Premium and Discount

What Is Premium and Discount?

In finance, a premium and discount describe the relationship between an asset's price and a predetermined reference value. When an asset's market price is higher than its reference value, it is trading at a premium. Conversely, when the market price is lower than its reference value, it is trading at a discount. This concept is fundamental to Valuation and applies across various financial instruments, including Bonds, Stocks, and certain types of funds. Understanding premium and discount helps investors assess whether an asset is relatively overvalued or undervalued compared to its intrinsic or stated worth.

History and Origin

The concept of premium and discount has been inherent in financial markets for centuries, particularly with the trading of debt instruments. Historically, the price of a debt security, such as a bond, would naturally fluctuate in the secondary market based on prevailing Interest rate environments and the creditworthiness of the issuer. When market interest rates rose above a bond's fixed coupon rate, the bond would trade at a discount to compensate new buyers for the lower yield. Conversely, if market rates fell, the bond would trade at a premium, as its higher coupon became more attractive. This inverse relationship between bond prices and interest rates is a foundational principle of fixed income markets. The Federal Reserve Bank of St. Louis has discussed this relationship, noting how changes in interest rates directly influence bond prices, leading to premiums or discounts from their face value.⁹

Key Takeaways

• A premium occurs when an asset's market price exceeds its reference value, while a discount occurs when it falls below it.
• The concept applies broadly across financial instruments, notably bonds and closed-end funds.
• For bonds, premiums and discounts are primarily driven by the relationship between the bond's coupon rate and prevailing market interest rates.
• For closed-end funds, premiums and discounts reflect supply and demand dynamics in the secondary market relative to the fund's underlying Net asset value.
• Investors consider premiums and discounts as indicators for potential investment opportunities or risks.

Formula and Calculation

The calculation of a premium or discount is straightforward:

For Bonds:
The price of a bond is the present value of its future cash flows (coupon payments and Par value). A bond trades at a premium if its price is greater than its par value, and at a discount if its price is less than its par value. This occurs when the bond's coupon rate differs from the prevailing market Yield to maturity.

The formula for a bond's price ( P ) is:
$P = \sum_{t=1}^{N} \frac{C}{(1+r)^t} + \frac{F}{(1+r)^N}$
Where:

• ( P ) = Current Market price of the bond
• ( C ) = Coupon payment per period
• ( r ) = Market interest rate or Yield to maturity per period
• ( F ) = Par value (or face value) of the bond
• ( N ) = Number of periods until maturity

If ( P > F ), the bond trades at a premium.
If ( P < F ), the bond trades at a discount.
If ( P = F ), the bond trades at par.

For Closed-End Funds (CEFs):
The premium or discount for a Closed-end funds is calculated relative to its Net asset value (NAV).

$\text{Premium/Discount (\%)} = \left( \frac{\text{Market Price per Share} - \text{NAV per Share}}{\text{NAV per Share}} \right) \times 100$

If the result is positive, it's a premium. If negative, it's a discount.

Interpreting Premium and Discount

Interpreting a premium or discount requires understanding the underlying asset and market conditions. For bonds, a premium suggests that the bond's coupon rate is more attractive than current market interest rates for similar-risk investments, while a discount indicates the opposite. Investors seeking higher current income might prefer premium bonds, while those looking for potential Capital gains might favor discount bonds, assuming interest rates rise or the bond approaches maturity.

For Closed-end funds, a premium or discount reflects the market's perception of the fund beyond its pure asset value. A premium might suggest high demand for the fund's investment strategy, a highly regarded manager, or limited supply of comparable investments. Conversely, a discount could signal low investor confidence, poor past performance, or high fees. Investors often monitor these figures as they can impact total returns.

Hypothetical Example

Consider a [Bonds] issued by Corporation X with a par value of $1,000, a 5% annual coupon, and 10 years until maturity.

• Scenario 1: Trading at Par
  If prevailing market interest rates for similar bonds are also 5%, the bond will likely trade at its Par value of $1,000.

• Scenario 2: Trading at a Premium
  Suppose prevailing market interest rates fall to 4%. A new bond with a 4% coupon would offer a $40 annual payment. Corporation X's bond, offering $50, is more attractive. To equalize the effective yield for new buyers, the Market price of Corporation X's bond will rise above $1,000 (e.g., to $1,081.11, at which point its Yield to maturity equals 4%). The bond is trading at a premium.

