For most securities, determining the rate of return on investment is a simple task. But for debt instruments, this can be more complicated because the short-term debt market has multiple methods of calculating yields, and they use different conventions when converting time periods to one year.

The following are the four main types of income:

- Bank discount rate of return (also known as bank discount benchmark)
- Holding period yield
- Effective annual output
- Money market rate of return

Understanding how these rates of return are calculated is essential to grasp the actual tool returns of investments.

## 1. Bank discount rate of return

T-Bills are quoted on a pure bank discount basis, where the quoted price is expressed as a percentage of the face value and is determined by using the 360-day counting convention to discount bonds. This assumes that there are 12 30-day months in a year. In this case, the formula for calculating the rate of return is very simple, which is the discount divided by the face value multiplied by 360, and then divided by the remaining days due.

The equation is:

Annualized Bank Discount Yield = (DF) × (360 t) where: D = discount F = face value t = number of days to maturity begin{aligned} &text{Annualized Bank Discount Yield} = left (frac{ D }{F} right) times left (frac{360}{t} right )\ &textbf{where:}\ &D = text{Discount}\ &F = text{Face value }\ &t = text{days from due date} end{aligned}

Annualized Bank Discount Yield=(FD)X(Ton36)Where:D=DiscountF=face valueTon=Days before maturity

For example, Joe bought a T-Bill with a face value of US$100,000 and paid US$97,000 for it—the equivalent of a discount of US$3,000. The expiry date is 279 days. The bank discount rate of return is 3.9%, which is calculated as follows:

0.03 (3, 000 ÷ 100, 000) × 1.29 (360 ÷ 279) = 0.0387, or 3.9% (rounded) begin{aligned} &0.03 (3,000 div 100,20109) div 100,0909 = 0.0387, \ &quadtext{or }3.9% text{ (rounded)} end{aligned}

.3(3,÷1,)X1.29(36÷279)=.387,or 3.9% (round up)

But using this annualized rate of return to determine returns has inherent problems. On the one hand, the rate of return uses a 360-day year to calculate the return that investors will receive. But this does not take into account the potential for compound returns.

The other three popular yield calculations can be said to better represent investor returns.

## 2. Holding period yield

By definition, the holding period yield (HPY) is calculated on the basis of the holding period only, so there is no need to include the number of days—just like the discounted yield of banks. In this case, you deduct the added value from the amount you paid, plus any interest or dividend payments, and then divide it by the purchase price. This non-annualized return is different from most return calculations that show annual returns. Also, whether it is assumed that interest or cash outlays will be paid at maturity.

As an equation, the holding period yield will be expressed as:

Yield during the holding period = P 1 − P 0 + D 1 P 0 where: P 1 = the amount received at maturity P 0 = the purchase price of the investment begin{aligned} &text{Holding Period Yield}=P_1- P_0+frac {D_1}{P_0}\ &textbf{where:}\ &P_1 = text{amount received at maturity}\ &P_0 = text{purchase price of investment}\ &D_1 = text {Interest received or distribution due to payment} end{aligned}

Holding period yield=phosphorus1–phosphorus+phosphorusD1Where:phosphorus1=Amount received duephosphorus=The purchase price of the investment

## 3. Effective annual output

The effective annual rate of return (EAY) can provide a more accurate rate of return, especially when there are alternative investments that can compound returns. This illustrates the interest earned by interest.

As an equation, the effective annual rate of return will be expressed as:

Effective annual yield = (1 + HPY) 3 6 5 1 t where: HPY = holding period yield t = number of days held to maturity begin{aligned} &text{Effective Annual Yield}=(1+ HPY)^{ 365}frac{1}{t}\ &textbf{where:}\ &HPY= text{holding period yield}\ &t = text{days from holding to maturity }\ end{align}

Effective annual output=(1+HphosphorusYes)365Ton1Where:HphosphorusYes=Holding period yieldTon=Number of days held to maturity

For example, if HPY is 3.87% in 279 days, then EAY will be 1.0387365÷279-1, which is 5.09%.

The frequency of compound interest applied to investments is very important and can significantly change your results. For time periods exceeding one year, the calculation is still valid and will give an absolute number smaller than HPY.

For example, if the HPY for 579 days is 3.87%, then the EAY will be 1.0387365÷579-1, which is 2.42%.

### Value reduction

For losses, the process is the same; the losses during the holding period need to be included in the actual annual rate of return. You still take one plus HPY, which is now a negative number. For example: 1 + (-0.5) = 0.95. If HPY loses 5% in 180 days, then EAY will be 0.95365÷180 -1, or -9.88%.

## 4. Money market rate of return

The money market rate of return (MMY) (also known as the CD equivalent rate of return) relies on a calculation that allows the quoted rate of return (on Treasury bills) to be compared with interest-bearing money market instruments. These investments have a short duration and are usually classified as cash equivalents. Money market instruments are quoted on a 360-day basis, so the money market rate of return is also used in the calculation of 360.

As an equation, the money market rate of return can be expressed as:

MMY = HPY × 360 expiry time where: HPY = holding period return ratebegin{aligned}&MMY=frac{HPYtimes 360}{text{TIME TO MATURITY}}\&textbf{where:} \ &HPY=text{Holding Period Yield}end{aligned}

ricericeYes=Mature timeHphosphorusYesX36Where:HphosphorusYes=Holding period yield

## Bottom line

The debt market uses a variety of calculations to determine the rate of return. Once the best method is determined, these short-term debt market yields can be used when discounting cash flows and calculating the actual returns on debt instruments such as Treasury bonds. As with any investment, the return on short-term debt should reflect risk, where lower risks are associated with lower returns, and higher-risk instruments may bring higher returns.

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