Yield to Maturity (YTM)

Yield to Maturity (YTM) is the total return an investor earns if they buy a bond at the current market price and hold it until it matures, accounting for all coupon payments and any gain or loss from the purchase price. The SIE exam tests your ability to recognize when YTM is the appropriate yield measure, how it compares to other yield calculations, and what factors affect it.

Core Concepts

What Yield to Maturity Is

YTM is the annualized rate of return on a bond if held to maturity, assuming all coupon payments are reinvested at the same rate. It reflects the bond's current market price, coupon rate, time to maturity, and par value. YTM is expressed as an annual percentage and is the most comprehensive measure of a bond's return because it accounts for:

• All coupon payments received over the bond's life
• The difference between the purchase price and par value (capital gain or loss)
• The time value of money

YTM is also called the basis of a bond. When a bond is quoted on a yield basis, that yield is the YTM.

When to Use This

• When comparing bonds with different coupon rates, maturities, and prices to determine which offers the best total return if held to maturity
• When the question asks for the bond's "yield," "basis," or "total return assuming the bond is held to maturity"
• When the investor's time horizon matches the bond's maturity and they plan to hold until redemption
• When you need the yield that equates the present value of all future cash flows to the current market price

How YTM Works

YTM is calculated by finding the discount rate that makes the present value of all future cash flows (coupon payments plus principal repayment) equal to the bond's current market price. The formula involves solving for the rate in the present value equation:

Where:
C = annual coupon payment
FV = face value (par value, typically $1,000)
n = number of years to maturity
YTM = yield to maturity (what we're solving for)

For the SIE exam, you won't calculate YTM manually using this formula. Instead, you need to understand the relationships between YTM and other bond characteristics:

• When a bond trades at par (price = $1,000), YTM = coupon rate = current yield
• When a bond trades at a discount (price < $1,000),="" ytm=""> current yield > coupon rate
• When a bond trades at a premium (price > $1,000), YTM < current="" yield="">< coupon="">

Example: A bond with a 5% coupon rate trading at $950 (discount) will have a YTM greater than 5% because the investor gets the $50 annual coupon plus a $50 gain at maturity ($1,000 par - $950 purchase price). Conversely, a bond trading at $1,050 (premium) will have a YTM less than 5% because the investor loses $50 at maturity.

When to Use This

• When the exam presents a bond price and asks you to identify the relationship between YTM, current yield, and nominal yield
• When determining which yield is highest or lowest for a bond trading at a discount or premium
• When you see "ranking" questions that ask you to order yields from highest to lowest

YTM vs. Other Yield Measures

Premium vs. Discount Bond Yield Relationships

Factors That Affect YTM

YTM changes when any of the following factors change:

• Market price: When the bond's market price decreases, YTM increases (inverse relationship). When price increases, YTM decreases.
• Time to maturity: For discount bonds, as time to maturity decreases, YTM decreases (the discount amortizes over fewer years). For premium bonds, as time to maturity decreases, YTM increases (the premium amortizes over fewer years).
• Credit quality changes: If the issuer's credit rating is downgraded, the bond's price typically falls, increasing YTM to compensate for higher risk.
• Interest rate environment: When market interest rates rise, existing bond prices fall and YTM rises. When market rates fall, existing bond prices rise and YTM falls.

The coupon rate and par value do not change once the bond is issued, but they do affect the calculation of YTM.

When to Use This

• When questions describe market conditions (interest rate changes, credit downgrades) and ask how YTM is affected
• When comparing bonds before and after a price change
• When identifying what causes YTM to increase or decrease

YTM and Callable Bonds

For callable bonds, investors must consider both Yield to Maturity (YTM) and Yield to Call (YTC). YTC calculates the return assuming the issuer calls the bond at the earliest call date. The lower of YTM or YTC is called yield to worst (YTW), and it represents the minimum return the investor might receive.

• If a bond is trading at a premium, YTC is typically lower than YTM because the investor loses the premium sooner if called early. The issuer is more likely to call a premium bond.
• If a bond is trading at a discount, YTM is typically lower than YTC because the investor gains the discount over the full maturity period. The issuer is less likely to call a discount bond.

Example: A bond trading at $1,100 (premium) has a YTM of 4% and a YTC of 3.5%. The yield to worst is 3.5%. An investor should assume the bond will be called early and use YTC for planning.

When to Use This

• When the question mentions a callable bond and asks for the most conservative yield assumption
• When comparing YTM and YTC and needing to identify yield to worst
• When determining the likelihood of a bond being called based on its premium or discount status

Commonly Tested Scenarios / Pitfalls

1. Scenario: An exam question presents a bond trading at $950 with a 6% coupon and asks you to identify which yield is highest.

