Discount Yield: Calculating Yield on Discounted Securities

A comprehensive guide to understand and calculate the discount yield on securities sold at a discount, such as U.S. Treasury bills. Details include the definition, formula, examples, and special considerations.

Discount yield refers to the yield on a security sold at a discount to its face value. It measures the annualized return an investor receives when purchasing a security at a discount and holding it until maturity. A common example is U.S. Treasury bills, which are sold at a discount and pay the face value at maturity.

Definition and Calculation

The discount yield is calculated by dividing the discount amount (the difference between the purchase price and the face value) by the face value, and then annualizing this by adjusting for the number of days to maturity. Here’s the formula:

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

Example Calculation

Consider a U.S. Treasury bill sold at $9,750 and maturing at $10,000 in 90 days:

1. Calculate the discount:

   $$ \text{Discount} = \text{Face Value} - \text{Purchase Price} = 10,000 - 9,750 = 250 $$

2. Divide the discount by the face value:

   $$ \frac{250}{10,000} = 0.025 $$

3. Annualize the yield by multiplying by the ratio of 360 to the days to maturity:

   $$ 0.025 \times \left( \frac{360}{90} \right) = 0.025 \times 4 = 0.10 $$

Thus, the annual discount yield is 10%.

Special Considerations

• 360-Day Year: The use of 360 days instead of 365 is a common convention in finance for simplicity.
• Short-Term Securities: Discount yield is primarily used for short-term securities like Treasury bills.
• Inflation Impact: Investors should consider the impact of inflation on the real yield.

Historical Context

The concept of discount yield became significant with the evolution of financial markets and government securities. U.S. Treasury bills, introduced in the 1920s, popularized the usage of discount yields as they provided a secure and predictable return mechanism for investors.

Applicability

Discount yield is crucial for investors in short-term fixed-income securities. It helps in comparing the annualized returns of various discounted instruments, ensuring informed investment decisions.

Comparisons and Related Terms

• Coupon Yield: Unlike discount yield, coupon yield pertains to bonds paying periodic interest (coupons).
• Current Yield: The ratio of annual coupon interest to market price of the bond.
• Yield to Maturity (YTM): Considers all interest payments, capital gain or loss, and time value of money until maturity.

FAQs

Why use 360 days instead of 365 in the discount yield formula?

The 360-day convention simplifies interest calculation and is standard in banking and finance.

Is the discount yield the same as the effective annual yield?

No, the effective annual yield accounts for compounding within the year, while discount yield is a straightforward annualization.

When should I use discount yield?

Use discount yield for short-term, zero-coupon securities like Treasury bills to assess returns.

References

1. U.S. Department of the Treasury. “Treasury Bills and the Discount Yield.”
2. Fabozzi, F. J. (2007). Fixed Income Analysis (2nd ed.).

Summary

Discount yield is an essential tool for evaluating the annualized return on discounted securities. By understanding its calculation and context, investors can make better decisions in the fixed-income market. Recalling that it utilizes a simplified 360-day year convention, investors can benefit from its straightforward application to short-term investments.