteristics of large data Used to make forecasts of large data Eg Average of weekly tests Eg Forecast on pass or not Sample Set of all possible members of a stated group Subset of population CFA level candidates globally CFA level candidates in class Nominal Ordinal Interval Higher level of measurement than nominal scales Provides relative ranking and assurance that differences between scale values are equal nT Contains least information Types of measurement scales re e Population Classification has no particular order Observation is assigned to a category Fi Eg MF’s star rating LOS b Parameter Measure used to describe a characteristic of a population Sample statistic Weakness - Zero doesn’t mean total absence Eg Temperature measurement Ratio Most refined level of measurement Provides ranking and equal differences between scale values Has a true zero point as origin Frequency distribution Tabular presentation of statistical data It is used to measure a characteristic of a sample Data employed with a frequency distribution may be measured using any type of measurement scale https://www.fintreeindia.com/ LOS c © 2017 FinTree Education Pvt Ltd Relative frequency and cumulative relative frequency Interval / class Frequency Cumulative frequency Relative frequency Cumulative relative frequency 10 - 15 7 (7/50) 14% 14% 15 - 20 12 19 (12/50) 24% 38% 20 - 25 21 40 (21/50) 42% 80% 25 - 30 10 50 (10/50) 20% 100% Total 50 100% Histogram and Frequency polygon LOS d Frequency Interval Interval midpoints Frequency polygon re Histogram e Frequency LOS e Measures of central tendency Weighted mean AM = 10 + 14 + + WM = 10(20%) + 14(20%) + 4(35%) + 8(25%) WM = 8.2 Geometric mean Harmonic mean GM = HM = √1.1 X 1.14 X 1.04 X 1.08 − 1/10 + 1/14 + 1/4 +1/8 GM = 8.94 HM = 7.32 Fi AM = nT Arithmetic mean Mean ª Sum of deviations from arithmetic mean is always zero ª To calculate portfolio return, weighted mean is used ª Geometric mean is used for calculating investment returns over multiple periods ª Harmonic mean is used to calculate average of ratios ª Arithmetic mean > Geometric mean > Harmonic mean https://www.fintreeindia.com/ Median © 2017 FinTree Education Pvt Ltd It is the midpoint of a data set Median = [(n+1) X 50%]th observation Data needs to be arranged in ascending order to calculate median using above formula 3 Mode Median = [(9+1) X 50%] = 5th observation Value that occurs most frequently in a data set A data set can have more than one mode or even no mode If a data set has one/two/three modes it is said to be unimodal/bimodal/trimodal LOS f Quartiles, quintiles, deciles, percentiles Quartiles e Distribution is divided into tenths Distribution is divided into fifths [(n + 1) × 25%]th [(n + 1) × 20%]th re Distribution is divided into quarters LOS g Percentiles Deciles Quintiles [(n + 1) × 10%]th Distribution is divided into hundreds [(n + 1) × 1%]th nT Measures of dispersion Mean absolute deviation (MAD) Variance Maximum value − minimum value ∑|(x − x)| n Population variance - Fi Range ∑ (x − μ)2 n Standard deviation Population SD - Sample SD - Sample variance ∑ (x − x)2 n−1 Variance = σ2 SD can be calculated directly on TI BA II plus professional Ÿ Use DATA (2nd 7) to enter data then, Ÿ Use STAT (2nd 8) to see SD https://www.fintreeindia.com/ © 2017 FinTree Education Pvt Ltd LOS h Chebyshev’s inequality Applies to sample or population data, normal or skewed distribution Calculated as, − 1/k2 60 Eg 70 SD = where k > 80 Chebyshev’s inequality = − 1/22 = − 1/4 K = 10/SD K=2 = 75% Interpretation: 75% observations lie within ±2 SD of mean LOS i Sharpe ratio Coefficient of variation (CV) It is used to measure excess return per unit of risk It is used to measure the risk per unit of expected return aka reward-to-variability ratio e CV = SDx X SR = Portfolio return − RFR SD of portfolio Lower the better re Higher the better Sharpe ratio Fi RFR 10 km Which is more economical ? Wrong interpretation - 25/3 = 8.33 Correct interpretation - 15/3 = Sharpe ratio = km km 15 km Motorcycle takes 2.2 ltrs of petrol to cover the entire distance 10 10 RFR nT Motorcycle takes ltrs of petrol to cover the entire distance ✘ 20/2.2 = 9.09 ✓ 25 − 10 ✓ 10/2.2 = 4.54 ✘ Rp − RFR SDp 20 − 10 2.2 https://www.fintreeindia.com/ © 2017 FinTree Education Pvt Ltd LOS j Skewness Negatively skewed/ left skew Positively skewed/ right skew No skew Normal distribution Skewed distribution Symmetrical distribution Asymmetrical distribution Skewness: Extent to which data is not symmetrical