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#CFA: Revise entire CFA syllabus 6 days- Quants
1.
Tips and Tricks for entire CFA syllabus 6 days Quants © EduPristine © EduPristine – www.edupristine.com
2.
Tips and Tricks: Quants Time Value of Money • Future value –
FV = PV*(1+1/Y)N • Present value • Annuities – Ordinary annuity – Annuity due PV of Annuity Due = PV of Ordinary Annuity * (1 + r) Perpetuities: annuities with an infinite life PVperpetuity = PMT / discount rate © EduPristine 1
3.
Tips and Tricks: Quants Contd … Holding Period Return Total return: Rt= [(Pt+Dt)/Pt‐1]‐1 Effective Annual Yield EAY = (1+HPY)365/t ‐
1 Bank Discount Yield RBD = D/F * 360/t Money Market Yield rMM = 360 * RBD /(360 – t * RBD) Rates of Return on a Portfolio: Difference in: • Time Weighted • Money Weighted © EduPristine 2
4.
Sharpe Ratio FORMULA Descriptive Statistics Measures excess return per unit of risk. Sharpe ratio = rprf
Expected Return / Std. Deviation Expected Return: E(X)=P(x1)x1+P(x2)x2+…….+P(xn)xn Probabilistic variance: σ2(x) = = P(x1)[x1‐E(X)]2+P(x2)[x2‐E(X)]2+…….+ P(xn)[xn‐E(X)]2 Average of squared deviations from mean. Population variance: X N 2 i 1 i X 2 N Sample variance: Xi X s 2 i 1 n 1 N 2 p r r Roy's safety‐ First ratio: p t arget p Sharpe Ratio uses risk free rate, Roys Ratio uses Min. hurdle rate For both ratios, larger is better. Standard deviation: or s Variance ROY’s Safety‐first Ratio FORMULA Coefficient of Variation Dispersion relative to mean of a distribution; CV=σ/μ (σ is std dev.) Correlation & Covariance Correlation = Corr(Ri, Rj) = Cov(Ri, Rj) / σ(Ri)*σ(Rj) Expected return, Variance of 2‐stock portfolio: E(Rp) = wAE(RA) + wBE(RB) VaR(Rp) =wA2σ2(RA)+ wB2σ2(RB) +2wA wBσ(RA) σ(RB)ρ(RA,, RB) Measurement Scales • Nominal Scale • Interval Scale • Ratio Scale © EduPristine 3
5.
Probability Empirical probability A Priori probability
Subjective probability Bayes' Theorem: P(A|B) = P(B│A)*P(A) / [P(B│A)*P(A)+P(B│Ac)*P(Ac)] Binomial Distribution nx P(X x) Cx p (1p) n © EduPristine x 4
6.
Skewness Kurtosis Negative‐Skewed Median Mode Mean Symmetric Mean = Median = Mode Positive‐Skewed Mode Median Mean © EduPristine 5
7.
Hypothesis Testing © EduPristine 6
8.
Sampling Biases Data Mining Sample Selection
Survivorship Look‐Ahead Time‐Period © EduPristine 7
9.
Technical Analysis Indicators Sentiment Based Indicators Price Based Indicators Put/Call Ratio
Moving Average Lines – mean of last n closing prices Volatility Index Bollinger Bands – standard deviation of closing prices over the last n days Oscillators Based on market prices, scaled to oscillate around a given value Margin Debt Short Interest Ratio Arms Index (TRIN) Mutual Fund Cash Position New Equity Issuance Rate of change oscillators Relative Strength Index Moving Average Convergence/Divergence Stochastic Oscillator © EduPristine 8
10.
Tips‐n‐Tricks One of the ways to quickly solve some questions on progressions is to remember the rule: AM > GM > HM Don't forget that sample mean and population mean and sample standard deviation and population standard deviation have different formulas (denominator: sample uses n‐1 vs. n of population). In the exam if sample standard deviation is given, it can be used directly to approximate the population standard deviation, there is no need to do extra calculations.
Whenever risk or vola lity is men oned in a ques on to be 6% it stands for "standard devia on" of the returns and not the Variance. Please do not make a mistake between Covariance and Correlation. Cov (A, B) should be replaced with Corr (A,B)*σA*σB wherever required. Please note that the formula for standard deviation of a portfolio is given below which has Covariance which can be later converted to Correlation: 2 2 w 2 A (1 - w) 2 B 2w(1 - w) Cov(A, B) Whenever you get a problem on normal distribution, draw a rough sketch of it in your paper and shade the relevant area. It will ensure that you will not get it wrong. Do not try to do mental calculations for such problems. A trick to remember the formula for the Safety First Ratio. It is similar to Sharpe ratio, just that it measures excess returns over a threshold return © EduPristine 9
11.
Thank You ! help@edupristine.com www.edupristine.com © EduPristine – www.edupristine.com
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