How to Calculate Discount Yield: A Comprehensive Guide for Investors

What is Discount Yield?

Discount yield is a specific type of yield calculation used for securities that are purchased at a price lower than their face value. Unlike other yield measures that consider the actual investment amount, discount yield focuses on the difference between the face value and the purchase price.

For example, if you buy a $10,000 Treasury bill for $9,700, the discount yield helps you understand the return on this investment. It is particularly useful for short-term investments where the security is sold at a discount and matures at its face value.

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The Formula for Discount Yield

To calculate discount yield, you use the following formula:

[

\text{Discount Yield} = \left( \frac{\text{Face Value} – \text{Purchase Price}}{\text{Face Value}} \right) \times \left( \frac{360}{\text{Days to Maturity}} \right)

]

Here’s a breakdown of the components:

• Face Value: The amount the security will be worth at maturity.

• Purchase Price: The amount you pay for the security.

• Days to Maturity: The number of days until the security matures.

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The formula uses a 360-day year and assumes each month has 30 days for simplification. This convention can sometimes lead to slight inaccuracies but makes calculations more straightforward.

Example Calculations

Let’s calculate the discount yield for a $10,000 Treasury bill purchased at $9,700 and maturing in 120 days.

1. Face Value = $10,000

2. Purchase Price = $9,700

3. Days to Maturity = 120 days

Using the formula:

[

\text{Discount Yield} = \left( \frac{10,000 – 9,700}{10,000} \right) \times \left( \frac{360}{120} \right)

]

[

\text{Discount Yield} = \left( \frac{300}{10,000} \right) \times 3 = 0.03 \times 3 = 0.09 \text{ or } 9\%

]

So, the discount yield for this Treasury bill is 9%.

Differences Between Discount Yield and Other Yield Measures

Discount yield differs from other yield measures in several ways:

• Bank Discount Yield (BDY): This measure also uses the face value but does not account for the compounding effect over time.

• Holding Period Yield (HPY): This yield is based on the actual investment amount and includes any capital gains or losses.

• Effective Annual Yield (EAY): This measure takes into account compounding and provides a more accurate annual return.

The main limitation of discount yield is its use of a simplified 360-day year and the fact that it does not reflect the actual amount invested.

Practical Applications and Limitations

Understanding discount yield is essential for making informed investment decisions, especially in short-term debt markets. Here are some practical implications:

• High discount yields may indicate higher returns but also potentially higher risks.

• Low discount yields might suggest lower returns but could be safer investments.

However, there are potential errors due to the 360-day year convention and the difference between face value and purchase price. Investors should be aware of these limitations when comparing different investment opportunities.

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