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Category: Level III
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}\\ \\…
Answering a Constructed Response (Essay) Question: Allocating Your Time
This will be a very short article. When you are allocating your time to answering a constructed response (i.e., essay, morning session) question, follow this simple rule: ⅔ – ¾ of your time should be spent thinking about your answer ¼ – ⅓ of your time should be spent writing your answer. Suppose that the question asks…
Essay (Constructed Response) Questions: What’s the Point?
A recent session with one of my tutoring candidates brought to mind an interesting idea that is more than worthy of an article of its own: What’s the point? When you are writing an answer to an AM (constructed response, essay) question, you should ask yourself one simple question: What’s the point of my answer?…
Adjusting the Allocation of an Equity/Fixed Income Portfolio using Equity/Bond Futures
Adjusting Allocation Only Adjusting the allocation of a portfolio that comprises both equity and fixed income is nothing more than a combination of: Adjusting the value of the equity portion of the portfolio by a given amount (up or down), and Adjusting the value of the fixed income portion of the portfolio by that same…
The Synthetics: Cash, Equity, and Fixed Income
Creating synthetic cash from an equity portfolio or a fixed income portfolio, creating synthetic equity from cash, and creating synthetic bonds from cash are, in principle, no different than adjusting the value/beta of an equity portfolio, or adjusting the value/duration of a fixed income portfolio, except for that one pesky characteristic of cash: cash always…
Adjusting the Value/Duration of a Fixed Income Portfolio using Bond Futures
Adjusting the Value of a Fixed Income Portfolio The typical formula for computing the number of bond futures contracts needed to adjust the value of a fixed income portfolio is: \[N_f\ =\ \frac{V_T\ -\ V_P}{V_f}\left(\frac{Dur_P}{Dur_f}\right)\left(yield\ \beta\right)\] where: \(N_f\): number of bond futures contracts to buy (i.e., take the long position) or sell (i.e., take the…
Adjusting the Value/Beta of an Equity Portfolio using Equity Futures
Adjusting the Value of an Equity Portfolio The typical formula for computing the number of equity futures contracts needed to adjust the value of an equity portfolio is: \[N_f\ =\ \frac{V_T\ -\ V_P}{V_f}\left(\frac{\beta_P}{\beta_f}\right)\] where: \(N_f\): number of equity futures contracts to buy (i.e., take the long position) or sell (i.e., take the short position) \(V_T\):…
Cash (Currency): the Wonky Commodity
Throughout Level II and Level III – and a little bit at Level I – we see calculations that involve commodities; e.g., calculating the price or value of a forward or futures contract on an underlying commodity. In all of those calculations, the quantity of the commodity is constant; for example, if you’re given the…
Dollar Duration and Dollar Beta
Dollar duration (or money duration) is a phrase that should be familiar to you by now: instead of measuring the percentage change in the value of a fixed income portfolio for a 1% change in yield to maturity (as modified or effective duration do), dollar duration measures the change in dollar (or other currency) value…
Getting from Here to There
Many applications of derivatives – forwards and futures in particular – in risk management boil down to getting from here to there: temporarily changing (adjusting) the: Value of an equity portfolio Beta of an equity portfolio Value of a fixed income portfolio Duration of a fixed income portfolio Allocation of an equity/fixed income portfolio There are formulae…