Negative skew in returns distributions indicates increased risk LOS k re e Locations of mean, median and mode Mean, median, mode LOS l Median Median Mean > Median > Mode Fi Mean Mode nT Mean = Median = Mode Mode Mean Mean < Median < Mode Kurtosis Mesokurtic distribution Leptokurtic distribution Platykurtic distribution Kurtosis = Kurtosis > Kurtosis < Excess kurtosis = Excess kurtosis = +ve Excess kurtosis = -ve Kurtosis: Measures the peakedness of a distribution Positive kurtosis in returns distributions indicates increased risk https://www.fintreeindia.com/ © 2017 FinTree Education Pvt Ltd LOS n Shortfall risk and Safety first ratio Shortfall risk Safety first ratio Probability that portfolio value or return will fall below a particular value or target over a given period of time Excess return per unit of risk over minimum acceptable return/threshold level SF ratio = Rp − Threshold return Sdp Higher the better Lower the better Eg Average return = 20% SD = 3% Threshold level = 15% Z-value = 15 − 20 = −1.66 Shortfall risk Probability at −1.66 z-value = 95.15% Therefore shortfall risk ; − 0.9515 = 4.85% LOS o 20% = 1.66 e 15% SF ratio = 20 - 15 nT re Normal and lognormal distribution Normal distribution Ÿ Ÿ No skew Not bounded by zero Lognormal distribution Ÿ Ÿ Ÿ Skewed to the right Bounded by zero Useful for modeling asset prices, because they can not take negative values Fi The logarithms of lognormally distributed random variables are normally distributred LOS p Discrete and continuous compounding Discrete compounding - Annual, semi-annual, quarterly, monthly etc Continuous compounding - No of compounding periods within a given time period https://www.fintreeindia.com/ © 2017 FinTree Education Pvt Ltd Continuous compounding calculations 100 20% 117.35 100 0.8 100 x e0.2 x 0.8 = 117.35 LOS q 20% ln 117.35 100 117.35 100 0.8 0.8 → 16% 20% 117.35 0.8 117.35 x e-0.2 x 0.8 = 100 → 20% Monte Carlo simulation Technique based on repeated generation of one or more risk factors that affect security values, to generate a distribution It is used to Its limitations are LOS r It is complex It is subject to model risk and input risk Simulation is not an analytic method, but a statistic one Ÿ Increased complexity does not necessarily ensure accuracy Ÿ Ÿ Ÿ e Value complex securities Simulate profits/losses from a trading strategy Calculate estimates of VaR to determine the riskiness of a portfolio Ÿ Simulate pension fund assets and liabilities to examine the variability of the differences between the two Ÿ Value portfolios of assets that not have normal returns distribution Ÿ Ÿ Ÿ re Historical simulation It is based on actual change in value or actual change in risk factor for some prior period Each iteration of simulation involves randomly selecting one of these past changes for each risk factor and calculating the value of the asset or portfolio in question, based on those changes in risk factor nT Its advantage is that it uses actual distribution of risk factors, which need not be estimated Fi Its limitations are : Past changes in risk factor may not be a good indication of future changes It can not address the sort of ‘whatif’ questions that Monte Carlo simulation can https://www.fintreeindia.com/ LOS a Simple random sampling and sampling distribution Sampling and Estimation © 2017 FinTree Education Pvt Ltd Simple random sampling Systematic sampling Method of selecting a sample in such a way that each item in the population has same likelihood of being included in the sample Another way to form an approximately random sample Eg Drawing a sample of apples from 50 to calculate average weight Eg Selecting every nth item from the population Sampling distribution - It is a probability distribution of all possible sample statistic computed from samples drawn from the population Sampling error = Sample statistic − Population parameter re LOS b e Sampling distribution does not have to be normal distribution Mean, Variance, Standard Deviation of sample Stratified random sampling - Uses a classification system to separate the population into small groups, based on one or more distinguishing characteristics Each subgroup is called as stratum nT LOS c Mean, Variance, Standard Deviation of population Fi Eg Avg calorie intake of a nation Sample3 Sample4 Sample5 Results of these samples are then pooled to form a combined sample N W C E Sample1 S Sample2 It is often used in bond indexing because of the difficulty and cost of replicating entire population of bonds