*The Business Professor*, updated December 4, 2019, last accessed August 7, 2020, https://thebusinessprofessor.com/lesson/bond-yield-definition/.

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**Bond Yield**** Definition**

When invested in, a security, bond, stock or asset yields a return, for bonds, yield the return tat an investor earns on bonds. Every investor desires a yield when they invest in a bond, in fact, yield serves as the willpower why most people make investments. There are various ways to classify or calculate a bond yield, these are;

- Yield to maturity
- Effective annual yield
- Bond equivalent yield.

The current yield of a bond can be realized by assessing the price of the bond and its interest payment otherwise called coupon rate.

### A Little More on What is Bond Yield

Investors purchase bonds with the expectation that they would receive interest on the bonds, otherwise known as the bond yield or returns. Bond issuers are liable to pay interest on bonds purchased by investors during the period in which the investor holds it. Aside from interest payments, upon maturity, investors are also paid the face value (par value), which is the price they purchased the bond.

**Equation for calculating coupon rate**

The coupon rate is the simplest way an investor can calculate the yield of a bond. Using this method, the yield is calculated as the coupon payment divided by the par value of the bond. However, before the coupon payment can be known, the coupon rate plays a significant role. The coupon rate is realized by dividing the face value of a bond by the interest paid on the bond for a year, this is otherwise called the coupon payments. For instance;

If the par (face) value of a bond is $2000 and the interest paid is $200, this means the coupon rate is 10%.

**Bond Yield Versus Price**

There is an interaction between the yield of a bond and the price, usually, an increase in the bond price translates to a decrease in bond yield, vice versa. The price of a bond is not static, so also is the interest rate, when there is a significant change in either interest rate and price, the yield of a bond is affected.

Also, when calculating the current yield of a bond, the bond price is also a vital metric. The coupon payment (otherwise known as interest) and the price of a bond are the two determinants of the current yield, which can, in turn, give an insight into the true yield of a bond.

**The equation for calculating current yield**

The current yield is one of the common methods for calculating the yield of a bond, this method uses the current price of a bond and the annual interest payments on a bond as determinants. The formula for calculating the current yield of a bond is;

Current Yield = Interest (coupon payments) / current price of a bond.

Despite that the current yield is the simplest way of calculating a bond’s yield, it is regarded as inaccurate given the fact that the method does not take factors such as time value and maturity value into account.

### Yield to Maturity

A bond’s yield to maturity (YTM) is often given as annual percentage rate (APR), this yield is the return an investor is expected to receive on a bond if held until maturity and all coupon and principal payments on the bond made. Yield to maturity is often applicable to long-term bonds or a fixed-security, it is otherwise called bok yield or redemption yield.

To calculate the yield to maturity (YTM) of a bond, the formula below will be used;

### Bond Equivalent Yield (BEY)

Bond equivalent yield (BEY) is a method that allows an investment or fixed-security whose payments are not annually to be calculated as an annual percentage yield. BEY takes into account bonds that pay their annual coupon semi-annually, quarterly or monthly. BEY is also used for calculating the annual yield of a bond sold at discount. Due to the different purposes that BEY serves, there are different methods used for calculating it. For instance, if the BEY of a bond that pays coupon semi-annually were to be calculated, the formula below will be used;

The YTM of the bond will be multiplied by two.

### Effective Annual Yield (EAY)

The effective annual yield (EAY) is a method for calculating the yield of the bond in the most precise way. The time value and maturity value of a bond are taken into account under the effective annual yield method. Through EAY, an investor can know the expected return on a bond over its holding period. EAY also accounts for additional interest earned on a bond, through the method of compounding the holding period return, EAY measures the accurate annual yield on a bond.

### Complications Finding a Bond’s Yield

Certain complications can arise from calculating the yield of a bond due to many factors. The major complications can arise due to;

- The need to calculate the accumulated interest of a bond, especially when held for a long period.
- Inflation in the price of a bond when there is a new buyer that affects the interest rate or coupon payments on the bond.
- Complications that results from ‘clean price’ ad ‘dirty price’.