• Scenario 3: Trading at a Discount
  Now, imagine market interest rates rise to 6%. A new bond with a 6% coupon offers $60 annually. Corporation X's bond, still paying $50, is less attractive. Its price must fall below $1,000 (e.g., to $925.61, making its Yield to maturity 6%) to entice buyers. The bond is trading at a discount.

Practical Applications

Premium and discount valuations are critical in several areas of finance:

• Bond Markets: Investors and analysts constantly monitor bond premiums and discounts to understand the relationship between a bond's fixed Interest rate and current market yields. This informs decisions on whether to buy, sell, or hold bonds, considering factors like interest rate risk. U.S. Treasury bond auction results frequently illustrate prices at or away from par, reflecting prevailing market conditions.⁵, ⁶, ⁷, ⁸
• Closed-End Funds (CEFs): Unlike Exchange-traded funds (ETFs), which typically trade very close to their Net asset value (NAV) due to an arbitrage mechanism, CEFs can trade at significant premiums or discounts. The U.S. Securities and Exchange Commission (SEC) provides guidance on CEFs, noting their potential to trade at premiums or discounts to NAV.⁴ This discrepancy offers potential opportunities or risks for investors, as buying at a discount might seem appealing, though the discount itself may persist.³
• Option contracts and Futures contracts: In derivatives, premiums often refer to the price paid for an option, while futures contracts can trade at a premium (contango) or discount (backwardation) to the spot price of the underlying asset, reflecting market expectations and cost of carry.
• Corporate Finance: When a company issues new [Stocks] or bonds, they may be offered at a premium or discount to their Book value or par value, respectively, depending on market demand and the company's financial health.

Limitations and Criticisms

While premium and discount provide valuable insights into [Valuation], they come with limitations and criticisms. For example, a bond trading at a discount might seem like a bargain, but if interest rates continue to rise, the bond's price could fall further. Similarly, buying a Closed-end funds at a steep discount to its Net asset value does not guarantee that the discount will narrow. Many factors influence CEF discounts, including market sentiment, fund-specific characteristics, and management reputation.² It is possible for the discount to persist, or even widen, negating the perceived "value." Morningstar, for instance, emphasizes that merely buying a CEF at a discount in hopes of it converging to NAV is a simplistic view and does not guarantee positive returns.¹ The Intrinsic value of the underlying assets or the bond's future cash flows are more critical determinants of long-term investment outcomes than the immediate premium or discount.

Premium and Discount vs. Par Value

The terms premium and discount are often discussed in relation to Par value, especially in the context of bonds. Par value is the stated or face value of a bond, which is the amount the issuer promises to repay at maturity. It is also the basis upon which coupon payments are calculated. A bond is said to trade at a premium if its Market price is higher than its par value, and at a discount if its market price is lower than its par value. Unlike premium and discount, which describe the current trading price relative to a benchmark, par value is a fixed, nominal value set at the time of issuance. The distinction highlights that while par value is a static reference, premiums and discounts are dynamic reflections of market forces and investor sentiment.

FAQs

What does it mean if a bond is trading at a discount?

If a bond is trading at a discount, its current Market price is less than its Par value. This usually happens when the bond's coupon rate (the interest it pays) is lower than the prevailing market Interest rate for similar bonds, making it less attractive to new investors unless they can buy it at a lower price.

Why do closed-end funds often trade at a discount or premium to their NAV?

Closed-end funds (CEFs) have a fixed number of shares that trade on an exchange, much like [Stocks]. Their price is determined by supply and demand in the secondary market, not directly by the value of their underlying assets. Therefore, if demand is high, the market price can exceed the fund's Net asset value (NAV), leading to a premium. If demand is low, the price can fall below NAV, resulting in a discount.

Can a stock trade at a premium or discount?

Yes, the concept applies to stocks, though the terminology might differ slightly. A stock is often said to trade at a premium or discount to its Book value, its perceived Intrinsic value, or industry averages for metrics like price-to-earnings (P/E) ratios. For example, a growth stock might trade at a premium P/E due to high expected future earnings, while a value stock might trade at a discount P/E if its future prospects are uncertain.

Is buying an asset at a discount always a good investment?

Not necessarily. While buying at a discount might seem like a bargain, it doesn't guarantee a good investment. For example, a bond trading at a deep discount might be issued by a company facing financial difficulties, increasing the risk of default. Similarly, a Closed-end funds trading at a discount might continue to do so, or its underlying assets could decline in value. Thorough analysis of the reasons for the discount and the asset's fundamentals is crucial.