The Federal Home Loan Mortgage Corporation (“Freddie Mac”) is a GSE chartered by the Congress of the United States in 1970 to improve the liquidity of the secondary mortgage market. Freddie Mac purchases mortgage loans from individual lenders and either sells securities backedby the mortgages to investors or holds the mortgages until maturity. Like Fannie Mae, Freddie Mac is similarly charged with providing access to mortgage finance for low-income families and underserved populations.Also like Fannie Mae, Freddie Mac is regulated by HUD for its housing mission and by OFHEO for safety/soundness issues. Freddie Mac maintains a direct line of credit with the U.S. Treasury.

Discount Notes

In 2000, Freddie Mac issued $2.076 trillion in discount notes. While a tissuance these notes can range in maturity from overnight to 365 days,half of these notes have maturities of three days or less. The most popular maturities are one month and three months. Freddie Mac discount notes are offered for sale continuously with rates posted 24 hours a day (businessdays) through a group of investment banks that belong to the Freddie Mac dealer group. These notes are issued in book entry form through the Federal Reserve Bank of New York and a minimum face value of$1,000 with increments of $1,000 there after. The pricing conventions are the same as U.S. Treasury bills.

Reference Bills

Freddie Mac’s Reference Bills® program was announced November 17,1999. The program is similar in structure to Fannie Mae’s BenchmarkBills. One important difference between the two is that Reference Bills®are offered in more maturities namely, one month (28 days), two months (56 days), three months (91 days), six months (182 days), and one year (364 days).

Like U.S. Treasury bills and Benchmark Bills, Reference Bills are sold weekly using a Dutch auction. 1-month and 2-month Reference Bills are auctioned each week on Monday, while 3-month maturities are auctioned weekly on Tuesday. The 6-month and 1-year Reference Bills are auctioned every four weeks on Tuesday on an alternating schedule such that every two weeks either a 6-month or a 1-year maturity will be auctioned. Inorder to give their investors flexibility, Freddie Mac offers multiple settlement dates. For Reference bills auctioned on Mondays, investors may choose between cash and regular settlement dates. For those auctioned onTuesdays, investors may choose between cash, regular, and skip-day settlement dates. Auctions of Reference Bills are announced on Thursday for the following week and have a minimum size of $1 billion.

Figure below presents a Bloomberg DES (Security Description) of a 3-month Reference Bill that was auctioned on September 11, 2001 and matures on September 25, 2001. Figure below presents YA (Discount/Yield Analysis). Note the yield on a bank discount basis for this Reference Bill is 2.28154. Given the yield on a bank discount basis, the price is found the same way as the price of a Treasury bill in Chapter by first solving for the dollar discount (D) as follows:

D = Yd × F × (t /360)


Yd = discount yield

F = face value

t = number of days until maturity

The price is then

price = F − D

With a settlement day of September 20, 2001, the Reference Bill has 63 days remaining until maturity. Assuming a face value of $100 and a yield on bank discount basis of 2.28154%, D is equal to

D = 0.0228154 × $100 × (84/360) = $0.532359

Bloomberg Security Description Screen of a Freddie Mac Reference Bill

Bloomberg Security Description Screen of a Freddie Mac Reference Bill


price = $100 − $0.532359 = $99.467641

This calculation agrees with the price displayed in the box on the upperleft-hand side of the screen in Figure below.

Also in the Figure below are various yield calculations located in a box on the left-hand side of the screen.The CD equivalent yield (also called money market equivalent yield) makes the quoted yield on a bank discount basis more comparable on other money market instruments that pay interest on a 360-day basis. Recall, the formula for the CD equivalent yield is


The notation is the same as above.

Bloomberg Yield Analysis Screen for a Freddie Mac Reference Bill

Bloomberg Yield Analysis Screen for a Freddie Mac Reference Bill

To illustrate the calculation of the CD equivalent yield,once again we use the information from Figure below.The yield on a bank discount basisis 2.28154%. The CD equivalent yield is computed as follows:

This calculation agrees with the yield presented in the screen.Just above the CD yield is simple interest. Simple interest is the ratio of the cash flow to be received from holding the security until maturity(i.e., the discount) to the security’s price annualized on the basis of a 360-day year. Recall from Chapter, the simple interest formula is simply

simple interest formula

To illustrate the calculation, let’s us continue to use the Reference Billin Figure below. The simple interest (ACT/360) is computed as follows:

simple interest formula

This calculation agrees with the one presented in the screen.

Another frequently used is called the bond-equivalent yield. This yield measure makes a yield quoted on a bank discount basis more comparable to yields on coupon Treasuries that use an actual/actual day count convention. Recall, the calculation of a bond equivalent yield depends on whether the discount instrument has 182days or less to maturity or more than 182 days. If the maturity is 182days or less, the calculation of the bond-equivalent yield is very straight forward. Let’s tackle the more involved case and consider a Reference Bill that has a maturity longer than 182 days.

When a discount instrument like a Reference Bill has a current maturity of more than 182 days, converting a yield on a bank discount basis into a bond-equivalent yield is more involved. Specifically,the calculation must reflect the fact that a Reference Bill does deliver cash flows prior to maturity while a coupon bond delivers coupon payments semiannually and the semi annual coupon payment can be reinvested.

As an example, let’s use a 1-year Reference Bill. Figure below presents a Bloomberg YA screen for this Reference Bill issued on September 12,2001. The price of this bill is 97.5271 (per $100 of face value). This bill matures on September 12, 2002 so as of September 20, 2001 (settlement date) there are 357 days to maturity. Since the year 2002 is a non-leap year, T = 365. Substituting this information in the expression above gives the bond-equivalent yield for this 1-year Reference Bill:


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