# tbilldisc2yield

Convert Treasury bill discount to equivalent yield

## Syntax

``[BEYield,MMYield] = tbilldisc2yield(Discount,Settle,Maturity)``

## Description

example

````[BEYield,MMYield] = tbilldisc2yield(Discount,Settle,Maturity)` converts the discount rate on Treasury bills into their respective money-market or bond-equivalent yields.```

## Examples

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This example shows how to convert the discount rate on Treasury bills into their respective money-market or bond-equivalent yields, given a Treasury bill with the following characteristics.

```Discount = 0.0497; Settle = '01-Oct-02'; Maturity = '31-Mar-03'; [BEYield MMYield] = tbilldisc2yield(Discount, Settle, Maturity)```
```BEYield = 0.0517 ```
```MMYield = 0.0510 ```

This example shows how to use `datetime` inputs to convert the discount rate on Treasury bills into their respective money-market or bond-equivalent yields, given a Treasury bill with the following characteristics.

```Discount = 0.0497; Settle = datetime(2002,10,1); Maturity = datetime(2003,3,31); [BEYield MMYield] = tbilldisc2yield(Discount, Settle, Maturity)```
```BEYield = 0.0517 ```
```MMYield = 0.0510 ```

## Input Arguments

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Discount rate of the Treasury bills, specified as a scalar of a `NTBILLS`-by-`1` vector of decimal values. The discount rate basis is actual/360.

Data Types: `double`

Settlement date of the Treasury bill, specified as a scalar or a `NTBILLS`-by-`1` vector using a datetime array, string array, or date character vectors. `Settle` must be earlier than `Maturity`.

To support existing code, `tbilldisc2yield` also accepts serial date numbers as inputs, but they are not recommended.

Data Types: `char` | `string` | `datetime`

Maturity date of the Treasury bill, specified as a scalar or a `NTBILLS`-by-`1` vector using a datetime array, string array, or date character vectors.

To support existing code, `tbilldisc2yield` also accepts serial date numbers as inputs, but they are not recommended.

Data Types: `char` | `string` | `datetime`

## Output Arguments

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Bond equivalent yields of the Treasury bills, returned as a `NTBILLS`-by-`1` vector. The bond-equivalent yield basis is actual/365.

Money-market yields of the Treasury bills, returned as a `NTBILLS`-by-`1` vector. The money-market yield basis is actual/360.

## References

[1] SIA Fixed Income Securities Formulas for Price, Yield, and Accrued Interest. Volume 1, 3rd edition, pp. 44–45.

[2] Krgin, D. Handbook of Global Fixed Income Calculations. Wiley, 2002.

[3] Stigum, M., Robinson, F. Money Market and Bond Calculation. McGraw-Hill, 1996.

## Version History

Introduced before R2006a

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