Definition
Discount Yield refers to the annualized yield of a security sold at a discount, such as U.S. Treasury bills (T-bills). It is a simple formula used to approximate the return on investment from the difference between the purchase price and the face value of the security.
Calculation
To calculate the annual discount yield:
- Determine the discount amount, which is the difference between the face value and the purchase price of the security.
- Divide the discount by the face value of the security.
- Multiply the resulting number by 360 (an approximation of the number of days in a year) and then divide by the number of days until maturity.
Example
Consider a U.S. Treasury bill purchased at $9,750 and maturing at $10,000 in 90 days:
- Discount = $10,000 (Face Value) - $9,750 (Purchase Price) = $250
- Discount Yield = $\frac{250}{10,000} \times \frac{360}{90} = 0.01 \times 4 = 0.04$ or 4%
Frequently Asked Questions
Q1: What is the benefit of using the discount yield method?
A1: The discount yield method is beneficial for investors looking for a straightforward way to calculate the annualized return on short-term debt securities sold at a discount.
Q2: Can the discount yield be applied to any security?
A2: No, discount yield specifically applies to securities sold at a discount, such as T-bills and commercial paper. It is not suitable for bonds or other securities sold with interest.
Q3: Does the discount yield account for compounding interest?
A3: No, discount yield does not account for the compounding of interest; it is a simple annualized percentage based only on the linear calculation.
Q4: Why do we use 360 instead of 365 days in the calculation?
A4: Using 360 days is a convention in the financial industry for ease of calculation, especially for short-term instruments.
Q5: How does the discount yield differ from the bond equivalent yield?
A5: The bond equivalent yield annualizes the yield over a 365-day period and semiannual compounding, providing a bond’s comparable rate for securities. Discount yield uses a 360-day base and does not consider compounding.
- Yield to Maturity (YTM): The total return anticipated if a bond is held until it matures, considering both interest payments and the difference between its current market price and par value.
- Current Yield: The annual interest payment divided by the current market price of the bond, not accounting for capital gains or losses at maturity.
- Bond Equivalent Yield (BEY): An annualized yield that helps compare discount securities with bonds that pay semiannual interest.
Online References
- Investopedia: Discount Yield
- Treasury Direct: Treasury Bills
Suggested Books for Further Studies
- “Fixed Income Securities: Tools for Today’s Markets” by Bruce Tuckman and Angel Serrat
- “The Bond Book” by Annette Thau
- “Investing in Bonds For Dummies” by Russell Wild
Fundamentals of Discount Yield: Finance Basics Quiz
### How do you calculate the discount yield of a security?
- [ ] By dividing the face value by the purchase price and then multiplying by the interest rate.
- [ ] By dividing the purchase price by the face value and then multiplying by 100.
- [x] By dividing the discount by the face value and multiplying by the quotient of 360 divided by the days to maturity.
- [ ] By multiplying the discount by the face value and dividing by 365.
> **Explanation:** The correct method to calculate the discount yield of a security involves dividing the discount amount by the face value, then multiplying the result by 360 divided by the number of remaining days to maturity.
### What does the discount yield not take into account?
- [ ] The maturity date
- [ ] The purchase price
- [ ] The face value
- [x] Compounding interest
> **Explanation:** The discount yield calculation does not take into account the compounding of interest. It is a simple annual percentage yield different from the more comprehensive yield measures accommodating compound interest.
### What is the common approximation of days used in discount yield calculations?
- [ ] 365 days
- [ ] 350 days
- [x] 360 days
- [ ] 355 days
> **Explanation:** 360 days is the accepted approximation in the financial industry for calculating discount yield, streamlining the math for financial instruments and making certain calculations easier.
### For a T-bill sold at a discount, what elements do you need to compute its discount yield?
- [x] The face value, purchase price, and the number of days until maturity
- [ ] The current market price, interest rate, and maturity date
- [ ] The face value, current price, and the annual interest payment
- [ ] The dividend yield and the market capitalization
> **Explanation:** To compute the discount yield of a T-bill, you need the face value, purchase price, and the specific number of days until the security reaches maturity.
### If a T-bill is bought for $9,800 and matures to $10,000 in 180 days, what is the discount yield?
- [ ] 4.07%
- [x] 4.00%
- [ ] 4.17%
- [ ] 4.27%
> **Explanation:** The discount of $200 divided by face value $10,000 equals .02. Multiplying by the fraction 360/180 gives a discount yield of 4.00%.
### Why is the discount yield method primarily used?
- [ ] To calculate long-term investment returns.
- [ ] To account for inflation rates.
- [x] To simplify the calculation of short-term securities sold at a discount.
- [ ] To forecast future market trends.
> **Explanation:** The primary usage of the discount yield calculation is to simplify the determination of returns on short-term securities such as T-bills that are sold at a discount and thus do not provide periodic interest payments.
### In a discount yield calculation, what is the “discount”?
- [ ] The interest received annually
- [ ] The face value of the security
- [x] The difference between the face value and the purchase price
- [ ] The total cost of ownership
> **Explanation:** In the context of discount yield, the "discount" is defined as the difference between the face value of the security and the purchase price, representing the gain upon reaching maturity.
### Which U.S. government security is commonly sold at a discount?
- [ ] Municipal bonds
- [x] Treasury bills (T-bills)
- [ ] Corporate bonds
- [ ] Mortgage-backed securities
> **Explanation:** Treasury bills (T-bills) are the primary type of U.S. government securities commonly sold at a discount, meaning they are sold for less than their face value and do not pay regular interest.
### How often is the discount calculated for most discount yield securities?
- [ ] Annually
- [x] At purchase and maturity
- [ ] Bi-annually
- [ ] Quarterly
> **Explanation:** The discount is typically calculated at the initial purchase and again at maturity for the majority of discount yield securities, providing the basis for determining the overall yield.
### Which free online resource provides thorough listings and explanations of discount securities?
- [ ] IRS.gov
- [x] Treasury Direct
- [ ] Investopedia
- [ ] SEC.gov
> **Explanation:** Treasury Direct (TreasuryDirect.gov) offers comprehensive information on discount securities such as U.S. Treasury bills, providing investors with essential resources and data.
Thank you for exploring our detailed guide on discount yield and working through our informative quiz insights. Keep improving your financial understanding and investment strategies!
