# Documentation

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# tfutyieldbyrepo

Calculates Treasury bond futures yield given the implied repo rates

## Syntax

```FwdYield = tfutyieldbyrepo(RepoData,ReinvestData,Yield,Settle,MatFut,ConvFactor,CouponRate,Maturity)
```

## Arguments

 `RepoData` Number of futures (`NFUT`) by `2` matrix of simple term repo/funding rates in decimal and their bases in the form of `[RepoRate RepoBasis]`. Specify `RepoBasis` as `2` = actual/360 or `3` = actual/365. `ReinvestData` Number of futures (`NFUT`) by `2` matrix of rates and bases for the reinvestment of intervening coupons in the form of `[ReinvestRate ReinvestBasis]`. `ReinvestRate` is the simple reinvestment rate, in decimal. Specify `ReinvestBasis` as `0` = not reinvested, `2` = actual/360, or `3` = actual/365. `Yield` Yield to maturity of Treasury bonds per \$100 notional at `Settle`. `Settle ` Settlement/valuation date of futures contract. `MatFut` Maturity date (or anticipated delivery dates) of futures contract. `ConvFactor` Conversion factor. See `convfactor`. `CouponRate` Underlying bond annual coupon, in decimal. `Maturity` Underlying bond maturity date.

Inputs (except `RepoData` and `ReinvestData`) must either be a scalar or a vector of size equal to the number of Treasury futures (`NFUT`) by `1` or `1`-by-`NFUT`.

## Description

`FwdYield = tfutyieldbyrepo(RepoData,ReinvestData,Yield,Settle,MatFut,ConvFactor,CouponRate,Maturity)` computes the theoretical futures bond yield given the settlement yield, the repo/funding rate, and the reinvestment rate.

`FwdYield` is the forward yield to maturity, in decimal, compounded semiannually.

## Examples

collapse all

This example shows how to compute the quoted futures bond yield, given the following data.

```RepoData = [0.020 2]; ReinvestData = [0.018 3]; Yield = [0.0215; 0.0257]; Settle = datenum('11/15/2002'); MatFut = [datenum('15-Dec-2002'); datenum('15-Mar-2003')]; ConvFactor = [1; 0.9854]; CouponRate = [0.06; 0.0575]; Maturity = [datenum('15-Aug-2009'); datenum('15-Aug-2010')]; FwdYield = tfutyieldbyrepo(RepoData, ReinvestData, Yield,... Settle, MatFut, ConvFactor, CouponRate, Maturity)```
```FwdYield = 0.0221 0.0282 ```