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NISM-Series-XXI-A: Portfolio Management Services (PMS) Distributors · Investments

Fixed Income Securities and Bond Valuation for NISM PMS Distributors

Updated 11 October 2026 · Fact-checked

A bond is a loan that pays fixed interest (coupon) and returns face value at maturity. Its price is the present value of those cash flows, so price and yield move in opposite directions. Yield to maturity is the discount rate that equates price to cash flows. Duration measures price sensitivity to yield changes.

Understand Fixed Income Securities and Bond Valuation

A bond is a debt security. You lend money to an issuer such as the government or a company. The issuer pays you interest, called the coupon, and repays the face value (par value) on the maturity date. The coupon rate is the coupon as a percentage of face value.

A bond's price is the present value of all its future cash flows, discounted at the market yield. The coupon is fixed. The market yield changes every day. So when market yields rise, the present value of those fixed cash flows falls, and the price falls. When yields fall, the price rises. This inverse relationship is the single most tested idea in this topic.

The price sits against face value in a simple way. If coupon rate equals yield, the bond trades at par. If coupon rate is higher than yield, it trades at a premium (above face value). If coupon rate is lower than yield, it trades at a discount (below face value). Over time, a bond's price moves towards face value as it nears maturity.

There are several yield measures. Current yield is annual coupon divided by current market price. Yield to maturity (YTM) is the single discount rate at which the present value of all remaining coupons and the face value equals the current price. It assumes you hold to maturity and reinvest coupons at the same YTM. Yield to call applies to callable bonds.

Risk comes in two main forms. Interest rate risk is the risk that prices fall when yields rise. Duration measures it. Macaulay duration is the weighted average time to receive cash flows. Modified duration converts it into the approximate percentage price change for a 1% change in yield. Longer maturity and lower coupon generally mean higher duration. Credit risk is the risk that the issuer fails to pay. Credit rating agencies rate issuers and instruments; higher ratings (AAA at the top) mean lower credit risk and usually lower yields. Government securities carry sovereign credit risk only in a very limited sense and are treated as having the lowest credit risk in rupee terms.

Key formulas to remember

Bond price
Price = Σ [C ÷ (1 + y)^t] + [F ÷ (1 + y)^n]
C is coupon per period, y is yield per period, F is face value, n is number of periods.
Current yield
Current yield = Annual coupon ÷ Market price × 100
Ignores capital gain or loss and time to maturity.
Approximate YTM
YTM ≈ [C + (F − P) ÷ n] ÷ [(F + P) ÷ 2]
Shortcut estimate. C is annual coupon, P is price, n is years to maturity. The exact YTM needs trial and error.
Modified duration
Modified duration = Macaulay duration ÷ (1 + y ÷ k)
y is YTM, k is coupons per year. For annual coupons, divide by (1 + y).
Price change from duration
% change in price ≈ − Modified duration × change in yield
Valid for small yield changes. Convexity corrects for larger changes.
Price versus par
Coupon rate > YTM: premium. Coupon rate = YTM: par. Coupon rate < YTM: discount.
Ordering holds for any bond at a point in time.
Zero coupon bond price
Price = F ÷ (1 + y)^n
Macaulay duration of a zero coupon bond equals its time to maturity.

How to solve Fixed Income Securities and Bond Valuation questions

Use this method for any bond question, whether it asks for price, yield, duration or risk.

  1. 1Read what is asked: price, yield, direction of change, duration or rating. Many questions are conceptual, not numeric.
  2. 2Write down face value, coupon rate, price, yield and years to maturity. Convert coupon rate into a rupee coupon on face value, not on price.
  3. 3Decide the direction first. If yield rises, price falls. If coupon rate is above yield, expect a premium.
  4. 4For a numeric price, discount each cash flow at the yield and add. For a one-year or zero coupon bond, one division is enough.
  5. 5For yield, use current yield if asked, or the approximate YTM formula. Check that YTM is above coupon rate when price is below face value.
  6. 6For duration questions, apply price change ≈ − modified duration × yield change. Keep the units in percent.
  7. 7Compare your answer with the options. Eliminate any option that moves in the wrong direction.

Quickest way: Direction-first elimination

When to use it: Use this for conceptual and comparison questions, where options often differ in direction or ordering.

