Intro to Linear Regression
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- Author: bionicturtledotcom
A really brief introduction to the "best fit" line through X:Y data.
Correlation & Covariance
- Length: 9:53
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- Author: bionicturtledotcom
Covariance is a measure of relationship (or co-movement) between two variables. Correlation is just the translation of covariance into a UNITLESS measure that we can understand (-1.0 to 1.0)
Z-spread (versus bond's nominal credit spread)
- Length: 8:19
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- Author: bionicturtledotcom
Tags: bond yield yield to maturity YTM spread z spread z-spread Treasury curve
(Please note: spreadsheet is available on the website). A nominal credit spread is the difference in yields (YTM), which are single factors; therefore, implicitly, the nominal spread compares flat curves. The Z-spread improves by giving the spread that adds across the entire spot (zero) rate...
Working capital (HPQ example)
- Length: 8:31
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Tags: working capital current assets liabilities
This is a brief illustration of the calculation of working capital (WC) using Hewlett Packard (ticker: HPQ) data from their latest quarterly filing (10Q): WC = current assets -- current liabilities. The solvency perspective. WC = (current assets excluding cash) -- current liabilities. The...
Repo (repurchase agreement)
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Tags: repo repurchase agreement haircut margin financial crisis
A repo is a secured loan. In August of 2007, repo lenders increased haircuts (initial margin) on repo transactions. The led to a run on the shadow banking system.
Counterparty credit exposure
- Length: 7:41
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- Author: bionicturtledotcom
Tags: counterparty credit risk exposure expected exposure EE potential future PFE value at var
Study note: Counterparty credit risk is harder because (i) the initial value is 0 and the future value is highly uncertain and (ii) the contract can gain or lose. Two key metrics are Expected Exposure and Potential Future Exposure (PFE, which is essentially a VaR)
Logistic distribution maps credit score to probability of default (PD)
- Length: 8:57
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- Author: bionicturtledotcom
Tags: logistic cumulative distribution function CDF credit score probability of default
The logistic function can be used to transform a credit score into a probability of default (PD). The advantages of the logistic are (i) it easy to calculate and (ii) as a cumulative distribution function (CDF) the output is, appropriately, a probability between 0 and 1.0. In this video, I show...
Spearman's rank correlation
- Length: 6:58
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- Author: bionicturtledotcom
Tags: spearman's pearson's correlation rank dependence
Spearman's is more flexible measure of correlation because 1. It requires ordinal rather than cardinal variables and 2. It does not presume linear relationship (it is a measure of monotone dependence) Note: you can download a copy of my spreadsheet on our website @ www.bionicturtle.com
Regression #1: Sample regression function (SRF)
- Length: 7:30
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Tags: Finance Quant Econometrics Statistics Regression
The population is unobserved. We draw samples and make inferences based on the samples. Each sample has a sample regression function (SRF).
Weighted average cost of capital (WACC)
- Length: 9:10
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Tags: wacc weighted average cost of capital debt equity
WACC is a marginal cost: we can't go to full leverage because the "cost of financial distress" increases the costs of financing.
Dividend discount (Gordon growth) model
- Length: 7:25
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Tags: dividend discount Gordon growth model CFA chartered financial analyst valuation
The Gordon growth model is the simples dividend discount model. It's disadvantage is the dubious assumption that a single dividend grows at a constant rate indefinitely. (our website has the spreadsheet and the derivation)
Regression #2: Ordinary Least Squares (OLS)
- Length: 9:28
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Tags: Finance Quant Econometrics Statistics Regression
OLS minimizes the residual sum of squares (RSS). RSS is the sum of each squared residual (residual = the observed Y minus the predicted "on the line" Y). Also, about the OLS: the average residual is always zero, and the line passes through the point (average X, average Y)
Treasury inflation-protected securities (TIPS)
- Length: 6:30
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- Author: bionicturtledotcom
Tags: Treasury inflation inflation-protected securities TIPS CPI
In a TIPS, the coupon (real yield) is fixed. The inflation-adjusted principal varies. But it redeems at the greater of [inflation-adjusted principal, initial par value]. Also, TIPS are linked to CPI, which is a government statistic and not necessarily your experience of inflation/deflation.
Standard error of estimate (SEE)
- Length: 8:56
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A linear regression gives us a best-fit line for a scatterplot of data. The standard error of estimate (SEE) is one of the metrics that tells us about the fit of the line to the data. The SEE is the standard deviation of the errors (or residuals)
Mortgage prepayment metrics CPR & SMM
- Length: 8:25
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- Author: bionicturtledotcom
Tags: mortgage prepayment CPR SMM
You can download the spreadsheet at our website. CPR (conditional or constant prepayment rate) is the annual prepayment rate; SMM (single monthly mortality) rate is the monthly equivalent.