Correct Approach: For a discount bond, YTM is the highest yield, followed by current yield, then nominal yield. Select YTM as the correct answer.

Check first: Is the bond trading at a discount (price < par),="" premium="" (price=""> par), or par (price = par)?

Do NOT do first: Do not assume all yields are the same or attempt to calculate each yield manually. The SIE tests your understanding of the relationship, not complex calculations.

Why other options are wrong: Current yield is lower than YTM because it doesn't account for the capital gain at maturity. Nominal yield is the lowest because it's fixed and doesn't reflect the discount purchase price.

2. Scenario: A question asks what happens to a bond's YTM when market interest rates rise.

Correct Approach: When market interest rates rise, bond prices fall, and YTM increases. The correct answer is that YTM increases.

Check first: Confirm whether the question is asking about the effect on YTM or on the bond's price. These move in opposite directions.

Do NOT do first: Do not confuse the coupon rate (which is fixed) with YTM (which fluctuates with market price). Rising rates do not change the coupon rate.

Why other options are wrong: Answers stating YTM decreases or remains unchanged ignore the inverse relationship between bond prices and yields. Answers referencing coupon rate changes are incorrect because coupon rates are fixed at issuance.

3. Scenario: A callable bond is trading at a premium, and you must determine which yield an investor should use for planning purposes.

Correct Approach: For a premium callable bond, use Yield to Call (YTC) because it represents the worst-case scenario (lowest return) if the bond is called early. This is also the yield to worst.

Check first: Determine if the bond is trading at a premium or discount, and whether it's callable.

Do NOT do first: Do not default to YTM without considering the call feature. Premium bonds are more likely to be called, making YTC the more conservative and appropriate measure.

Why other options are wrong: YTM assumes the bond is held to maturity, which is unlikely for a premium callable bond. Current yield and nominal yield ignore both the call feature and the capital loss at call.

4. Scenario: You're asked to rank yields from highest to lowest for a bond trading at $1,050.

Correct Approach: For a premium bond (price > $1,000), the ranking is: Nominal Yield > Current Yield > YTM. Select this order.

Check first: Identify whether the bond is at a discount, premium, or par by comparing the price to $1,000.

Do NOT do first: Do not reverse the order or assume all yields are equal. The premium means the investor loses money at maturity, which lowers YTM relative to other yields.

Why other options are wrong: Any order that places YTM above current yield or current yield above nominal yield contradicts the premium bond relationship. Discount bond rankings (YTM highest) are the opposite and incorrect here.

5. Scenario: A question describes a bond purchased at par and asks what happens to YTM over time if market rates remain unchanged.

Correct Approach: If purchased at par and market rates remain stable, the bond's price stays near par, and YTM remains approximately equal to the coupon rate. YTM does not change significantly.

Check first: Confirm whether the question specifies changes in market rates, credit quality, or time to maturity. If none are mentioned, assume stability.

Do NOT do first: Do not assume YTM automatically increases or decreases over time without a change in price or market conditions. Time alone doesn't change YTM if the bond remains at par.

Why other options are wrong: Answers suggesting YTM rises or falls assume a price change that hasn't occurred. YTM is not affected by the passage of time if the bond's price remains stable.

Step-by-Step Procedures or Methods

Task: Determining the relationship between YTM, current yield, and nominal yield for a bond.

1. Identify the bond's current market price and compare it to par value ($1,000).
2. If price < $1,000="" (discount="" bond),="" remember:="" ytm=""> Current Yield > Nominal Yield.
3. If price = $1,000 (par bond), remember: YTM = Current Yield = Nominal Yield.
4. If price > $1,000 (premium bond), remember: Nominal Yield > Current Yield > YTM.
5. Select the answer that correctly ranks the yields or identifies the highest/lowest yield based on the bond's pricing.

Task: Evaluating whether to use YTM or YTC for a callable bond.

1. Determine if the bond is callable and identify the call date and call price.
2. Check if the bond is trading at a premium (price > par) or discount (price <>
3. If the bond is at a premium, calculate or compare YTC, as it will be lower than YTM (yield to worst).
4. If the bond is at a discount, use YTM, as it will be lower than YTC (yield to worst).
5. Use the lower yield (yield to worst) for conservative planning and investment decisions.

Task: Understanding the impact of interest rate changes on YTM.