https://www.fintreeindia.com/ © 2017 FinTree Education Pvt Ltd LOS d Time-series and Cross-sectional data Time-series data Cross-sectional data It consists of observations taken over a period of time It consists of observations taken at a single point in time Time-series and cross-sectional data can be pooled in the same data set Longitudinal data - Observations over time of multiple characteristics of the same entity Eg Unemployment, GDP growth rates, inflation of a country over 10 years Panel data - Observations over time of same characteristic of the multiple entities Eg analysis of D/E ratio of 20 companies over quarters Panel and longitudinal data are typically presented in table or spreadsheat form Central limit theorem LOS e ª ª Variance equals ‘σ2/n’ as sample size becomes large If sample size n, is sufficiently large (n ≥ 30), the sampling distribution of the sample means will be approximately normal re ª e ª Sample mean(x) approaches population mean(μ) as sample size becomes large If central limit theorem works, population mean(μ) = mean of sampling distribution Standard deviation of sampling distribution = σ/√n (standard error) nT ª LOS f Standard error of sample mean Population variance unknown σ √n s √n Fi Population variance known LOS g Describe properties of an estimator ª Unbiasedness - It is one for which the expected value of the estimator is equal to the parameter you are trying to estimate ª Efficiency - Unbiased estimator is also efficient if the variance of its sampling distribution is smaller than other unbiased estimators of parameter you are trying to estimate ª Consistency - An estimator for which the accuracy of the parameter estimate increases as the sample size increases https://www.fintreeindia.com/ © 2017 FinTree Education Pvt Ltd LOS h Point estimate and confidence interval estimate Point estimate - It is a single sample value used to estimate population parameter Confidence interval It is a range of values in which population parameter is estimate - expected to lie LOS i Properties of t-distribution Student’s t-distribution It is a bell-shaped probability distribution è è It is symmetrical about its mean It is appropriate to use when n < 30, population variance is unknown and distribution is normal LOS j ª It is defined by degrees of freedom(DoF) (n − 1) ª It has more probability in the tails (fat tails) ª As DoF increase, t-distribution approaches standard normal distribution (z-distribution) ª t-distribution is flatter and has fatter tails than normal distribution ª As number of observations increase, distribution becomes more peaked and tails become thin i.e it converges to z-distribution Computation and interpretation of confidence interval e è Significance level (α) = − Confidence interval re 90% confidence level = 10% significance level = 5% in each tail Construction of confidence interval nT Point estimate ± (Reliability factor × Standard error) Selection of test for reliability factor Fi Population variance is known Non -normal distribution Normal distribution Population variance is unknown Non -normal distribution Normal distribution Z - distribution t - distribution n ≥ 30 n < 30 n ≥ 30 n < 30 Z - distribution No t/z distribution No https://www.fintreeindia.com/ LOS k © 2017 FinTree Education Pvt Ltd Appropriate sample size and different biases Sample size ª Generally large sample size is better (consistency property of an estimator) ª issues with larger sample size; Œ Larger samples may contain observations from a different population, which may not improve precision of our population parameter estimates Larger sample size may not be cost effective Different types of biases · · · · Survivorship bias Look-ahead bias · Some data is systematically excluded from the analysis, usually because of lack of availability · · Most common form of bias Most mutual fund databases only include the existing funds(survivors) · Occurs when a study tests a relationship using sample data that was not available on the test date e Sample selection bias Data mining occurs when analysts use same database to search for patterns until one that works for them is discovered Data mining bias refers to overestimated results because it involves data mining Lack of an economic theory that is consistent with the empirical results To avoid data mining, test the potentially profitable trading value on a data set different from the one used to develop the rule MPS BVPS · Available at the end of accounting period Not available at the