1. Introduction

In recent years, bond markets have become increasingly important for both investors and policymakers. Bonds are not only the key instrument in fixed income portfolio but also serve as the indicator of the country’s economy. Bonds price has shown a greater volatility which largely driven by the shift in interest rates, the expectation of inflations and the uncertainty of the global economy [1-3].

Another key element in the fixed income market is the yield curves, which indicate the relationships between the interest rates and different maturities. The shape of the yield curve closely correlates with the market sentiment, monetary policy and the outlook of the economy. Moreover, yield curve dynamics are tied with bond price, since the discount rate is affected in valuation [3,4].

Understanding the correlation between the bond price and yield curve is essential for anticipate the macroeconomic development, assessing the rate of interest rate and making proper investment decisions. These two components are highly connected with each other since the change of bond price could influence the yield curve, vise versa.

This research explores the relationship between Treasury bond price volatility and yield curve movements. This research contributes to enhancing investors' portfolio management in highly uncertain interest rate environments and providing policymakers with insights into how monetary policy and market expectations affect bond prices and the broader economy.

2. Theoretical foundations

The price of the bond is determined by the present value of future cash flows. These cash flows can include periodic coupon payments and the payback of the bond face value at the maturity. The bond is valued by discounting all the future payments into the present times through the use of appropriate interest rate [1].

For zero-coupon bonds, the present value can be represented as:

$$ \mathrm{P}\mathrm{V}=\frac{\mathrm{F}\mathrm{V}}{{(1+\mathrm{r})}^{\mathrm{n}}}$$(1)

Where PV is the present value of the bond price, FV is the face value, r is the interest rate, and n is the time to maturity.

For coupon bonds, the present value is calculated by discounting all future coupon payments and the final value. Bonds price usually fluctuate reversely with the change of the interest rate. The increase in interest rate indicates the present value of the future coupon payments fall, which lead to the decline in bond price.

Duration and convexity are two key concepts when pricing the bond. Duration measures the sensitivity of the bond toward the variation in interest rate. On the other hand, convexity represents the nonlinear relationship between yield and price. These concepts are crucial for understanding how the change of interest rate can affect the bond price [5].

The yield curve, which shows the relationship between bond yields and time to maturity, is crucial for fundamental income analysis as it reflects market expectations of future interest rates, inflation, and economic growth. Typically, an upward-sloping yield curve indicates expected economic growth and higher future rates, generally favored by investors [4,6].

The flat shape of the yield curve implies the uncertainty or the economic is in the transition.

Inverted yield curve is interpreted as a signal of recession or lower interest rates in future [7].

Since bond prices are calculated using discount rates, changes in the yield curve directly affect how those rates are applied. A steeper yield curve implies the rates are rising, which is likely to reduce the value of the bonds that lasts for a long time. Conversely, a flatter curve tends to increase the relative value of long-term bonds due to lower discounting rate.

3. Key determinant of bond price volatility

3.1. Change of interest rate

One of the most essential drivers that can affect the bond price is the change of the interest rate. The price of the bond is determined by the present value of future cash flows. A increase in the interest rate within the market indicates the discount rate will be increased correspondingly. Therefore, it reduces the present value of those cash flows and lower the bond price. Conversely, the decrease in interest rate can lead to the increase in bond price.

The inverse relationship between interest rate and bond is crucial for investors when considering the long-term investment. It is more sensitive toward the change in interest rate since the duration of the investment across a long time frame. Duration measures the percentage change in a bond’s price for the change in interest rates. Long maturity time with lower coupon payments usually refers to greater price sensitivity. Moreover, Convexity can adjust previous estimation by accounting for the curvature of the price-yield relationship, especially within large rate shifts [1].

Practically, the decision made by the central bank or the government can arise a significant change in the bond price.

3.2. Inflation expectations

Inflation is common phenomenon in the money market, leading to a decrease in purchasing power for the public. As a result, when inflation expectations rise, investors typically demand higher yields to compensate for the loss in purchasing power. Inflation expectations are a key component of nominal yield curves. If investors anticipate higher inflation in the future, the yield curve tends to steepen. Conversely, if inflation expectations decrease, the yield curve flattens, indicating higher bond prices. This is often triggered by economic recession or counter-cyclical monetary policy [8].

There are lots of indicators of the inflation such as the consumer price index. It evaluates the public happiness of lives. Thus, the inflation plays an important role in both affecting bond prices and shaping the yield curve.

3.3. Investor sentiment and market risk perception

The behavior of the investors in the market could possibly affect the bond price volatility. If the investors are having lots of stress that brought by the society, such as the war, or some geological events. They are likely to reduce the investment or invest the capital into relatively safer assets. In this case, the government bonds, US Treasury assets, is regarded as the investment with lower risks, which is more favorable by those investors. The rise of demand can lead to increase in bond price and lower yields.

