#cfa: revise entire cfa syllabus 6 days- quants
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CFA RevisionTRANSCRIPT
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Tips and Tricks for entire CFA syllabus6 days
Quants
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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
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Tips and Tricks: Quants Contd …
Holding Period Return
Rates of Return on a Portfolio: Difference in: • Time Weighted
• Money Weighted
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Total return:Rt= [(Pt+Dt)/Pt‐1]‐1Total return:Rt= [(Pt+Dt)/Pt‐1]‐1
Effective Annual YieldEAY = (1+HPY)365/t ‐ 1Effective Annual YieldEAY = (1+HPY)365/t ‐ 1
Bank Discount YieldRBD = D/F * 360/tBank Discount YieldRBD = D/F * 360/t
Money Market YieldrMM = 360 * RBD /(360 – t * RBD)Money Market YieldrMM = 360 * RBD /(360 – t * RBD)
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Descriptive Statistics
Expected Return / Std. Deviation
ROY’s Safety‐first Ratio FORMULA Coefficient of Variation
Measurement Scales• Nominal Scale• Interval Scale• Ratio Scale
Sharpe Ratio FORMULA
Correlation & Covariance
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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
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
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) =wA
2σ2(RA)+ wB2σ2(RB) +2wA wBσ(RA) σ(RB)ρ(RA,, RB)
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) =wA
2σ2(RA)+ wB2σ2(RB) +2wA wBσ(RA) σ(RB)ρ(RA,, RB)
Measures excess return per unit of risk.Sharpe ratio =
Roy's safety‐ First ratio:
Sharpe Ratio uses risk free rate,Roys Ratio uses Min. hurdle rateFor both ratios, larger is better.
Measures excess return per unit of risk.Sharpe ratio =
Roy's safety‐ First ratio:
Sharpe Ratio uses risk free rate,Roys Ratio uses Min. hurdle rateFor both ratios, larger is better.
p
fp rr
p
ettp rr arg
Dispersion relative to mean of a distribution; CV=σ/μ (σ is std dev.)Dispersion relative to mean of a distribution; CV=σ/μ (σ is std dev.)
Average of squared deviations from mean. Population variance:
Sample variance:
Standard deviation:
Average of squared deviations from mean. Population variance:
Sample variance:
Standard deviation:
N
XXN
ii
1
2
2
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2
2
n
XXs
N
ii
Variancesor
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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
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xnxx
n ppCxXP )1()(
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SkewnessSkewness KurtosisKurtosis
Mean
Median Mode
Negative‐Skewed
Mean = Median = Mode
Symmetric
Mean
MedianMode
Positive‐Skewed
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Hypothesis Testing
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Sampling Biases
Data Mining
Sample Selection
Survivorship
Look‐Ahead
Time‐Period
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Technical Analysis Indicators
Price Based Indicators
Moving Average Lines – mean of last n closing prices
Bollinger Bands – standard deviation of closing prices over the last n days
Oscillators
Based on market prices, scaled to oscillate around a given value
Rate of change oscillators
Relative Strength Index
Moving Average Convergence/Divergence
Stochastic Oscillator
Sentiment Based Indicators
Put/Call Ratio
Volatility Index
Margin Debt
Short Interest Ratio
Arms Index (TRIN)
Mutual Fund Cash Position
New Equity Issuance
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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:
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
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B)Cov(A, w)-2w(1 w)-(1 w 2B
22A
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