# Yield to Maturity Concept

The yield to maturity (YTM) of a bond represents the annual rate of return for the full life of the bond. The YTM assumes the investor will hold the bond to maturity, and that all interest payments will (hypothetically) be reinvested at the YTM rate.

For example, a bond with a maturity of 10 years and a YTM of 5% implies that buying this bond and holding it for the full ten years would give the investor an annual return of 5% on the invested capital.

Given the bond’s price, par value, maturity date, coupon rate and coupon payment schedule, the YTM represents the time value of money – incorporating the aforementioned variables – that sets the bond price equal to the present value of the future payments of the bond, including coupon payments and principal redemption. The YTM is equal to the bond’s discount rate and internal rate of return.

## Define Yield to Maturity

Yield to maturity is the implied annual rate of return on a long-term interest-bearing investment, such as a bond, if the investment is held to maturity and all interest payments are reinvested at the YTM rate.

### Current Yield Calculation

The current yield of a bond differs from the yield to maturity. The current yield of a bond represents the implied return on the bond for one year, given the coupon payments and the current market price. For example, if an investor buys a bond for \$95 with an annual coupon payment of \$5, the current yield for that bond would be 5.26% (.0526 = 5/95). The current yield formula is:

Current Yield = Annual Payment/Current Market Price

### Yield to Maturity – Bond Price

If a bond’s yield to maturity is greater than its current yield, the bond is selling at a discount, or a price less than par value. If YTM is less than current yield, the bond is selling at a premium, or a price above the par value. If YTM equals current yield, the bond is selling at par value.

Discount Price – Yield to Maturity > Current Yield

Premium Price – Yield to Maturity < Current Yield

Par Value Price – Yield to Maturity = Current Yield

### Bond Yield To Maturity Formula

The formula for a bond’s yield to maturity is complicated and solving it mathematically often requires a process of trial and error. It is possible to get an approximate YTM for a bond using a bond yield table. The best way to compute the YTM for a bond is to use a financial calculator. Using a financial calculator, punching in four out of five of the relevant variables (price, par value, maturity, coupon payment, YTM) will give you the fifth variable.

To calculate the bond’s YTM, solve this formula for YTM:

Price = Coupon Payment x 1/YTM (1 – (1/((1+YTM)^Time Periods)) + Future Value/((1 + YTM)^Time Periods) 0

# Interest Rate Risk Definition

Interest rate risk is the risk or volatility associated with bonds or long term debt as their interest rates, coupon, yield to maturity, and maturity dates move within the market.

## Factors of Interest Rate Risk

There are typically five types of interest rate risk on bonds and debt instruments as follows:

1) Bond prices and their yields are inversely related. Thus, if a interest rate increases the bond price falls or drops to a discount, and if the interest rate drops the bond prices rises or is considered at a premium. The fluctuations in the market is an interest rate risk that must be accounted for accordingly when investing.

2) The longer the maturity the more sensitive a bond or debt instrument is to interest rate changes. As a bond comes closer to its maturity the price fluctuates less and less from changes in the market. This means that a shorter term security has less interest rate risk.

3) An increase in interest rates will yield a much larger change in a bond than a decrease of the same amount. This means that a bond has the ability to lose its overall value in price than it does in gaining or selling at a premium.

4) Prices of low coupon bonds are much more sensitive to market yield changes than the prices of higher coupon bonds.

5) A bond or debt instrument’s price is much more sensitive if that particular bond has a lower yield to maturity. Thus, the higher the yield to maturity the less sensitive the bond price.

Note: None of these factors matter if a person plans on holding a bond or debt instrument until its maturity. If a person holds a bond until its maturity the fact that interest rates fluctuate is irrelevant because all bonds pay coupons and finally the face value at maturity. This means that this person will automatically make the desired return and therefore need not worry about interest rate risk measures.

### Interest Rate Risk Example

Chuck wants to invest in a debt instrument, and comes across some lucrative bonds. He has narrowed the search down to two, and is trying to decide between bond A and bond B. Both bonds pay a coupon of 8% and have a current yield to maturity of 6%. The only large difference between them is that the maturity for bond A is 5 years and B has a maturity of 30 years. After consulting with a close friend Chuck decides to buy bond A because his friend tells him there is less interest rate risk inherent in bond A.

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