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There are three ways the Treasury Rate is used in calculations. Out of these three, which...

There are three ways the Treasury Rate is used in calculations. Out of these three, which do you see being most accurate?

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Expert Solution

The Treasury Department uses two methods to calculate the yield on T-bills with maturities of less than a year: the discount method and the investment method.

Under the discount yield method, the return as a percent of the face value, not the purchase value, is calculated. For example, an investor that purchases a 90-day T-bill for $9,800 per $10,000 face value will have a yield of:

Discount Yield = [($10,000 - $9,800) / $10,000] x (360/91) = 7.91%

Under the investment yield method, the Treasury yield is calculated as a percent of the purchase price, not the face value. Following our example above, the yield under this method is:

Investment Yield = [($10,000 - $9,800) / $9,800] x (365/91) = 8.19%

Note that the number of days per year used under both methods is different. The discount method uses 360, which is the number of days used by banks to determine short-term interest rates. The investment yield uses the number of days of a calendar year, which is 365 or 366. Given that the purchase price of a Treasury bill is always less than the face value, the discount method tends to understate the yield.

Yield on Treasury Notes and Bonds

The rate of return for investors holding Treasury notes and Treasury bonds includes the coupon payments that they receive semi-annually and the face value of the bond that they are repaid at maturity. T-notes and bonds can be purchased at par, at a discount, or at a premium, depending on the demand and supply of these securities at auction or in the secondary markets. If a Treasury is purchased at par, then its yield equals its coupon rate; if at a discount, yield will be higher than coupon rate and yield will be lower than coupon rate if purchased at a premium.

The formula for calculating the Treasury yield on notes and bonds held to maturity is:

Treasury Yield = [C + ((FV - PP) / T)] ÷ [(FV + PP)/2]

where C= coupon rate

FV = face value

PP = purchase price

T = time to maturity  

The yield on a 10-year note with 3% coupon purchased at a premium for $10,300 and held to maturity is:

Treasury Yield = [$300 + (($10,000 - $10,300) / 10)] ÷ [($10,000 + $10,300)/2]

= $270 / $10,150 = 2.66%

Because of their low risk, Treasuries have a low return compared to many other investments. Very low Treasury yields, like the ones observed in 2020 thus far, can drive investors into riskier investments, such as stocks, which have higher returns.


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