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Binomial Tree

Introduction The Financial Risk Manager (FRM) introduces binomial trees by applying them to value derivatives for two asset classes, equities and bonds. For stock options, the text is John Hull’s Options, Futures and Derivatives; for bonds, the text is Bruce Tuckman’s Fixed Income Securities. Both are excellent and have been assigned in the syllabus for... Read More

Spot Rates

Spot prices are a basic building block in finance, but they are tricky when the commodity is money. When the commodity is money, spot prices are called spot rates (a.k.a., spot interest rate). A spot price is simply the market's current price to buy or sell a commodity for immediate delivery. Spot prices are so... Read More

FRM Study Tips

After registering for the FRM exam and purchasing study materials, many new FRM candidates find it difficult to figure out where to begin with their FRM study plan. It is very important to have a study plan because without one, you may not be able to get through the entire GARP curriculum. The GARP curriculum provides... Read More

Modified Duration

Our forum contains hundreds of questions about duration. Duration often vexes new candidates, in part because there are several types. Let's first settle a confusion: the units of all durations are years (time). So, regardless of which duration, we can typically say something like "The bond's duration is 4.52 years." I taught duration several years... Read More

What Is a Z Table?

Functions based on the normal distribution are easy to retrieve in code or excel, so we do not really need z tables anymore, in practice. But we still want to understand the z table. Why? Because the popular exam calculators (TI BA II+ and HP 12c) do not include z table functionality, so we do... Read More

Statistical Inference: Hypothesis Testing and Confidence Intervals

320.1. Recently 25 banks were surveyed. Their sample average total capital is 8.40% (i.e., Tier 1 plus Tier 2 as a percentage of risk-weighted assets, RWA) with a sample standard deviation of 1.0%. Our one-sided null hypothesis is that the population's "true" average total capital is less than or equal to 8.0%. With 95.0% confidence,... Read More

Economic Capital (Schroeck)

Learning outcomes: Evaluate a bank’s economic capital relative to its level of credit risk. Identify and describe important factors used to calculate economic capital for credit risk: probability of default, exposure, and loss rate. Questions: 505.1. According to Schroeck, economic capital is an estimate of the overall level of capital necessary to guarantee the solvencyof... Read More