1. The relationship between a bond\'s price and the yield to maturity is an inve

Question

1. The relationship between a bond's price and the yield to maturity is an inverse relationship. Please explain; make sure you don't simply restate the inverse relationship, but explain the reasoning. If you can remember and understand the "why", you will never forget this important relationship. Examples are encouraged.

.2   Why are stock valuation models dependent upon expected dividends, future dividend growth, and an appropriate discount rate? Please be sure to review how we value any financial asset which will help dissect this answer.

Explanation / Answer

1. The fact that bond prices and yields move in opposite directions is often confusing to new investors. Bond prices and yields are like a seesaw: when bond yields go up, prices go down, and when bond yields go down, prices go up. In other words, a move in the 10-year Treasury yield from 2.2% to 2.6% indicatesnegative market conditions, while a move from 2.6% to 2.2% indicates positive market performance.

The key to understanding the relaionship is to realize that from the time bonds are issued until the date that they mature, they trade in the open market – where prices and yields are always changing. As a result, yields converge to the point where investors are being paid approximately the same yield for the same level of risk. This prevents investors from being able to purchase a 10-year U.S. Treasury note with a yield to maurity of 8% when another one is yielding 3% - no more than a store could charge $5 for a gallon of milk when the store across the street is charging $3.

The best way to gain a sense of the relationship between prices and yields is to look at some examples.

Consider a corporate bond that comes to market in a given year with a coupon of 4% (let’s call it “Bond A”). Prevailing rates rise during the next 12 months, and one year later the same company issues a new bond (Bond B) – but this time with a yield of 4.5%. At this point, why would an investor purchase Bond A with a yield of 4% when he or she could buy Bond B with a yield of 4.5%? Nobody would do that, of course, so the price of Bond A needs to adjust downward in order to attract buyers. But how far does its price fall?

Here’s how the math works: Bond A is priced at $1000 with a coupon of 4%, and its initial yield to maturity is 4%. In other words, it pays $40 annually. Over the course of the following year, the yield on Bond A has moved to 4.5% to be competitive with prevailing rates (as reflected in the 4.5% yield on Bond B). Since the coupon always stays the same, the price must fall to $900 in order for the bond’s yield to remain the same as Bond B. Why? Because $40 divided by $900 equates to a 4.5% yield. The relationship isn’t this exact in real life, but this example helps provide an illustration of how the process works.

2.

Approximate future dividend payments and growth:

This is not always an easy task, because companies do not offer the same dividend payouts each year. Dividends are the shares of earnings that corporations choose to redistribute to their shareholders. Corporations vary these payments, but as a rule of thumb investors usually assume that corporations redistribute a given percentage of their earnings to their shareholders. Of course, this raises the additional challenge of forecasting future income, which is usually accomplished by forecasting growth or decline in sales and expenses over future years. Then they can calculate the amount of money that is expected to be paid out in the form of dividends and divide that by the number of shares outstanding to determine the amount of dividends each investor is paid for every share they own.

Determine a discount rate for future payments:

Determining the value of a share of stock isn’t as simple as adding up all future dividend payments. Payments made in the near future are considerably more valuable than those made in later years due to the time value of money. Imagine that an investor plans to invest for a five year horizon. The payments he receives after the first year can be reinvested for four years, whereas the payments he receives after five years cannot be reinvested. Therefore, the payments he receives in one year are a lot more valuable. Investors need a method of discounting the value of these dividends. This is accomplished by determining a required rate of return for investors, which is usually assumed to be the amount of money they could earn investing in the stock market as a whole (usually approximated with the estimated return of the S&P index) or a combination of investing in stocks and bonds yielding the current rate of interest.

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