valuation

risk

portfolio

dcf

wacc

iphone

cfa

 

>

 

 

Quantitative

 

Weight on the exam = 12%

Number of formulas = 27

CFA formulas

quantitative economics financials

corpfin portfolio equity

fixedincome derivatives alternative

Effective annual rate

ear

Effective annual rate is an annual rate of interest when compounding occurs more often than once a year.

EAR - effective annual rate

i - annual interest rate

n - number of compounding periods

Back on top

Future value

fv

Future value measures nominal value of money at a specified time in the future

FV - future value

PV - present value

r - periodic rate

k - number of compounding periods

n - number of years

Back on top

Present value

pv

Present value is a current value of some future cash flow

PV - present value

FV - future value

r - periodic rate

k - number of compounding periods

n - number of years

Back on top

Annuity due

An annuity-due is an annuity when payments are made at the beginning of each period (not in the end as for usual annuity)

Present value of an annuity due

pvdue

Future value of an annuity due

fvdue

PVdue - present value of an annuity due

PVord - present value of an ordinary annuity

FVdue - future value of an annuity due

FVord - future value of an ordinary annuity

r - periodic rate

k - number of compounding periods

Back on top

Perpetuity

perpetuity

Perpetuity is an annuity in which the periodic payments continue indefinitely

PVperp - present value of a perpetuity

P - periodic payment

i - periodic interest rate

Back on top

Net present value

npv

Net present value is a sum of present values of individual cash flows.

NPV - net present value

CF0 - initial investment in the project

CF1 - cash flow in period 1

CF2 - cash flow in period 2

CFn - cash flow in period n

r - discount rate

Back on top

Holding period yield

fv

Holding period yield (or holding period return) is a total return on an assets over the period during which it was held

P1 - current price

P0 - purchase price

D1 - dividend paid during a holding period

Back on top

Bank discount yield

bdy

Bank discount yield is the annualized percentage discount from face value.

BDY - bank discount yield

$discount - dollar discount from face value

face value - face value of the bond

days - days until maturity

360 - days in a year

Back on top

Effective annual yield

Effective annual yield converts holding period yield (HPY) to a compound annual yield based on a 365-day year to make the yield comparable with other investments.

eay

EAY - effective annual yield

HPY - holding period yield

t - days to maturity

365 - days in a year

Back on top

Money market yield

mmy

Money market yield is an annualized holding period yield without compounding based on a 360-days year

MMY - money market yield

HPY - holding period yield

t - days to maturity

360 - days in a year

Back on top

Geometric mean return

geomean

The geometric mean return formula is used to calculate the average rate per period on an investment that is compounded over multiple periods.

Rg - geometric mean return

R1 - return in period 1

R2 - return in period 2

Rn - return in period n

Back on top

Weighted mean

weightedmean

sumw

Weighted mean is a mean in which different parameters have different weights. The sum of weights is equal to 1.

Xw - weighted mean value

X1 - value of parameter 1

X2 - value of parameter 2

Xn - value of parameter n

w1 - weight of parameter 1

w2 - weight of parameter 2

wn - weight of parameter n

Back on top

Variance

Variance is the average of the squared deviations from the mean. Variance is used to measure how far a set of numbers are spread out from each other.

Population variance

popvar

σ² - population variance

Xi - observation value

μ - population mean

N - number of observations

Sample variance

samvar

s² - sample mean

Xi - observation value

X - sample mean

n - number of observations

Back on top

Coefficient of variation

cv

Coefficient of variation measures variability in relation to the mean and is used to compare the relative dispersion in one type of data with the relative dispersion in another type of data.

CV - coefficient of variation

σ - standard deviation of returns

μ - mean return

Back on top

Sharpe ratio

sharpe

Sharpe ratio measures excess return per unit of risk

SR - sharpe ratio

Rp - return of the portfolio

Rrf - risk-free rate

σp - portfolio risk

Back on top

Multiplication rule

sharpe

The probability of A and B occurs together (joint probability) is the probability that A occurs, given that probability B occurs, multiplied by probability B.

P(AB) - joint probability of two events

P(A|B) - the probability that A occurs, given that probability B occurs

P(B) - the probability of B occurs

Back on top

Addition rule

sharpe

The probability that either A or B occurs equal to the sum of probability that A occurs and probability that B occurs minus the probability that A and B occurs at the same time.

