Pictured below is a hypothetical 10-year, bond with a 1.5% semi-annual coupon complete with cashflows by period. For this bond there are 21 different payments shaded in blue: 20 interest payments and the final repayment of principal in the last period. ![[Pasted image 20231023095553.png]] Any financial contract or securities usually involves a series of payments over a period of time. The [[Time Value of Money]] allows us to discount these future cashflows to determine what they are worth today. In the example above, the $72.75 price for this series of cashflows will earn you a "yield-to-maturity" of 5.00%. ## Yield-To-Maturity vs. CAGR When people generally refer to interest rates they are referring to yield-to-maturity. This is different than other rates of return as it assumes that the interest payments are reinvested at the same yield-to-maturity. This often is not feasible so when you buy a bond most of the time you will not actually realize the yield-to-maturity. If we add up all the cashflows from this bond it totals $115.00. Therefore, when we pay $72.75 for the bond we will earn a profit of $42.3 over the ten-years until maturity. This represents a Compound Annual Growth Rate (CAGR) of 4.69% which is 31bps lower than the yield to maturity because it does not include any reinvestment income. ## Reinvestment Income When we buy the bond we have to wait ten years to get our money back, but we will also get interest payments every six-months. This interim cashflow is very important as it lowers our overall [[Risk|risk]] and it allows us to reinvest that cashflow. How we invest that cashflow has an influence on the return we actually realize for the bond. In the example above, we assume we can reinvest the interest payments at the current cash rate of 5.3% over the life of the bond. In this case we actually realize a yield-to-maturity of 5.47% and a CAGR of 5.08%. This is because we earned an additional $4.45 in interest income over the ten years, a 10.5% increase in total profit. ## Price and Convexity Bonds are usually quoted in yield and that yield is used to compute a price for the bond. If the contractual cashflows are simple, as in our example above, the price for a given yield is easy to compute. Bonds can be thought of as having two "prices", the actual dollar price of the contract, and the assumed investment return on that contract. The important thing to understand is that prices and yields move in opposite directions. In other words, as yields rise, price falls. However, this relationship is not linear and this non-linearity is something we call convexity. You can see an example of a positively convex bond below. ![[Pasted image 20231020105924.png]] ## Terminal Value For principal and interest (P&I) bonds the terminal value is typically the largest determinant of the price of the bond since it is the largest single cashflow in the stream of future cashflows. In general, the riskier the terminal value the higher the yield for that bond. This has the effect of lowering the value that you pay for that uncertain future outcome today. Another consideration in figuring the present value of a bond is the shape of the cashflow profile. If more cashflows occur in the near future there is less risk and uncertainty and those cashflows should carry a lower discount rate or yield. **Case Studies:** - [CHG Issue #127: The Importance of Bonds]() Explore Further: Tags: Your support for Cedars Hill Group is greatly appreciated <form action="https://www.paypal.com/donate" method="post" target="_top"> <input type="hidden" name="hosted_button_id" value="74PGN8ZXHQVHS" /> <input type="image" src="https://www.paypalobjects.com/en_US/i/btn/btn_donate_LG.gif" border="0" name="submit" title="PayPal - The safer, easier way to pay online!" alt="Donate with PayPal button" /> <img alt="" border="0" src="https://www.paypal.com/en_US/i/scr/pixel.gif" width="1" height="1" /> </form>