# Level III Derivatives

## 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 […]

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## 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 […]

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## 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 […]

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## 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) $V_T$: […]

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## 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 […]

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## 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 […]