end of accounting period Therefore it is estimated Can result if the time period over which the data is gathered is either too short or too long Fi nT Time-period bias re Data mining Hypothesis Testing https://www.fintreeindia.com/ © 2017 FinTree Education Pvt Ltd LOS a Hypothesis - It is a statement about the value of a population parameter developed for the purpose of testing a theory or belief Steps of hypothesis testing Null and Alternative hypothesis State the hypothesis (Defining null and alternative) Alternative Hypothesis Hypothesis that the researcher wants to reject Hoped for outcome Designated as H0 Designated as Ha Has ‘=’ ‘≥’ or ‘≤’sign Has ‘>’ ‘ opening price Fi Cl price - Initiated as a point on the left side of the line Point & figure charts Same data as bar charts Use cross-hatches & vertical lines as symbols nT Show closing prices as data points on a continuous line Candlestick charts Box is filled if closing price < opening price ∆ in the direction of price Horizontal axis reflects no of ∆ in price not time Price change represents the height which is ‘box size’ Price moves are much more visible ª Relative strength analysis - Asset closing price/Benchmark value ê ầ in trend - Asset is outperforming ª È in trend - Asset is underperforming ª Volume chart - Usually included at the bottom of many charts Volume is on vertical axis https://www.fintreeindia.com/ © 2017 FinTree Education Pvt Ltd LOS c Trend in prices Uptrend Downtrend Reaching higher highs & retracing higher lows Lower lows & retracing lower highs Shows demand is increasing relative to supply Shows supply is increasing relative to demand Trend line connects increasing lows Trend line connects increasing highs Breakdown below uptrend line (significant price change) Breakdown above uptrend line (significant price change) Support Level - Price range in which buying activity is sufficient to stop decline in price Change in polarity - Breached resistance levels become support levels & vice versa e Resistance Level - Price range in which selling activity is sufficient to stop rise in price LOS d Common chart patterns Double top & triple top Signals the end of a trend Analyst use size of H&S pattern to project price target Continuation patterns Indicate weakening buying pressure (Similar to H&S) Selling pressure appears after resistance level nT Head & shoulder (H&S) patterns must be preceded by uptrend & inverse H&S must be preceded by downtrends re Reversal patterns Used to predict the resumption of a market trend Double bottom & triple bottom for downtrends Fi Triangles Form when the range between high and low prices narrows Can be symmetrical, ascending or descending Suggest buying & selling pressure roughly equal Measuring implication: height of triangle at formation Rectangles Form when trading temporarily range b/w support & resistance level Is a form of continuation pattern with one formed by connecting the high prices and the other by connecting the lows Flags & pennants - Form over a short period of time, on a daily price chart of triangle and rectangle at formation https://www.fintreeindia.com/ LOS e © 2017 FinTree Education Pvt Ltd Common technical analysis indicators Price based indicators Moving average lines Bollinger bands Mean of closing prices over a specified number of periods The longer the time-frame used to create moving average (MA) “n”, smoother the avg line In uptrend - Price is higher than moving avg & vice versa MA for different periods can be used together Oscillators Based on standard deviation of closing prices over last n periods Analyst draw high & low bands above & below nperiod MA Long-term investors may buy (sell) when price significantly exceeds (falls below) the upper (lower) bound Charts used to identify convergence or divergence of oscillator & market prices Convergence - Oscillator shows same pattern as prices Prices above Bollinger bonds indicates overbought market Divergence - Oscillator shows different pattern than prices Prices below Bollinger bonds indicates oversold market re Dead cross - Short-term MA crosses from above longterm moving average, indicates sell signal Based on market prices but scaled so that they ‘oscillate’ around a value or between two values e Contrarian strategy - Buy (sell) when price reaches the upper (lower) band Golden cross - Short-term M.A crosses from underneath long-term MA, indicates buy signal Tool to identify overbought or oversold market Examples of oscillators ROC (Momentum) MACD Stochastic