# Level II

## Binomial Pricing Trees (for Options)

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 (you are here) 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 […]

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## Valuing Bonds with Embedded Options

Bonds can be sold with a variety of embedded options, for example: Call options Put options Prepayment options Conversion options In this article, we will concentrate on callable bonds and putable bonds, although we’ll mention prepayable and convertible bonds as well. The common method of valuing a callable or putable bond is to use a […]

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## Valuing Floating-Rate Bonds

Some floating-rate bonds are easy to value: if the coupon resets to the market rate, then the value of the bond will reset to par.  (Of course, this assumes that by “the market rate” we mean the rate appropriate for a given bond, which may have to include risk premia above the Treasury rate.  If […]

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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 […]

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## 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 an α: a level of significance.  The best description I’ve heard is that α is the chosen level […]

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## 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 […]

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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 […]

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## Degrees of Freedom

Suppose that, for reasons known only to yourself and your therapist, you need to know the average height of all giraffes in the world.  Desperately.  You face a number of obstacles, not the least of which is that there are estimated to be about 80,000 giraffes in the world, and giraffes are notoriously difficult to […]

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## Durbin-Watson Statistic (Test)

The Durbin-Watson (DW) statistic is used in a test for serial correlation of residuals (i.e., error terms) in several types of regression models: Simple regression models Multiple regression models Time-series trend models DW is not appropriate for testing for serial correlation of residuals in autoregressive (AR) models.  The CFA curriculum doesn’t specify exactly why DW […]

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## Valuing Equity Swaps

Equity swaps are just as easy to value as plain vanilla interest rate swaps; once again, as with all derivatives, the formula for the value is: $Value\ =\ PV(what\ you\ will\ receive)\ –\ PV(what\ you\ will\ pay)$ If one leg is a fixed or floating rate, it is valued exactly as described for plain vanilla […]