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Month: April 2013
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Bayes’ Formula
Bayes’ Formula is frequently presented in statistics texts as important (it is), profound (it isn’t, particularly), and difficult (it isn’t, remotely). If you understand conditional probability, then Bayes’ Formula is trivial. Let me show you: We start with the probability of two events, A and B: \[P(AB)\ =\ P(A|B)\ ×\ P(B)\] Similarly, for the probability…
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Pricing Derivatives
Pricing derivatives – forwards, futures, FRAs, and swaps – is generally not difficult, and the principle that underlies all pricing relationships is quite easy: arbitrage. The first thing you need to know is exactly what is meant by the price of a derivative. The price of: A forward/futures contract is the agreed price of the…
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Pricing FRAs
An FRA is essentially an agreement to enter into two loans (one long, one short) in the future: a fixed-rate loan and a floating-rate loan. (The difference between an FRA and an actual agreement to enter into these two loans is that the FRA will be settled at the beginning of the loan period, whereas…
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Pricing Forwards and Futures
Remember that the price of a forward/future contract is the agreed price of the underlying at the expiration of the contract, which has to be: \[F_T\ =\ S_0\left(1\ +\ r_f\right)^T\] where: \(T\): expiration of the forward/futures contract \(F_T\): forward/futures price of the underlying (at time \(T\)) \(S_0\): spot price of the underlying today \(r_f\): effective…
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Pricing Plain Vanilla Interest Rate Swaps
Remember that the price of a plain vanilla interest rate swap is the fixed rate on the swap. The key to pricing swaps is the realization that a swap is essentially an exchange of bonds. A plain vanilla (fixed-for-floating) interest rate swap can be replicated by the fixed payer issuing a fixed-rate bond to the…
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DTAs and DTLs – How to Keep Them Straight
FRA is unquestionably one of the more difficult topic areas for Level I candidates, because it requires memorization of a lot of ideas, rather than developing those ideas from first principles. There are, however, some ideas in FRA that can be developed from first principles, which will make them easier to recall on exam day. …
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Valuing a Currency Forward: Whence Came That Formula?
The formulae for valuing all derivatives are essentially the same: \[Value\ =\ PV\left(what\ you\ will\ receive\right)\ –\ PV\left(what\ you\ will\ pay\right)\] The one valuing formula that needs some explanation is the formula for valuing a currency forward; it is slightly different from the other formulae, but the difference is never explained. Here goes: Given: \(V_t\):…
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Inflation in Required Rate of Return – to Tax, or Not to Tax?
A common question that plagues many Level III candidates is how to treat inflation when calculating a nominal, before-tax required rate of return for an individual investor: do you add inflation to the real after-tax return, then compute the before-tax return, or do you start with the real after-tax return, compute the before-tax return, then…
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Applying Level I Economics to Your Level I Studying
The most important topic in Econ is marginal revenue product: the idea that you maximize your profit (minimize your cost) when the ratio of marginal revenue product to input price for all inputs is the same: \[\frac{MRP_{1}}{P_{1}} = \frac{MRP_{2}}{P_{2}} = \cdots = \frac{MRP_{n}}{P_{n}}\] That is, it’s the most important if you can apply it to…
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How to Approach the Level III CFA Exam
If you’ve never taken the Level III CFA exam, you’re in for a real treat. (If you’ve taken it before, you already know what I mean.) As with the Level I and Level II exams, this exam will be six hours – three in the morning, and three in the afternoon – and it will…