RSI - Relative Strength Index MACD - Moving average convergence /divergence Calculated from latest closing price & highest & lowest prices Based on ratio Total price increase Total price decrease Uses exponentially smoothed market values Use two lines bounded & 100 Buy when the oscillator changes from −ve to +ve in uptrend (vice versa) Oscillate b/w & 100 Oscillate around but not bounded Can be around or around 100 Value < 30 = Oversold market nT RSI ROC - Rate of change Fi Calculated as 100 × Diff b/w last closing price & closing price ‘x’ days ago Value > 70 = Overbought market MACD line crossing above the smoother signal line - Buy (vice versa) %K = Diff b/w latest price & recent low as % of diff b/w recent high & lows %D = Avg of last three %K values calculated daily https://www.fintreeindia.com/ © 2017 FinTree Education Pvt Ltd Non-price based indicators Sentiment indicators Flow of funds indicators Margin Debt (MD) CBOE Volatility Index (VIX) Put/Call ratio Put volume Call volume Viewed as contrarian indicator Extremely high ratio = Bearish outlook (vice versa) Measure volatility of options on S&P 500 stock index High VIX = fear declines in stock market Technical analysts interpret VIX in contrarian way Ç in MD, Ç buying, when reach their limit, buying È, prices È, investor sell securities to meet margin calls Ç MD coincides with Ç prices & È MD with È prices Margin Debt (MD) TRIN Measure of funds flowing into or out of advancing & declining stocks Some analysts may believe that if ratio increases, market should express decrease in price and vice versa Mutual fund cash position Ratio = Fund’s cash Total assets Ç in MD investor wants to buy more stocks nT TRIN = No of advancing issues/No of declining issues Volume of advancing issues/Volume of declining issues Short interest ratio = Short interest / Avg daily trading volume re Short term trading index aka Arms index Short interest is no of shares borrowed & sold short e Ç in ratio = Market sentiment is extremely negative likely increase in price Short interest ratio È in MD investor wants to buy more stocks Index value close to = Flowing evenly to advancing & declining stocks New equity issuance IPO add to supply of stocks Downtrend = Ratio Ç Secondary issues not increase the supply of stock but rather increase shares available for trading Technical analysts view mutual fund cash as contrarian indicator Issuer tends to issue when market peaks, so issuance coincide with high price Uptrend = Ratio È Value > = Majority in declining stocks Fi Value < = Majority in advancing stocks Sentiment indicators - Used to gain insight into trends Flow of funds indicators - Useful for observing changes in demand & supply of securities https://www.fintreeindia.com/ © 2017 FinTree Education Pvt Ltd LOS f Cycle Periods Presidential Cycles Decennial Patterns Kondratieff wave Tied to US Presidential elections cycle with the third year being prior to election year Broken down on the basis of the last digit in the year; years ending with a 0(5) have had the worst (best) performance 18-year cycles or 54-year cycles LOS g Elliott wave theory ª It is based on a belief that financial market prices can be described by an interconnected set of cycles ª Waves refer to chart patterns ª Uptrend - upward waves & downward waves ª Downtrend - downward waves & upward waves e ª Fibonacci ratios - Ratios of the size of the subsequent wave re ª Fibonacci numbers are found by starting with and and the each subsequent number in the sequence is the sum of the two previous numbers Eg 0, 1, 1, 2, 3, 5, and so on ª Ratio of 0.618 and 1.618 used to project price targets LOS h Intermarket analysis nT It refers to analysis of interrelationship among MV of asset classes (e.g stocks, bonds) Fi Relative strength ratio - To identify outperforming asset class, then assets within class ... N =1 I/Y = 13 .25 PV = -10 0 FV = 11 3.25 N=1X2=2 I/Y = 13 .25/2 = 6.625 PV = -10 0 FV = 11 3.68 LOS e Monthly N=1X4=4 I/Y = 13 .25/4 = 3. 312 5 PV = -10 0 FV = 11 3.92 N = X 12 = 12 I/Y = 13 .25 /12 = 1. 104... https://www.fintreeindia.com/ © 2 017 FinTree Education Pvt Ltd Continuous compounding calculations 10 0 20% 11 7.35 10 0 0.8 10 0 x e0.2 x 0.8 = 11 7.35 LOS q 20% ln 11 7.35 10 0 11 7.35 10 0 0.8 0.8 → 16 % 20% 11 7.35 0.8 11 7.35... tendency Weighted mean AM = 10 + 14 + + WM = 10 (20%) + 14 (20%) + 4(35%) + 8(25%) WM = 8.2 Geometric mean Harmonic mean GM = HM = 1. 1 X 1. 14 X 1. 04 X 1. 08 − 1/ 10 + 1/ 14 + 1/ 4 +1/ 8 GM = 8.94 HM = 7.32