CFA1 Quans

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п»їQuantitative methods

Time value of money

Effective total annual rate (EAR)

Effective gross annual rate (EAR) = (1+stated annual rate/frequency, m) ^ m-1 Annuities

Ordinary annuities: cash flow towards the end of each period, normal one particular; Annuities due: cash flow at the start of each period, first payment =t0; Calculator setting: [2nd][BGN]-[2ND][SET]; same procedure for problem to END; Repayment at start of following three years, N=4, always plus one using annuities due This can be a BGN query, if initial payment is definitely today!

When ever calculate PHOTOVOLTAIC, make FV=0; when compute FV, help to make PV=0 (0 must be input as well) Perpetuity: PV=PMT/(I/Y)

Loan payment

Borrow 10, 000 at 10%, semiannual, 10years. CLT outstanding financial loan after two year payment? Use calculator get PMT=802. 43

Payment 1: Fascination: 10, 000*0. 05=500; Main: 802. 43-500=302. 43 Repayment 2: Interest: (10, 000-302. 43)*0. 05=484. 88; Principal: 802. 43-484. 88=317. fifty-five Remaining stability: 10, 000-302. 43-317. 55=9, 380. 02

Rate of compound progress

Sales for last five years: four. 5, five. 7, a few. 3, six. 9, several. 1, CPT compound total annual growth rate? FV=7. you, PV=-4. 5, N=4, PMT=0, CPT-I/Y (5 years growth represent 5 years growth) Continuously compounded rate

Successful annual rate=eR*t-1, where to is holding period

Calculator: ln(1+HPR)=Rcc

Reduced Cash Flow Applications

Cash flow for perpetuity circumstance

CPT NPV: cash flow/discount rate-CF0

CPT IRR: Funds flow/IRR=CF0

Money-weighted return and time-weighted return

Same problem: buy inventory $100 by t=0, get another same stock $120 and receive $2 gross at t=1, sell two stocks pertaining to $130/each and receive $2 dividend/each by t=3 For cash weighted: apply the concept of IRR

Put in 100 at t=0, and deposit 118 (120-2) at t=1, and receive 264 at t=2 Use calculator: CF0=-100, CF1=-118, CF2=264, CPT→IRR

For time-weighted (preferred, because not afflicted with timing of cash inflow and outflow): Compute return for each holding period:

Holding period you: beginning value=100; dividend paid=2; ending value=120 Holding period 2: start value=240; gross paid=4; ending value=260 HPR1= (120+2)/100-1=22%; HPR2= (260+4)/240-1=10%

(1+time-weighted return)^2=(1. 22*1. 10)в†’(1. 22*1. 10)square root-1 Bank lower price yield, keeping period deliver, effective gross annual yield, market bourse yield Traditional bank discount yield (BDY) = for T-bill

Holding period yield (HPY) = pertaining to T-bill

Effective annual produce (EAY) sama dengan (1+HPY)365/t -1

Money market yield (CD equivalent yield) sama dengan HPY*(360/t)

Connect equivalent deliver

Convert HPY to powerful yield

3-month HPY (2%)в†’semiannual effective produce: (1. 02)^2-1=4. 04%, some. 04*2=8. 08% (annual) Twelve-monthly (8%) в†’semiannual effective deliver: =1. 08^0. 5-1=3. 923%, 3. 923*2=7. 846% (annual) Statistical principles and Industry returns

Arithmetic, geometric, harmonic means

Geometric mean: used for calculating purchase return or compound expansion rates; Elizabeth. g. (CPT return, +1) 1+R=

Harmonic mean: utilized for average expense of share purchased over time E. g. a real estate investor buy inventory over 90 days for $8, $9, $12; harmonic mean= HarmonicпјњGeometricпјњArithmetic

Mean absolute change and difference

Mean total deviation (MAD) =

Population variance=; if sample variance, divided by (n-1) Chebyshev's inequality

1-1/k2, % of observations lie within just В±k normal deviations of the mean (for any distribution) E. g. k=2 regular deviations в†’1-1/22=0. 75=75%

Pourcentage of Deviation and Sharpe Ratio

Pourcentage of Variant (CV) = Standard deviation/mean

Sharp proportion: (portfolio return-risk free rate)/portfolio standard change Probability Concepts


Probability occur is definitely 1/8,, vice versa


P(AB)=P(A∣B) * P(B) →AB同时发生的概率=A发生的概率(B确定发生)×B发生的概率 P(A and B)=P(A)*P(B) →two independent events

P(A Or B)=P(A)+P(B)-P(AB)


Bayes' formula

P(A|B)=P(B|A)/P(B) *P(A)

Covariance and Correlation

Cov(A, B)=

Cor(R1, R2)=Cov(R1, R2)/Пѓ(R1)Пѓ(R2)


Factorial: no groups, d terms=n!

Labeling formula: three or more sub-groups;

Combination formulation: only two groups, no order...

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