Short-term debt markets have a direct effect on borrowing and lending, which affects investment analysis as well. Through the discounting of potential investments, the money market can help determine alternative returns and thus compare an investor's options.

**Tutorial**: **Money Market**

Debt markets have various ways of presenting and calculating the yield on your investment. Determining the yield seems straight forward when you think about normal investments, but in debt instruments the yield can sometimes get a little complicated. Take Treasury bills (T-Bills) for instance. The U.S. issues debt to investors and sets a specific amount that will be paid at maturity. This is called the face value. To determine the return, you need to look at the cost to purchase this. The difference between the cost and the face value is called the discount. But, to make things a little more complicated the length of time is not a year â€” it could be a couple of days, or a couple of months. Different types of yields use different conventions in converting this time period into a year. So, you will need to compare the face value to the amount promised to be paid back and convert the time period to a one year yield. (To learn more about the U.S. Treasury, see *The Treasury And The Federal Reserve*.)

There are four main types of yields that will be covered, which will help you navigate the different ways returns are presented: the bank discount yield (also called bank discount basis), holding period yield, effective annual yield and the money market yield. (To learn more, see: *Finding The Best Yields.)*

## Bank Discount Yield

T-Bills are quoted on a pure discount basis, which means the agreement states the total money that will be paid at maturity, and the investor pays a lower amount. The difference between these two numbers (the discount) is the return, but to get a yield it still needs to be converted to a yearly percentage.

In this situation, the formula for calculating the yield is simply the discount, divided by the face value, multiplied by 360 and then divided by the amount of days remaining to maturity.

Annualized yield on a bank discount basis =

**Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (D / F) * (360 / t)**

Where:

D = Discount

F = Face value

t = Number of days until maturity

For example, Joe purchases a T-Bill with a face value of $100,000 and pays $97,000 for it. The maturity date is in 279 days. What is the bank discount yield?

Bank discount yield = (D/F) x (360/t)

= (3,000/100,000) x (360/279)

= 0.0387

= 3.9%

But, there are a couple of problems with using this annualized yield in determining your return. For example, this yield uses a 360-day year to calculate the return an investor would receive. Also, it does not take into account the potential for compounded returns, and only assumes you have no other investment options.

The remaining three popular yield calculations give a better representation of an investor's return.

## Holding Period Yield

The holding period yield by definition is only calculated on a holding period basis. So there is no need to include the number of days, which was included in the bank discount yield. It seems pretty straight forward, that you take the increase in value from what you paid, add on any interest or dividend payments and divide it by how much you purchased it for. This is the unannualized return, which is different than most return calculations that like to show returns on a yearly basis. Also, the interest or cash disbursement paid, is assumed to happen at the time of maturity.

**Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â HPY =Â P_{1} â€” P_{0} + D_{1} /Â P_{0}**

Where:

P_{1} = amount received at maturity

P_{0} = purchase price of the investment

D_{1} = interest received or distribution paid at maturity

## Effective Annual Yield

The effective annual yield can give a more accurate yield, especially when alternative investments are available which can compound the returns. This accounts for interest earned on interest.

**Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â EAY = (1 + HPY)^{365/t} â€” 1**

Where:

HPY = holding period yield

t = number of days held until maturity

For example, if the HPY was 3.87% over 279 days, then the EAY would be 1.0387^{365/279} -1 or 5.09%

The compounding frequency that applies to the investment is extremely important, and can significantly alter your result. For periods longer than a year, the calculation still works and will give a smaller, absolute number than the HPY.

For example, if the HPY was 3.87% over 579 days, then the EAY would be 1.0387^{365/579} -1 or 2.42%.

*Decrease In Value*

For losses, the process is the same; the loss over the holding period would need to be made into the effective annual yield. You still take one plus the HPY which is now a negative number, for example 1 + (-0.5) = 0.95.

For example, if the HPY was a loss of 5% over 180 days, then the EAY would be 0.95^{365/180} -1 or -9.88%.

## Money Market Yield

The money market yield is also known as the CD-equivalent yield, and is the fourth way we can calculate yield. This calculation allows the quoted yield (which is in on a T-Bill) to be compared to an interest-bearing money market instrument. These investments have a duration that will be shorter term, and are often classified as cash equivalents. Money market instruments quote on a 360-day basis so the money market yield also uses 360 in its calculation.

*Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â MMY* = 360 * Y_{BD} / 360 â€” (t * Y_{BD)}

Where:

Y_{BD} = yield on a bank discount basis calculated earlier

t = days held until maturity

## The Bottom Line

Calculating the different types of yields can get confusing when they seem so similar. There are several ways in which returns are presented in the debt market, and we can use these calculations to determine the yield. Once found, the yields from these short-term debt markets can be used when discounting cash flows. In the short-term, institutions can raise cash or invest at these rates. And like any investment, the return should reflect the risk; the lower the risk, the lower the return.