  1. Ask: did yield go up or down? Price moves the opposite way.
  2. Compare coupon rate with yield to decide premium, par or discount.
  3. For two bonds, the one with higher duration (longer maturity, lower coupon) moves more in price.
  4. For ratings, lower rating means higher credit risk and higher required yield.
  5. Only calculate if two options survive.

Common mistakes in Fixed Income Securities and Bond Valuation

  • Saying price rises when yield rises.

    Students link higher yield with higher value.

    Fix: Remember that fixed cash flows are discounted at a higher rate, so present value falls. Price and yield always move opposite.

  • Calculating the coupon on market price instead of face value.

    Price and face value are confused when a bond trades away from par.

    Fix: Coupon rupees = coupon rate × face value. Use market price only in current yield and YTM.

  • Treating current yield as YTM.

    Both are called yields and look alike.

    Fix: Current yield uses only coupon and price. YTM also includes the gain or loss to face value over the remaining life.

  • Forgetting the negative sign in the duration formula.

    Students focus on the size of the number.

    Fix: A rise in yield lowers price. Write the minus sign every time and state the direction in your answer.

  • Thinking a longer maturity bond always has higher duration regardless of coupon.

    Duration is memorised as maturity.

    Fix: Duration rises with maturity but falls with higher coupon and higher yield. Only a zero coupon bond has duration equal to maturity.

  • Assuming a higher-yielding bond is better.

    Yield is read as pure return.

    Fix: A higher yield often compensates for lower credit quality or longer duration. Always link yield to the risk taken.

Worked examples

Example 1

A bond has face value ₹1,000, a 10% annual coupon and 2 years to maturity. The market yield is 8% per annum. What is its price (to the nearest rupee)?

Show the solution
  1. Coupon = 10% × ₹1,000 = ₹100 a year.
  2. Discount year 1 coupon: 100 ÷ 1.08 = 92.59.
  3. Discount year 2 coupon and face value: 1,100 ÷ (1.08)² = 1,100 ÷ 1.1664 = 943.07.
  4. Add: 92.59 + 943.07 = 1,035.66.
  5. Check: coupon rate 10% is above yield 8%, so the bond should trade at a premium. ₹1,036 is above ₹1,000.

Answer: About ₹1,036, a premium to face value.

Example 2

A bond has modified duration of 5. The market yield rises by 0.50 percentage points. What is the approximate percentage change in its price?

Show the solution
  1. Use % change in price ≈ − modified duration × change in yield.
  2. Change in yield = 0.50%.
  3. % change = − 5 × 0.50% = − 2.5%.
  4. Yield rose, so price falls, which matches the negative sign.

Answer: The price falls by approximately 2.5%.

Exam tips

  • Expect many direct questions on the inverse price-yield link. Answer them from logic, not calculation.
  • Learn the premium, par and discount rule using coupon rate against yield. It is a frequent trap.
  • Duration questions usually need one multiplication. Do not forget that the answer is approximate and applies to small yield changes.
  • PMS Distributors negative marking is 10% of the marks for a question, so a guess costs little, but eliminate wrong options first.
  • For credit questions, link lower rating to higher credit risk and higher yield demanded.

Practice questions from Investments

Fixed Income Securities and Bond Valuation in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Fixed Income Securities and Bond Valuation: frequently asked questions

What is the relationship between bond price and yield?

They move in opposite directions. When market yields rise, existing bonds with fixed coupons become less attractive and their prices fall. When yields fall, prices rise.

How do you calculate yield to maturity?

YTM is the discount rate that makes the present value of all remaining coupons and face value equal to the price. In exams, you may use the approximate formula: [coupon + (face value − price) ÷ years] ÷ [(face value + price) ÷ 2].

What is modified duration in bonds?

Modified duration estimates the percentage change in a bond's price for a 1% change in yield. A bond with modified duration of 4 loses about 4% if yield rises by 1%. It works best for small yield changes.

What does a credit rating tell you about a bond?

A credit rating from a rating agency indicates the issuer's ability to pay interest and principal on time. Higher ratings mean lower credit risk. Lower-rated bonds usually offer higher yields to compensate investors.