Coefficient of determination (r-squared)
- Length: 9:50
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- Author: bionicturtledotcom
In a linear regression, you often see the R-squared quoted. To explain the R-squared (coefficient of determination), I compare it to the standard error of estimate (a measure of the line's accuracy) and the correlation (the square root of the coefficient of determination). All three, loosely...
Normal mixture distribution
- Length: 5:50
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- Author: bionicturtledotcom
Tags: probability distribution
A normal mixture distribution can model fat tails
Central limit theorem
- Length: 8:49
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The CLT says the sample mean will be normally distributed regardless of the population distribution; it's power is uncanny.
Intro to logarithms
- Length: 9:54
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The inverse of a logarithmic function is an exponential functions. And if we use a base of natural e, we can compute continuously compounded returns
Gaussian copula
- Length: 7:30
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Tags: Gaussian copula distribution normal credit crisis
The Gaussian copula was gainfully employed prior to the credit crisis, and it has pretty much been shamed. Mathematically, it's an elegant way to join marginal distributions and handle default correlation. But it requires too many simplifying assumptions.
Credit default swap (CDS)
- Length: 5:57
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A CDS is a bilateral contract between two counterparties. The protection buyer is buying insurance: he/she pays premiums in exchange for a payoff in case there is a CREDIT EVENT (a trigger)
How to value an interest rate swap
- Length: 9:14
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- Author: bionicturtledotcom
Tags: Finance derivatives interest rate swaps
At inception, the value of the swap is zero or nearly zero. Subsequently, the value of the swap will differ from zero. Under this approach, we simply treat the swap as two bonds: a fixed-coupon bond and a floating-coupon bond. The value of the swap is difference between the two.
Volatility: Moving Average Approaches
- Length: 9:15
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- Author: bionicturtledotcom
Within stochastic volatility, moving average is the simplest approach. It simply calculates volatility as the unweighted standard deviation of a window of X trading days. Here I show the three "flavors:" population variance (volatility = SQRT[variance]), sample, and simple
Terms about distributions: PDF, PMF and CDF
- Length: 9:58
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- Author: bionicturtledotcom
Tags: Quant Finance Probability
Distributions characterize random variables. Random variables are either discrete (PMF) or continuous (PDF). About these distributions, we can ask either an "equal to" (PDF/PMF) question or a "less than" question (CDF). But all distributions have the same job: characterize the random variable.
Lognormal distribution
- Length: 8:36
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Here I explain an idea that is confusing the first time you see it: a variable is lognormally distributed if its log (or natural log) is normally distributed. I use an example of future stock price: it the rate of return is normally distributed (it can be negative), the future stock price level...
Three approaches to value at risk (VaR)
- Length: 5:55
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This is a brief introduction to the three basic approaches to value at risk (VaR): Historical simulation, Monte Carlo simulation, Parametric VaR (eg, delta normal)
Interest rate swap
- Length: 7:4
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Tags: Finance derivatives interest rate swaps
This illustrates how an interest rate swap can transform a floating-rate obligation into a fixed-rate obligation and vice-versa
Basel II Overview
- Length: 9:57
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Tags: basel capital credit market operational risk
Quick overview of Basel II framework that sets capital requirements for banks. Three pillars contains the rules & support (supervisor review, market discipline) that say how much eligible regulatory capital must be held against risk-weighted assets.
Regression #3: Standard Error in Linear Regression
- Length: 9:57
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- Author: bionicturtledotcom
Tags: excel statistics regression quant quantitative
A simple (two-variable) regression has three standard errors: one for each coefficient (slope, intercept) and one for the predicted Y (standard error of regression). While the population regression function (PRF) is singular, sample regression functions (SRF) are plural. Each sample produces a...
Put call parity
- Length: 6:51
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- Author: bionicturtledotcom
Tags: Finance Excel Derivatives Stock Options
Put call parity derives from the idea we can have two portfolios (one with an option, the other with a put) that have identical payoffs regardless of what happens to the stock. This gives a way to link the value of a call option with a put option.
Capital market line (CML)
- Length: 10:17
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Tags: beta capital cml line market portfolio volatility
The capital market line is determined by a mix of: the riskfree asset and the market portfolio. The market portfolio, in turn, consists of all risky assets (this example has only two assets).
