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ECONOMICAL EFFICIENT EFFECTIVE

ÉLANGUIDES

We believe that we offer the MOST EFFECTIVE study materials for CFA exam prep. Register for the free trial on our website to obtain FREE access to the following study materials. Lecture videos, study guide readings and practice questions for Study Session 3 (Quantitative Methods) Lecture videos, study guide readings and practice questions for Study Session 16 (Fixed Income)

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QUANTITATIVE METHODS

FVN = PV (1+ r)N

PV = FV

1 + r)N

PVAnnuity Due = PVOrdinary Annuity (1 + r)

FVAnnuity Due = FVOrdinary Annuity (1 + r)

PV(perpetuity) =PMT

I /Y

FVN = PVe rs * N

EAR = (1 + Periodic interest rate)N- 1

wher e: r BD = the annualized yield on a bank discount basis. D = the dollar discount (face value - purchase price)

F = the face value of the bill

t = number of days remaining until maturityr BD =

D 360 F t

where: P

0 = initial price of the investment.

P

1 = price received from the instrument at maturity/sale.

D

1 = interest or dividend received from the investment.HPY = P1 - P0 + D1 = P1 + D1 - 1

P0 P0

where C F t = the expected net cash flow at time t

N = the investment's projected life

r = the discount rate or appropriate cost of capital C Ft 1 + r)t t=0N

NPV =Net Present Value

B a nk Discount Yield Holding Period YieldThe Future Value of a Single Cash Flow T he Present Value of a Single Cash Flow

Present Value of a Perpetuity

Continuous Compounding and Future Values

E f f ective Annual Rates

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3QUANTITATIVE METHODS

EAY= (1 + HPY)365/t - 1

wher e:

HPY = holding period yield

t = numbers of days remaining till maturity R

MM = HPY (360/t)R

MM = 360 rBD

360 - (t rBD)

HPY = (1 + EAY)t/365 - 1

B

EY = [(1 + EAY) ^ 0.5 - 1]

Where,

x i = is the ith observation. with Xi > 0 for i = 1, 2,..., N. E f f ective Annual Yield

Money Market Yield

B o nd Equalent Yield

Population Mean

Sample Mean

Geometric Mean

Harmonic Mean

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4QUANTITATIVE METHODS

Range = Maximum value - Minimum value

Where:

n = number of items in the data set = the arithmetic mean of the sample where: y = percentage point at which we are dividing the distribution L y = location (L) of the percentile (Py) in the data set sorted in ascending order where: X i = observation i = population mean

N = size of the populationPercentiles

Range

Mean Absolute Deviation

Population Variance

Population Standard Deviation

where: n = sample size.

Sample variance =Sample Variance

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5QUANTITATIVE METHODS

where: = mean portfolio return = risk-free return = standard deviation of portfolio returns s s where: s = sample standard deviation = the sample mean. C o efficient of variationSample Standard Deviation

Coefficient of Variation

Sharpe Ratio

S K =n i = 1(X i - X)3 s3n n 1 n 2 As n becomes large, the expression reduces to the mean cubed deviation. where: s = sample standard deviation n n i = 1(X i - X)3 s3SK Sample skewness, also known as sample relative skewness, is calculated as:

© 2011 ELAN GUIDES

6QUANTITATIVE METHODS

Where the odds for are given as 'a to b', then:Odds for an event

Where the odds against are given as 'a to b', then:Odds for an eventSample Kurtosis uses standard deviations to the fourth power. Sample excess kurtosis is

calculated as: For a sample size greater than 100, a sample excess kurtosis of greater than 1.0 would be considered unusually high. Most equity return series have been found to be leptokurtic.K E =n i = 1(X i - X)4 s4n(n + 1) n 1 n 2 n 3

3(n - 1)2

n 2 n 3 where: s = sample standard deviation n n i = 1(X i - X)4 s4KE 3As n becomes large the equation simplifies to:

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