*The Business Professor*, updated January 24, 2020, last accessed October 27, 2020, https://thebusinessprofessor.com/lesson/bond-discount-definition/.

### Bond Discount Definition

Bond discount refers to the amount by which a bond market’s price is lesser than the principal amount ready at maturity. This amount, known as a par value or face value, is usually $1,000.

### Bond Discount Break Down

A bondâs primary characteristics are its face value, market price, and coupon rate. An issuer pays coupons to the bondholders as a reward for the amount loaned within a particular period. The amount of principal loan is paid back to the investor at maturity. This amount equals the bondâs face value. $1,000 is the par of the majority of corporate bonds. Certain bonds are sold at a discount, at par, or even at a premium.

A bond thatâs sold at face has a coupon rate equivalent to the economy’s predominant interest rate. An investor that buys this bond would have an investment return that’s ascertained by the cyclic coupon payments. A bond whose market price is greater than its face value is known as a premium bond. Supposing the stated interest of the bond is more than those anticipated by the present bond market, then the bond would be attractive to investors.

The market price of a bond given at a discounted price is usually below the par value, thus appreciating capital upon maturity because the greater par value is paid once the bond is due. The existing difference showing that the market price of a bond is lesser than its par value is the bond discount. For instance, a bond having a $1,000 par value that’s trading at exactly $980 has a $20 bond discount. Furthermore, it is used to refer to the rate of the bond discount, an interest used in pricing bonds through current valuation calculations.

Once the interest rate of the market surpasses the bond’s coupon rate, bonds are then sold at a discount. For understanding, recall that bonds sold at face have coupon rates equivalent to the interest rate of the market. Once interest rate rises above coupon rate, the bondholders would then hold a bond with lesser interest payments. The existing bonds then experience value dip to show that new issues in the markets have rates that are more attractive. Supposing the value of the bond drops below face value, investors have a higher tendency to buy it since, at maturity, they would be paid back the face value. The current coupon payment value, as well as, the principal value needs to be ascertained in order to calculate the bond discount.

For instance, imagine a bond having a $1,000 par value expected to mature within 3 years. Its coupon rate is 3.5% while the market’s interest rate is a bit higher at 5%. Because interests are paid on a biannual basis, then the number of coupon payments would be 3 yrs x 2= 6, while interest rate for each period would be 5% Ăˇ 2 = 2.5%. Based on the information, the principal repayment’s present value at maturity would be:

PVprincipal = $1,000 Ăˇ (1.0256) = $862.30

Next, the current coupon payment value has to be calculated. 3.5% Ăˇ 2 = 1.75% would be the coupon rate per period. Then each interest payment per period would be 1.75% x $1,000 = $17.50.

Then PVcoupon = (17.50 Ăˇ 1.025) + (17.50 Ăˇ 1.0252) + (17.50 Ăˇ 1.0253) + (17.50 Ăˇ 1.0254) + (17.50 Ăˇ 1.0255) + (17.50/1.0256)

Thus, PVcoupon = 17.07 + 16.66 + 16.25 + 15.85 + 15.47 + 15.09 = $96.39.

The bond’s market price is the summation of the current coupon payment value and the principal.

Market Price = $862.30 + $96.39 = $958.69.

Because the market price is lower than the face value, then the bond currently trades at a ($41.31) discount i.e. $1,000 – $958.69 = $41.31. Thus, 41.31 Ăˇ $1,000 = 4.13% is the bond discount rate.

There are various reasons bonds trade at a discount to face value. Bonds that are on the secondary market having fixed coupons would trade at discounted rates once interest rates of the market begin rising. While the investor gets that exact coupon, the bond is discounted so as to correspond with predominant market yields. Furthermore, discounts also happen when supply of bond surpasses demand, when credit rating of the bond is reduced, or when there is an increase in the perceived default risk. On the other hand, a better credit rating or a falling interest rate might result in a bond trading at a premium. Often, bonds which are short-term are given at a discount, mainly in a situation where the bond is a zero-coupon bond. However, bonds that are on the secondary market might be trading at a bond discount. This happens when supply surpasses demand.