Solvency Ratios, CFA L1 (Financial Statements)
- Length: 8:4
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Tags: CFA solvency balance sheet
Solvency ratis are either debt ratios (balance sheet-balance sheet) or coverage ratios (income statement-interest)
How to get yield to maturity (YTM) with Excel & TI BA II+
- Length: 8:57
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Yield to maturity (YTM, yield) is the bond's internal rate of return (IRR). It is the rate that discounts future cash flows to the current market price.
Contango & backwardation in commodity forward markets
- Length: 7:47
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- Author: bionicturtledotcom
Tags: Finance Derivatives Commodities
Contango and backwardation are about the relationship between the spot and forward price. If Forward is greater than Spot, it's contango (upward sloping forward curve). If Forward is less than Spot, it's backwardation (inverted forward curve). The "normal" prefix refers to relationship to...
Profitability Ratios, CFA L1 (Financial Statements)
- Length: 10:31
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- Author: bionicturtledotcom
Tags: CFA ratios gross profit ROI ROA ROE
Return on Sales (income statement) and Return on Invesmtent (returns to balance sheet).
Black-Scholes versus Binomial
- Length: 5:47
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- Author: bionicturtledotcom
Tags: Finance Derivatives Stock Options
The world's quickest summary comparison between the two common ways to price an option.
Regression #4: ANOVA table in regression
- Length: 9:14
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- Author: bionicturtledotcom
Tags: Excel Quant Statistics Regression Finance
The ANOVA table explains the sources of variation.
Cost of carry model to price forwards & futures
- Length: 8:33
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- Author: bionicturtledotcom
Tags: Finance derivatives commodity
The cost of carry model is universally helpful. It summarizes the link between the spot price and the (theoretical) futures price for a commodity.
Forward rate agreement (FRA)
- Length: 8:52
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Tags: Finance Futures Excel Fixed Income Bonds
An FRA is a contract that lets the buyer (who is long the rate) lock-in an interest (borrowing) rate. In this example, the FRA buyer locks in LIBOR at 3%
Intro to Quant Finance: Periodic Rate of Return
- Length: 9:40
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Tags: Finance Excel Quantitative Quant
Periodic rate of return
Intro to Quant Finance: Value at Risk (VaR)
- Length: 9:48
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Tags: Finance Excel Quantitative Quant
The basic approach to VaR is delta normal: a scaled standard deviation
Liquidity Ratios, CFA L1 (Financial Statements)
- Length: 7:32
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- Author: bionicturtledotcom
Tags: CFA liquidity current ratio quick ratio cash ratio
Liquidity is a short-term issue (I like to think of liquidity as -running out of time.- A liquidity problem per se is one that time can fix). Liquidity ratios measure a firm's ability to meet its short-term obligations; or measure how quickly assets are converted into cash.
Two step binomial
- Length: 8:57
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Tags: Finance Derivatives Stock Options
Here is an spreadsheet example of pricing a European call option on a stock index (eg, Dow Jones Utility) with a two step binomial. There are two basic process steps: 1. Build forward the "tree" of asset prices, 2. Then backward induction: value the option at each node as the...
Exponentially weighted moving average (EWMA)
- Length: 8:56
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The EWMA approach to volatility is an improvement over simple volatility because it assigns greater weight to more recent observations (in fact, the weights are proportional)
Bayes' Formula
- Length: 6:37
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Bayes' Theorem formulas an intuitive idea: we adjust our perspective (the probability set) given new, relevant information. Formally, Bayes' Theorem helps us move from an unconditional probability (what are the odds the economy will grow?) to a conditional probability (given new evidence, what...
Binomial (one step) for option price
- Length: 6:53
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- Author: bionicturtledotcom
Tags: Finance Derivatives Stock Options Binomial
The binomial solves for the price of an option by creating a riskless portfolio.
Why we use log returns in finance
- Length: 6:17
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Tags: 0203 logreturns
log returns
Monte carlo simulation: Brownian motion
- Length: 9:28
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Tags: Finance monte carlo simulation value at risk
This is a classic building block for Monte Carlos simulation: Brownian motion to model a stock price. The periodic return (note the return is expressed in continuous compounding) is a function of two components: 1. constant drift, and 2. random shock; ie, volatility multiplied by a randomized...
Technical Analysis, Intro: CFA L1
- Length: 8:19
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- Author: bionicturtledotcom
Tags: technical charts candlestick
Tenets of technical analysis; common charts
Confidence interval
- Length: 8:16
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- Author: bionicturtledotcom
Tags: Finance Quant Excel Statistics Probability
I illustrate the confidence interval construction with an example: the P/E ratio of 28 companies. The point is to say with confidence (eg, 95%) that the "true" population lies within an interval.
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