CFA Level 1 Prep - Quantitative Methods

Rate of Return

Zero Coupon Bonds

These are bonds with no payments during the term and are issued at a discount to their face value (Future value), providing profit at maturity when the bond is redeemed at full value.

Fixed Coupon Bonds

Unlike zero coupon bonds, payments are made at regular periods and aat maturity, you get paid the face value

Amortizing bond

You make payments to principal at some level

Discounted Cash Flows

Suggests that FV = PV(1+r)^t

Real Return

It is the return after inflation is removed. How much did my purchasing power actually increase? 1+ real return = (1+nominal_return)/(1+inflation_premium)

Gross return

Is what is left after fees related to generating the return is deducted

Net Return

return after management and commission fees removed

Nominal return

Return after adjusting for inflation

Nominal risk-free rate

Return on an investment with no default risk and before inflation eg T-bills

Real risk -ree rate

Risk-free return after inflation

Leveraged Return

Borrowed money to invest more than your capital = [R_T(V_o+V_b)-(R_b*V_b)]/V_o where R_T is total return on investment, V_o is money you own and put into the investment, V_b is money you borrowed to put into the investment, R_b is the interest on the borrowed money

Money-Weighted Return

it is IRR taking into account all cash inflows and outflows. PV_inflows = PV_outflows

Holding Period Return

How much did i lose or gain whilst holding the investment

Central tendency

Measure of reward

Dispersion

Measure of risk

mean absolute deviation

is the average of the absolute values of the deviations of individual observations from the arithmetic mean

Relative dispersion

is the amount of variability in a distribution around a reference point or benchmark. Relative dispersion is commonly measured with the coefficient of variation (CV)

CV

standard deviation of x / average value of x

target downside deviation

measure of downside risk also known as target semideviation

Sample skewness

is equal to the sum of the cubed deviations from the mean divided by the cubed standard deviation and by the number of observations

Kurtosis

measure of the degree to which a distribution is more or less peaked than a normal distribution.

Leptokurtic

describes a distribution that is more peaked than a normal distribution

platykurtic

refers to a distribution that is less peaked, or flatter than a normal one.

mesokurtic

if it has the same kurtosis as a normal distribution

excess kurtosis

A distribution that has either more or less kurtosis than the normal distribution

Covariance

Measure of how two variables move together

correlation coefficient

Measure of the linear relationship between two variables

Spurious correlation

refers to correlation that is either the result of chance or present due to changes in both variables over time that is caused by their association with a third variable

Skewness

Refers to degree which a distribution is not symmetrical

expected value of a random variable

It is the weighted average of the possible outcomes for the variable

volatility of a random variable

It is the Variance and standard deviation measure the dispersion of a random variable around its expected value

Bayes' formula

It is used to update a given set of prior probabilities for a given event in response to the arrival of new information

jackknife

calculates multiple sample means, each with one of the observations removed from the sample.

Simple Random Sampling

method of selecting a sample in such a way that each item or person in the population being studied has the same likelihood of being included in the sample

Stratified random sampling

uses a classification system to separate the population into smaller groups based on one or more distinguishing characteristics

Cluster sampling

based on subsets of a population, but in this case, we are assuming that each subset (cluster) is representative of the overall population with respect to the item we are sampling

one-stage cluster sampling

a random sample of clusters is selected, and all the data in those clusters comprise the sample

two-stage cluster sampling

random samples from each of the selected clusters comprise the sample.

Type I error

This is the rejection of the null hypothesis when it is actually true

Type II error

This is the failure to reject the null hypothesis when it is actually false

Significance level

Probability of making a type I error

Power of a Test

Probability of accurately rejecting a null hypothesis when false = 1- P(type II error)

p-value

probability of obtaining a test statistic that would lead to a rejection of the null hypothesis, assuming the null hypothesis is true.

F- test

Used when comparing the equality of two population variances

Chi-squared

Used concerning the value of a population variance

T-test

Used when comparing the equality of two population means. Use paired when dependent or pooled when independent

Z-test

Used concerning the value of population mean when sample size is large enough