P(A or B) - the probability that either A or B occurs

P(A) - the probability that A occurs

P(B) - the probability that B occurs

P(AB) - joint probability of two events (A and B occurs at the same time)

If A and B are mutually exclusive, then P(AB)=0 and P(A or B) = P(A) + P(B).

Back on top

Total probability rule

totrule

The total probability rule explains an unconditional probability of an event, in terms of that event's conditional probabilities in a series of mutually exclusive, exhaustive scenarios.

P(R) - the probability that R occurs

P(R|I) - the probability that R occurs, given that probability I occurs

P(I) - the probability that I occurs

P(R|IC) - the probability that R occurs, given that probability IC occurs

P(IC) - the probability that IC occurs

I and IC are mutually exclusive and exhaustive set of events

Back on top

Correlation coefficient

correlation

Correlation coefficient measures the strength and the direction of a linear relationship between two variables. The correlation coefficient can range from -1 to +1

COR(Ri,Rj) - correlation coefficient between Ri and Rj

Cov(Ri,Rj) - covariation coefficient between Ri and Rj

σ(Ri) - standard deviation of Ri

σ(Rj) - standard deviation of Rj

Back on top

Portfolio expected return

sharpe

Expected return of portfolio of two assets is the weighted average of the expected returns on the assets which comprise the portfolio.

E(Rp) - expected portfolio return

wA - weight of asset A in the portfolio

RA - return of asset A

wB - weight of asset B in the portfolio

RB - return of asset B

Back on top

Portfolio variance

portvar1

portvar2

portvar3

Portfolio variance is a measure of the risk (volatility) of a portfolio. Variance of a portfolio of two assets is a combination of the return variance and co-variance of each security and its proportion in that portfolio.

Varp - portfolio variance

wA - weight of asset A in the portfolio

σA - standard deviation of asset A

σA2 - dispersion of asset A

wB - weight of asset B in the portfolio

σB - standard deviation of asset B

σB2 - dispersion of asset B

pA,B - correlation coefficient between assets A and B

CovA,B - covariation coefficient between assets A and B

Back on top

Binomial distribution

binom1

binom2

binom3

Binomial distribution is a statistical distribution giving the probability of obtaining a specified number of successes in a specified number of independent trials of an experiment with a constant probability of success in each. The probability of success is p while the probability of failure equals 1-p. The formula above calculates the probability of x successes in n trials.

p(x) - the probability of x successes in n trials

x - number of successes

n - number of trials

p - probability of success in each trial

1-p - probability of failure in each trial

Back on top

Z-value

zvalue

Z-value indicates how many standard deviations an observation is above or below the mean.

x - observation

μ - population mean

σ - standard deviation

Back on top

Standard error

sterror

Standard error of the sample mean is the standard deviation of the distribution of the sample means. If the standard deviation of the population (σ) is known the standard error of the sample mean is calculated with the formula above.

SE - standard error of the sample mean

σ - standard deviation of the population

n - size of the sample

Back on top

Confidence interval

confint

Confidence interval is a particular kind of interval estimate of a population parameter and is used to indicate the reliability of an estimate.Confidence interval with a known variance (formula above) is very important for hypothesis testing.

CI - confidence interval

x - mean value

zα/2 - reliability factor, a standard normal random variable for which the probability in the right-hand tale of the distribution is &alpha/2.

σ - standard deviation of the population

n - size of the sample

σ/n - standard error

Back on top

Safety-first ratio

sfr

Roy's safety-first ratio states that the optimal portfolio minimizes the probability that the return of the portfolio falls below some minimum acceptable level (threshold level).

SFR - safety-first ratio

Rp - portfolio return.

RL - threshold level return.

σp< - portfolio standard deviation

Back on top

Continuously compounded returns

Descretely compounded returns are returns with a given compounding period such as quaterly (4) or monthly (12). As we increase the compounding period the effective annual return also increases. The limit of this increase is continuously compounded return.

ccr

hprccr

CCR -continuously compounded return

HPR - holding period return

S1 - ending value

S0< - beginning value

Back on top

Sampling error of the mean

Sampling error is a difference between a sample statistic (mean, variance, standard deviation of the sample) and its corresponding population parameter.

samerror

SEM - sampling error of the mean

x - sample mean

μ - population mean

Back on top

 

HTML Comment Box is loading comments...

DISCLAIMER. Neither this site, the available materials, nor its contents (including any information concerning any securities mentioned on this site) constitutes an advertisement of any securities or an offer to sell or a solicitation of an offer to purchase any securities.

 

If you have any questions, comments or suggestions please contact me - iamanalista@gmail.com