Introduction

Financial Toolbox™ software provides the following suite of functions for computing price and yield on Treasury bills.

For all functions with yield in the computation, you can specify yield as money-market or bond-equivalent yield. The functions all assume a face value of $100 for each Treasury bill.

Treasury Bill Repurchase Agreements

The following example shows how to compute the break-even discount rate. This is the rate that correctly prices the Treasury bill such that the profit from selling the tail equals 0.

Maturity = '26-Dec-2002';
InitialDiscount = 0.0161;
PurchaseDate = '26-Sep-2002';
SaleDate = '26-Oct-2002';
RepoRate = 0.0149;

BreakevenDiscount = tbillrepo(RepoRate, InitialDiscount, ... 
PurchaseDate, SaleDate, Maturity)

BreakevenDiscount =

    0.0167

You can check the result of this computation by examining the cash flows in and out from the repurchase transaction. First compute the price of the Treasury bill on the purchase date (September 26).

PriceOnPurchaseDate = tbillprice(InitialDiscount, ... 
PurchaseDate, Maturity, 3)

PriceOnPurchaseDate =

   99.5930

Next compute the interest due on the repurchase agreement.

RepoInterest = ... 
RepoRate*PriceOnPurchaseDate*days360(PurchaseDate,SaleDate)/360

RepoInterest =

    0.1237

RepoInterest for a 1.49% 30-day term repurchase agreement (30/360 basis) is 0.1237.

Finally, compute the price of the Treasury bill on the sale date (October 26).

PriceOnSaleDate = tbillprice(BreakevenDiscount, SaleDate, ... 
Maturity, 3)

PriceOnSaleDate =

   99.7167

Examining the cash flows, observe that the break-even discount causes the sum of the price on the purchase date plus the accrued 30-day interest to be equal to the price on sale date. The next table shows the cash flows.

Treasury Bill Yields

Using the same data as before, you can examine the money-market and bond-equivalent yields of the Treasury bill at the time of purchase and sale. The function tbilldisc2yield can perform both computations at one time.

Maturity = '26-Dec-2002';
InitialDiscount = 0.0161;
PurchaseDate = '26-Sep-2002';
SaleDate = '26-Oct-2002';
RepoRate = 0.0149;
BreakevenDiscount = tbillrepo(RepoRate, InitialDiscount, ... 
PurchaseDate, SaleDate, Maturity)

[BEYield, MMYield] = ...
tbilldisc2yield([InitialDiscount; BreakevenDiscount], ... 
[PurchaseDate; SaleDate], Maturity)

BreakevenDiscount =

    0.0167


BEYield =

    0.0164
    0.0170


MMYield =

    0.0162
    0.0168

For the short Treasury bill (fewer than 182 days to maturity), the money-market yield is 360/365 of the bond-equivalent yield, as this example shows.