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Author: Bill Campbell
Cash Flow Matching
As an approach to asset-liability management (ALM), cash flow matching has advantages and disadvantages. The primary advantages are that: It works perfectly. It is relatively simple to understand. The primary disadvantages are that: It can be costly (i.e., the interest that you earn on your assets may be low). It may be difficult to implement…
Option-Adjusted Spread (OAS)
Option-adjusted spread (OAS) is a yield spread (i.e., an interest rate) that is added to the (1-period forward) interest rate at each node in a binomial tree; specifically, it is the spread that when added to the discount rates results in the tree giving the current market price for a particular bond, after accounting for…
Binomial Trees (for Fixed Income)
Binomial trees are used in a variety of contexts in finance: Calculating probabilities for Bayes’ Formula type problems Calculating the value of options on stocks, commodities, and so on Calculating the option-adjusted spread (OAS) for bonds Calculating the value of bonds with embedded options Calculating the value of floating-rate bonds Calculating the value of interest…
Creating a Binomial Interest Rate Tree
To create a binomial interest rate tree, you need to start with: A yield curve An interest rate volatility The yield curve can be a par curve, a spot curve, or a forward curve. (If you’re a bit fuzzy on the differences among these curves, look here.) For the remainder of this article, we’ll assume…
p vs. α
Candidates galore have problems (nightmares, really . . . but let’s not rub it in) with p-values. I’m here to tell you that understanding p-values is easy. Seriously: easy. A p-value is nothing more nor less than a level of significance, just like α. The best description I’ve heard is that α is the chosen…
Inventory Methods: FIFO vs. LIFO vs. Average Cost vs. Specific Identification and Periodic vs. Perpetual
I apologize in advance: this article’s long. Every inventory method has two important characteristics: How will costs be assigned to cost of goods sold (COGS) and ending inventory (EI)? When will those costs be assigned to COGS and EI? There are four possible answers to the first question: First-in, first-out (FIFO) Last-in, first-out (LIFO) Average…
Time Value of Money: Using Timelines
Much of finance centers around the idea of the time value of money: a dollar (or euro, or yen, or pound, or yuan, or franc, or won, or ruble, or bhat, or rupee, or whatever) today is worth more than a dollar (or euro, or . . . well, you get the idea) tomorrow, because…
R² vs. Adjusted R²
There’s a lot more to R2 and adjusted R2 than appears in the CFA curriculum. I’ll discuss what you need to know for the exam; the rest you can get from a statistics textbook if you’re interested. R2 Whether for a simple (i.e., single) regression or a multiple regression, R2 is the percentage of the…
Leverage-Adjusted Duration Gap (LADG)
This is an easy one, fortunately. The definition of LADG is: \[LADG\ =\ Dur_{Assets}\ -\ \frac{L}{A}Dur_{Liabilities}\] where: \(Dur_{Assets}\): (effective) duration of assets \(Dur_{Liabilities}\): (effective) duration of liabilities \(L\): market value of liabilities \(A\): market value of assets If we multiply both sides of this equation by A, we get: \begin{align}\left(A\right)LADG\ &=\ \left(A\right)Dur_{Assets}\ -\ \left(L\right)Dur_{Liabilities}\\ \\…
Key Rate Duration
In computing modified (or effective) duration for a portfolio of securities, we change the par interest rate (the yield to maturity) at every maturity by some small amount up and down (±Δy), and determine the percentage price change in the portfolio for 1% change in yield. In essence, we add ±Δy to the entire par…