**Reference for âBond Discountâ**

https://www.investopedia.com/terms/d/discountbond.asp

https://www.investopedia.com/terms/d/discountbond.asp

https://www.investopedia.com/terms/b/bond-discount.asp

https://www.wikihow.com/Calculate-Bond-Discount-Rate

https://corporatefinanceinstitute.com/resources/knowledge/trading-investing/discount-bond/

**Academic research on âBond Discountâ**

**An exactÂ bondÂ option formula**, Jamshidian, F. (1989). An exact bond option formula. *The journal of Finance*,Â *44*(1), 205-209. This paper derives a closedâform solution for European options on pure discount bonds, assuming a meanâreverting Gaussian interest rate model as in Vasicek [8]. The formula is extended to European options on discount bond portfolios.

**Stock-bond correlations, **Ilmanen, A. (2003). Stock-bond correlations.Â *The Journal of Fixed Income*,Â *13*(2), 55. Stock-bond correlation has recently turned from positive to negative. Exhibit 1 plots the annual return series for equities and bonds. Three periods of decoupling stand out-near 1930, near 1960, and near 2000. Exhibit 2 shows the history of 12-month trailing stock-bond correlations since 1926. Clearly, the relation between the two main asset classes has not been particularly stable. The correlation has tended to be positive but has occasionally dipped below zero for extended periods. The three episodes of negative correlations-1929-1932, 1956-1965, and 1998-2001-coincide with the decoupling of stock and bond performance in Exhibit 1.1 Should we expect stock-bond correlation to be mildly positive, as in the last 40 years, or mildly negative as it has been for the last four years? The answer is important for long-term asset allocation decisions since correlations across asset classes are one key input in portfolio optimization and asset-liability management exercises as well as for hybrid derivatives valuation. Moreover, negative correlation makes government bonds excellent hedges against major systematic risks-recession, deflation, equity weakness, and other financial market crises-and this attractive feature may justify an exceptionally low bond risk premium, that is, higher government bond valuations.

**Evaluating governmentÂ bondÂ fund performance with stochasticÂ discountÂ factors** **Ferson, W., Henry, T. R., & Kisgen, D. J. (2006). Evaluating government bond fund performance with stochastic discount factors.Â ***The Review of Financial Studies***,Â ***19***(2), 423-455. **This article shows how to evaluate the performance of managed portfolios using stochastic discount factors (SDFs) from continuous-time term structure models. These models imply empirical factors that include time averages of the underlying state variables. The approach addresses a performance measurement bias, described byÂ Goetzmann, Ingersoll, and Ivkovic (2000) andÂ Ferson and Khang (2002), arising because fund managers may trade within the return measurement interval or hold positions in replicable options. The empirical factors contribute explanatory power in factor model regressions and reduce model pricing errors. We illustrate the approach on US government bond funds during 1986â2000.

**Does the liquidity of a debt issue increase with its size? Evidence from the corporateÂ bondÂ and medium****â****term note markets**, Crabbe, L. E., & Turner, C. M. (1995). Does the liquidity of a debt issue increase with its size? Evidence from the corporate bond and mediumâterm note markets.Â *The Journal of Finance*,Â *50*(5), 1719-1734. To investigate the liquidity of large issues, this study tests for yield differences between corporate bonds and mediumâterm notes (MTNs). In the sample, MTNs have an average issue size of $4 million, compared with $265 million for bonds. Among MTNs that have the same issuance date, the same maturity date, and the same corporate issuer, we find no relation between size and yields. Moreover, bonds and MTNs have statistically equivalent yields. Thus, rather than suggesting that large issues have greater liquidity, these findings indicate that large and small securities issued by the same borrower are close substitutes.

**EvaluatingÂ fixed incomeÂ fund performance with stochasticÂ discountÂ factors**, Ferson, W. E., Kisgen, D. J., & Henry, T. R. (2003, April). Evaluating fixed income fund performance with stochastic discount factors. InÂ *EFA 2003 Annual Conference paper*Â (No. 486). We evaluate the performance of fixed income mutual funds using stochastic discount factors from continuous-time term structure models. Time-aggregation of the models for discrete returns generates additional empirical “factors,” and these factors contribute significant explanatory power to empirical the models. We provide the first conditional performance evaluation for US fixed income mutual funds, conditioning on a variety of discrete ex ante characterizations of the state of the term structure and the economy. During 1985-1999 fixed income funds returned less on average than passive benchmarks that don’t pay expenses, but not in all economic states. Fixed income funds typically do poorly when short term interest rates or industrial capacity utilization rates are high, and offer higher returns when quality-related credit spreads are high. We find more heterogeneity across fund styles than across characteristics-based fund groups. Mortgage funds under perform a GNMA index in all economic states. These excess returns are reduced, and typically become insignificant, when we adjust for risk using the stochastic discount factors.