Market behavior during the global events such as the 2008 global financial crisis or the pandemic explained explicitly how sentiments can affect the change in price. In these cases, bond prices may move not because of interest rate changes, but due to the risk. This indicate volatility that is in nature, and often difficult to predict simply through some models.

4. The connection between bond prices and yield curves movement

The interaction between bond price volatility and the change of the yield curve is due to the variation of the interest rate. This part investigates the cause-and-effect relationship that connecting with the shift of the yield curve correspond to the change in bond price.

The yield curve illustrates the term structure of interest rates and serves as a tool for calculating bond prices by discounting future cash flows to their present value. Various factors can influence the shape of the yield curve, including investor sentiment and inflation expectations. These factors can alter discount rates across different maturities, thereby affecting bond prices. The present value is calculated by discounting the future payments back. Thus, the bond price will be changed as well. A steeper yield curve implies the increases in long term interest rate compared with the short-term rates. In this case, bonds with a long duration time can experience a significant reduction of the value since the future cash flows are discounting back in a lower value. Conversely, a flattening or inverted curve may result in a relative increase in the prices of long-term bonds. Investors anticipate slower growth or future rate cuts and move capital toward longer maturities [9].

The variation of bond prices in response to yield curve shifts largely depends on the durations and the maturity time of the bond. Bonds with longer maturity time are usually more sensitive to shifts in interest rates. A parallel upward shift in the curve may cause the decline in bond price since both the short term and long-term interest rate are increasing. In contrasts, when the yield curve becomes steeper, the yield may increase, leading to a sharper reduction in long-term bond prices compared with short-term bonds.

The relationships can also involve the expectations. Expectations of the public is one of the important factors that discussed previously. When investors expect the central bank to raise interest rates, they may begin selling bonds, particularly the bond with long maturity time. the anticipation can affect the yield which cause it to increase and also the price can be dropped. This instances can happen even before the change of the policy. Similarly, if investors expect the economy will suffer recession, then they could invest in long term government bond, pushing the price to increase and the reduction of long-term yields, which can flatten or inverted the yield curve.

The pandemic is an example that how investors react to the crisis that suffered by the society. In order to response toward the crisis, the US Federal Reserves decrease the interest rate, which lead to the collapse of the yield curve in short end. At the same time, there are strong demand for the long-term treasury bond that led to lower yield. Overall, the flattened and inverted curve is formed correspond with the increase in price of long-term treasury bond.

5. Implications for policy makers

For central banks and some other monetary authorities, the shape and movement of the yield curve offer valuable insights into how markets perceive the current and future stance of monetary policy. An upward-sloping yield curve suggests that investors expect interest rates to increase. However, a flat or inverted yield curve is often interpreted as a signal of recession or policy misalignment [3,7,10].

Through the observation of how bond prices could response to the policy that made by the government, it is obvious for policymakers to determine whether the policy is effective or not. If the yield of the bond does not adjust to the expectation, then it can reflect the issues of the credibility of the policy. Therefore, communicating transparently is one of the effective ways to help stabilize the market and reduce the volatility of the bond price. In addition, the yield curve is not only the tools for prediction but also can be used as the indicator of potential risks. It is essential for policymakers to consider their intervention within the market if the yield curve starts to become extremely flattened or steepened.

Moreover, it is crucial for investors to understand how the yield curve may indicate the variance of the bond price so that they can avoid making some high-risk investment. When investors predict a steepening yield curve, which is caused by the increase in long term rates, investors choose to reduce the holding of bonds that has a long maturity time in order to prevent the loss. In contrast, when yield curves are flattened, it could be better for investors to invest in the long-term bonds. Thus, it is helpful for investors to purchase both short term or long-term bonds and split the time to maturity for each of the bond to prevent the loss from unexpected events.

6. Conclusion

This article examines the correlation between bond price volatility and yield curve movements. The findings show that changes in the shape of yield curves directly impact the discount rates used to calculate bond cash flows. The effects of these shifts vary across different maturities, depending on the bond’s duration and sensitivity to long- or short-term interest rates. The relationship between bonds and yield curves is not purely mechanical; other factors such as investor sentiment and market expectations also play important roles. Yield curve movements can influence bond values, and bond market reactions can, in turn, affect future yield curve movements.

However, this review is not precise enough since there is lack of specifical calculation process to prove the relationship. It is mostly retaining the conclusion based on the fact that already exist. The argument is not convincible. With the detailed calculation, it could make the abstract concept to be more visible and understandable. There are some improvements that can be made in further research. Quantitative analysis is necessary for the deeper investigation of the bond since it can better demonstrate with the previous relationships. Also, there are various categories of bond that can be discussed further, such as corporate bond, which is different with bond that issued by the US government.