Question

Explain the inverse relationship between bond prices and yield. Define yield to maturity. Discuss term to maturity and interest rate differentials. Explain the yield curve. Discuss expectations theory. Discuss credit risk. Define real interest rate.

Answer 1

Inverse Relation between bond prices and yield:

As bond prices increase, bond yields fall. For example, assume an investor purchases a bond with a 10% annual coupon rate and a par value of $1,000. Each year, the bond pays 10%, or $100, in interest. Its annual yield is the interest divided by its par value. As $100 divided by $1,000 is 10%, the bond's nominal yield is 10%, the same as its coupon rate.

Eventually, the investor decides to sell the bond for $900. The new owner of the bond receives interest based on the face value of the bond, so he continues to receive $100 per year until the bond matures. However, because he only paid $900 for the bond, his rate of return is $100/$900 or 11.1%. If he sells the bond for a lower price, its yield increases again. If he sells for a higher price, its yield falls.

Yield to maturity:

Yield to maturity (YTM) is the total return anticipated on a bond if the bond is held until it matures. Yield to maturity is considered a long-term bond yield, but is expressed as an annual rate. In other words, it is the internal rate of return (IRR) of an investment in a bond if the investor holds the bond until maturity and if all payments are made as scheduled.

Yield to maturity is also referred to as book yield or redemption yield.

Term to Maturity

Term to maturity refers to the remaining life of a debt instrument. With bonds, term to maturity is the time between when the bond is issued and when it matures, known as its maturity date, at which time the issuer must redeem the bond by paying the principal or face value. Between the issue date and maturity date, the bond issuer will make couponpayments to the bond holder.

Bonds can be grouped into three broad categories depending on their terms to maturity: short term bonds of 1 to 5 years, intermediate term bonds of 5 to 12 years, and long term bonds of 12 to 30 years. The longer the term to maturity, the higher the interest rate tends to be, and the less volatile a bond’s market price tends to be. Also, the further a bond is from its maturity date, the larger the difference between its purchase price and its redemption value, which is also referred to as its principal, par or face value.

If an investor expects interest rates to increase, she will most likely purchase a bond with a shorter term to maturity. She will do this to avoid being locked into a bond that ends up paying a below-market interest rate, or having to sell that bond at a loss in order to get capital to reinvest in a new, higher-interest bond. The bond’s coupon and term to maturity are used in determining the bond’s market price and its yield to maturity.

For many bonds, the term to maturity is fixed. However, a bond’s term to maturity can be changed if the bond has a call provision, a put provision or a conversion provision.

Interest Rate Differential

The interest rate differential (IRD) measures the gap in interest rates between two similar interest-bearing assets. Traders in the foreign exchange market use interest rate differentials (IRD) when pricing forward exchange rates. Based on the interest rate parity, a trader can create an expectation of the future exchange rate between two currencies and set the premium, or discount, on the current market exchange rate futures contracts.
The interest rate differential is also used in the housing market to describe the difference between the interest rate and a bank's posted rate on the prepayment date for mortgages. The IRD is a key component of the carry trade. A carry trade is a strategy that foreign exchange traders use in an attempt to profit from the difference between interest rates, and if traders are long a currency pair, they may be able profit from a rise in currency pair.

Interest Rate Differential Mortgage Example

When homebuyers borrow money to purchase houses, there may be an interest rate differential. For example, say a homebuyer purchased a home and took out a mortgage at a rate of 5.50% for 30 years. Assume 25 years have passed and the borrower only has five years left in his mortgage term. The lender could use the current market interest rate it is offering for a five-year mortgage to determine the interest rate differential. If the current market interest rate on a five-year mortgage is 3.85%, the interest rate differential is 1.65%, or 0.1375% per month.

Yield Curve

A yield curve is a line that plots the interest rates, at a set point in time, of bonds having equal credit quality but differing maturity dates. The most frequently reported yield curve compares the three-month, two-year, five-year and 30-year U.S. Treasury debt. This yield curve is used as a benchmark for other debt in the market, such as mortgage rates or bank lending rates, and it is also used to predict changes in economic output and growth.

Expectation Theory

The Expectations Theory – also known as the Unbiased Expectations Theory – states that long-term interest rates hold a forecast for short-term interest rates in the future. The theory postulates that an investor earns the same amount of interest by investing in a one-year bond in the present and rolling the investment into a different one-year bond after one year as compared to purchasing a two-year bond in the present.
In some instances, the expectations theory is utilized as an explanation for the yield curve. However, the theory has been shown to be inaccurate in execution, because interest rates typically stay flat when the yield curve is normal. Essentially, the expectations theory is known to over-estimate future short-term interest rates.

Example

Consider that the present bond market provides investors with a two-year bond that has an interest rate of 20% and a one-year bond with an interest rate of 18%. The expectations theory can be utilized to forecast the interest rate for the one-year bond in one year. The first step of the calculation is to add one to the two-year bond’s interest rate. In this example, the result is 1.2, or 120%.

The next step is to square the result; 1.2 squared results in 1.44. This number is then divided by the current one-year interest rate plus one. This means that 1.44 is divided by 1.18 to equal 1.22. Subtracting one from that sum is the final step and results in a predicted one-year bond interest rate of 22% for the following year.

In this example, the investor, theoretically, is earning an equivalent return to the present interest rate of a two-year bond. If the investor chooses to invest in a one-year bond at 18%, he has to hope for the bond yield to increase to 22% for the following year’s one-year bond.

Credit Risk

Credit risk refers to the risk that a borrower may not repay a loan and that the lender may lose the principal of the loan or the interest associated with it. Credit risk arises because borrowers expect to use future cash flows to pay current debts; it's almost never possible to ensure that borrowers will definitely have the funds to repay their debts. Interest payments from the borrower or issuer of a debt obligation are a lender's or investor's reward for assuming credit risk.

Credit risks are calculated based on the borrowers' overall ability to repay. To assess credit risk on a consumer loan, lenders look at the five C's: an applicant's credit history, his capacity to repay, his capital, the loan's conditions and associated collateral.

Similarly, if an investor is thinking about buying a bond, he looks at the credit rating of the bond. If it has a low rating, the company or government issuing it has a high risk of default. Conversely, if it has a high rating, it is considered to be a safe investment. Agencies such as Moody's and Fitch evaluate the credit risks of thousands of corporate bond issuers and municipalities on an ongoing basis.

For example, if an investor wants to limit his exposure to credit risk, he may opt to buy a municipal bond with a AAA rating. In contrast, if he doesn't mind a bit of risk, he may buy a bond with a lower rating in exchange for the potential of earning more interest.

Real Interest Rate

A real interest rate is an interest rate that has been adjusted to remove the effects of inflation to reflect the real cost of funds to the borrower and the real yield to the lender or to an investor. The real interest rate of an investment is calculated as the amount by which the nominal interest rate is higher than the inflation rate:

Real Interest Rate = Nominal Interest Rate - Inflation (Expected or Actual)

If, for example, an investor were able to lock in a 5% interest rate for the coming year and anticipated a 2% rise in prices, they would expect to earn a real interest rate of 3%.The expected real interest rate is not a single number, as different investors have different expectations of future inflation. Since the inflation rate over the course of a loan is not known initially, volatility in inflation represents a risk to both the lender and the borrower.