The bond market and policy interest rates set by a country’s central bank have a direct relationship. Afterall, investors earn an ‘interest’ or coupon on a bond. In this article, we shall explore this interrelationship between bond prices, inflation & interest rates. We shall also understand how to calculate new bond prices upon such interest rate changes

Interest rates have a inverse relationship to the prices of bonds prices. In other words, **when interest rates rise, the bond prices fall**. Further, the longer the bond’s maturity, the more is it likely to fluctuate in relation to the interest rates.

## The Inverse Relationship between Bond Prices and Interest Rates

The illustration shows the inverse relationship between interest rates and bond prices.

- When interest rates fall, the bond prices go up. And when bond prices go up, the bond yields fall
- When interest rates go up, the bond prices fall down. And when bond prices fall down, the bond yields rises

### Why bond prices change in line with interest rate fluctuations

Governments and businesses raise money though the sale of bonds. Individuals, institutions, pension funds, mutual funds and even foreign governments buy these bonds as safe and predictable instruments. And like every financial instrument, bonds can be bought and sold most times as tradeable instruments.

When a central bank increases the interest rates, newly issued bonds are available at a much higher interest rate. This interest rate is higher as compared to existing bonds which carry a lower coupon rate.

Therefore, there is a drop in demand for lower-yield bonds which means these low-yield bond prices are going to fall.

The exact reverse happens when interest rates drop which puts up a premium on the higher coupon bonds which drive up their prices.

The SEC (Securities and Exchange Commission) too wrote a paper on the interplay of interest rate, bond prices and bond yield.

This cause-effect is true across all countries. In India, the same can be seen when RBI interest rates go up or down.

Let’s understand this further using a simple scenario.

### Scenario of interest rate going down and bond price going up

A treasury bond is available at ₹1,000 and offers a 6% coupon rate for the next 10 years. You go ahead and purchase it.

There are two things you need to understand here.

1. *A bond’s coupon rate is the interest you will receive on an annual basis for holding the bond. This coupon rate is irrespective of whatever is the price of the bond. In our scenario, it means the holder of the bond will receive ₹60 (i.e. ₹1,000 * 6%) every year.*

*2. The price of bond, like every financial instrument, goes up and down based on multiple factors like demand, supply, interest rate etc. Bonds are marketable instruments li*ke stocks.

One year later, the central bank decides to drop the interest rate to 4%. This means all future bonds will be available at a coupon of 4%.

However, your bond will continue to pay you a 6% coupon. This makes your bond more valuable than the bonds that are paying only 4%.

This drives up the price of your bond. Your bond should be priced at much higher than ₹1,000. Let’s say this revised price of the bond is now ₹1,100.

Now, you have a buyer for your 6% bond which still has 9 years left for maturity. The buyer of your bond will have to pay ₹1,100 against which he will be able to earn 6% for the next 9 years.

From an yield perspective, note that the buyer of the bond doesn’t really have a 6% yield as he did not buy the bond at ₹1,000 but is buying it at a higher price of ₹1,100.

So, the yield for the new buyer will be –

6% divided by ₹1,100 = 5.45%

A category of mutual funds that gets affected due to these changes in interest rates are the debt mutual funds. Do read the part on one of my articles on the subject where I explain how interest rates changes affect the returns and risk parameters of debt funds.

## How are Bond Prices Calculated?

Bonds are priced based on the time value of money. Each coupon payment is discounted to the current time based on the interest rate.

### Formula to Calculate Bond Prices

where,

- C = coupon payments
- i = interest rate
- n = number of payments
- M = par value of the bond

### Example of Bond Price Calculations

Let’s understand bond price calculation with an example.

- Par value of the bond = ₹1,000 (M)
- Coupon = ₹60 (C; coupon rate = 6%)
- Bond maturity = 10 years (n)
- Interest rate = 5% (i)

At a 5% interest rate, the current price of the bond is ₹1,077

Now let’s say the central bank raises the interest rate to 7%.

Since interest rates and bond prices move in opposite directions, we should expect a dip in the bond price. Let’s see how that changes things for us.

At a 7% interest rate, the new price of the bond is ₹929

This is how bond prices change upon any changes in the interest rate. Since every market has mispricing, these changes often give way to opportunities where you can purchase high yielding bonds are lower than market price.

## Additional Resources

Here are some articles you can read to get better details on financial and stock metrics

- Rakesh Jhunjhunwala and his secrets to investing (Part 1)
- Building a high return portfolio with index funds – a step-by-step approach
- Complete SIP Investment Guide (over 8000 words compedium updated until 2020)
- The trillion dollar index fund story that John Bogle started in the 1970s
- Best SIP for achieving long term goals