### Bond Yield Summary

In a nutshell, a bond’s yield refers to the total return an investor expects to receive for holding a bond for a specified period of time, or until maturity. The coupon payments on a bond, otherwise called interest rates and other cahs flows realized from the bond amount to the yield. There are many methods used in calculating a bond’s yield, the simplest method is the current yield while the most accurate or precise method is the effective annual yield (EAY). Other methods to calculate a bond’s yield are yield to maturity (YTM), and bond equivalent yield (BEY).

**Reference for “Bond Yield”**

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

https://www.investopedia.com/university/bonds/bonds3.asp

https://www.investopedia.com/video/play/understanding-bond-prices-and-yields/

https://www.sbp.org.pk/ecodata/Auction-Investment.pdf

**Academic research on “Bond Yield”**

**Do bonds span the fixed income markets? Theory and evidence for unspanned stochastic volatility, **Collin‐Dufresne, P., & Goldstein, R. S. (2002). Do bonds span the fixed income markets? Theory and evidence for unspanned stochastic volatility. *The Journal of Finance*, *57*(4), 1685-1730. Most term structure models assume bond markets are complete, that is, that all fixed income derivatives can be perfectly replicated using solely bonds. How ever, we find that, in practice, swap rates have limited explanatory power for returns on at‐the‐money straddles—portfolios mainly exposed to volatility risk. We term this empirical feature unspanned stochastic volatility (USV). While USV can be captured within an HJM framework, we demonstrate that bivariate models cannot exhibit USV. We determine necessary and sufficient conditions for trivariate Markov affine systems to exhibit USV. For such USV models, bonds alone may not be sufficient to identify all parameters. Rather, derivatives are needed.

**Risk in fixed-income hedge fund styles** **Fung, W., & Hsieh, D. A. (2002). Risk in fixed-income hedge fund styles. ***Journal of Fixed Income***, ***12***(2), 6-27. **This paper studies the risk in fixed-income hedge fund styles. Principal component analysis is applied to groups of fixed-income hedge funds to extract common sources of risk and return. These common sources of risk are related to market risk factors, such as changes in interest rate spreads and options on interest rate spreads. We call these asset based style factors (“ABS”). The paper finds that fixed-income hedge funds tend to be exposed to a common ABS factor: credit spreads.

**The relation between treasury yields and corporate bond yield spreads, **Duffee, G. R. (1998). The relation between treasury yields and corporate bond yield spreads. *The Journal of Finance*, *53*(6), 2225-2241. Because the option to call a corporate bond should rise in value when bond yields fall, the relation between noncallable Treasury yields and spreads of corporate bond yields over Treasury yields should depend on the callability of the corporate bond. I confirm this hypothesis for investment‐grade corporate bonds. Although yield spreads on both callable and noncallable corporate bonds fall when Treasury yields rise, this relation is much stronger for callable bonds. This result has important implications for interpreting the behavior of yields on commonly used corporate bond indexes, which are composed primarily of callable bonds.

**Equity volatility and corporate bond yields, **Campbell, J. Y., & Taksler, G. B. (2003). Equity volatility and corporate bond yields. *The Journal of Finance*, *58*(6), 2321-2350. This paper explores the effect of equity volatility on corporate bond yields. Panel data for the late 1990s show that idiosyncratic firm‐level volatility can explain as much cross‐sectional variation in yields as can credit ratings. This finding, together with the upward trend in idiosyncratic equity volatility documented by Campbell, Lettau, Malkiel, and Xu (2001), helps to explain recent increases in corporate bond yields.

**Forecasting the term structure of government bond yields, **Diebold, F. X., & Li, C. (2006). Forecasting the term structure of government bond yields. *Journal of econometrics*, *130*(2), 337-364. Despite powerful advances in yield curve modeling in the last 20 years, comparatively little attention has been paid to the key practical problem of forecasting the yield curve. In this paper we do so. We use neither the no-arbitrage approach nor the equilibrium approach. Instead, we use variations on the Nelson–Siegel exponential components framework to model the entire yield curve, period-by-period, as a three-dimensional parameter evolving dynamically. We show that the three time-varying parameters may be interpreted as factors corresponding to level, slope and curvature, and that they may be estimated with high efficiency. We propose and estimate autoregressive models for the factors, and we show that our models are consistent with a variety of stylized facts regarding the yield curve. We use our models to produce term-structure forecasts at both short and long horizons, with encouraging results. In particular, our forecasts appear much more accurate at long horizons than various standard benchmark forecasts.