1. Identify the direction of the interest rate change (rising or falling).
2. If interest rates rise, bond prices fall, so YTM increases.
3. If interest rates fall, bond prices rise, so YTM decreases.
4. Remember the inverse relationship: bond prices and yields always move in opposite directions.
5. Select the answer that correctly states the effect on YTM given the rate change.

Practice Questions

Q1: A bond is currently trading at $1,080 with a 5% coupon rate. Which of the following statements is correct?
(a) YTM is higher than current yield
(b) YTM is equal to the nominal yield
(c) YTM is lower than current yield
(d) YTM is higher than the nominal yield

Ans: (c)
The bond is trading at a premium ($1,080 > $1,000), so the yield ranking is: Nominal Yield (5%) > Current Yield > YTM. YTM is the lowest because the investor loses $80 at maturity. (a) is incorrect because YTM is lowest for premium bonds. (b) is incorrect because YTM equals nominal yield only at par. (d) reverses the correct relationship.

Q2: An investor is comparing two bonds with the same maturity. Bond A is trading at $950, and Bond B is trading at $1,050. Both have a 6% coupon. Which bond has the higher YTM?
(a) Bond A
(b) Bond B
(c) Both have the same YTM
(d) Cannot be determined without knowing the issuer

Ans: (a)
Bond A is trading at a discount, so its YTM is higher than its 6% coupon. Bond B is trading at a premium, so its YTM is lower than 6%. Therefore, Bond A has the higher YTM. (b) is wrong because premium bonds have lower YTM. (c) is incorrect because the different prices result in different YTMs. (d) is incorrect because YTM depends on price, coupon, and maturity, not the issuer.

Q3: A callable bond is trading at $1,100 with a YTM of 4.5% and a YTC of 3.8%. What is the yield to worst?
(a) 4.5%
(b) 3.8%
(c) The nominal yield
(d) Cannot be determined

Ans: (b)
Yield to worst is the lower of YTM and YTC. Since the bond is at a premium and callable, YTC (3.8%) is lower and represents the worst-case return. (a) is incorrect because it's the higher yield. (c) is incorrect because nominal yield is not used for yield to worst. (d) is wrong because we have the necessary information.

Q4: Market interest rates have just decreased. What effect does this have on the YTM of existing bonds?
(a) YTM increases
(b) YTM decreases
(c) YTM remains unchanged
(d) YTM equals the new market rate

Ans: (b)
When market interest rates decrease, existing bond prices rise, and YTM decreases due to the inverse relationship between price and yield. (a) reverses the correct relationship. (c) is incorrect because YTM changes with price. (d) is incorrect because existing bond YTMs adjust through price changes, not by matching new rates exactly.

Q5: A bond is purchased at par. Which of the following is TRUE?
(a) Current yield is higher than YTM
(b) YTM is higher than nominal yield
(c) YTM equals the coupon rate
(d) YTM is lower than current yield

Ans: (c)
When a bond is purchased at par, YTM = Current Yield = Nominal Yield (coupon rate). There is no capital gain or loss at maturity. (a) and (d) are incorrect because all three yields are equal at par. (b) is incorrect because YTM equals, not exceeds, the nominal yield at par.

Q6: Which of the following would cause a bond's YTM to increase?
(a) The bond's price increases
(b) The issuer's credit rating is upgraded
(c) Market interest rates rise
(d) The bond's coupon rate increases

Ans: (c)
When market interest rates rise, bond prices fall, and YTM increases to remain competitive with new issues. (a) is incorrect because rising prices decrease YTM. (b) is incorrect because upgrades typically increase price and decrease YTM. (d) is incorrect because the coupon rate is fixed at issuance and doesn't change.

Quick Review

• YTM is the total annualized return if a bond is held to maturity, accounting for coupon payments and any capital gain or loss.
• For a discount bond (price < $1,000):="" ytm=""> Current Yield > Nominal Yield.
• For a par bond (price = $1,000): YTM = Current Yield = Nominal Yield.
• For a premium bond (price > $1,000): Nominal Yield > Current Yield > YTM.
• YTM and bond prices have an inverse relationship: when price increases, YTM decreases; when price decreases, YTM increases.
• For callable bonds, yield to worst is the lower of YTM or YTC. Use YTC for premium callable bonds; use YTM for discount callable bonds.
• When market interest rates rise, existing bond prices fall and YTM rises. When rates fall, prices rise and YTM falls.
• The coupon rate and par value are fixed and do not change after issuance, but they affect YTM calculations.
• YTM is also called the bond's basis. When a bond is quoted on a yield basis, that yield is the YTM.
• YTM assumes all coupon payments are reinvested at the same rate, which may not occur in practice but is the standard assumption for exam purposes.