#### Interest rates are one of the most important factors while determining the bond value. All other factors like payments, number of periods etc are standard i.e. the numbers supplied to us are the numbers that have to be used in the formula for calculating present value. However, this is not the case with interest rates. Interest rates are subjective.

The number used in the formula depends upon the intuition and judgment of the investor. Since different investors use different interest rates while making their calculation, they arrive at different fair values for the same bond. Hence, there is difference of opinion. Some people may find the bond undervalued while some may find it overvalued. This is why trade takes place.However, we need to be aware as to how different assumptions about the interest rates affect the value of the bond. Let’s have a look at the same in this article:

## Inverse Relation

Interest rates have an inverse relation with bonds and all fixed income securities in general. This simply means that an interest rate fall will lead to a price increase in the value of a bond whereas a rise in interest rate will lead to a fall in the market value of the bond. Theoretically the rise and fall happens after the news of the interest rate change has become known to the public at large i.e. it is a fact. However, in reality the market prices in expected changes in the interest rates. So by the time, the interest rates are announced, the value is already priced in and the fall or rise is relatively smaller. The important point is that the market works on opinions or future expectations and not on the basis of facts.**Example:**

Let’s consider the example of a bond which has a face value of $1000. It has a coupon rate of 10% per annum and is expected to pay semi-annual coupons for the next 4 years. So we need to see 3 possibilities:

**When Market Interest Rates are the Same as the Coupon Value ?:**When the interest rates are at 10%, the market value of this bond is $1000 as per the discounted cash flow valuation model for bond prices**When Market Interest Rates are Greater than the Coupon Value?:**When the interest rates are at 12%, the market value of this bond is $900.65 as per the discounted cash flow valuation model for bond prices. Note as the interest rates went up from 10% to 12%, the value of the bond fell from $1000 to $900.**When Market Interest Rates are Less than the Coupon Value?:**When the interest rates are at 8%, the market value of this bond is $1114.93 as per the discounted cash flow valuation model for bond prices. Note as the interest rates went up from 10% to 8%, the value of the bond fell from $1000 to $1114.93.

## Logic behind Inverse Relation

The logic behind the inverse relation is really simple too. In case of fixed income securities we have locked in the nominal value of the money that we will receive. So the coupon payments are going to be the same, no matter what the interest rate is. This is because the coupon payments are fixed anyways.But it is the real value of money which changes. So when interest rates go up, investors have the opportunity to invest their money in other bonds which currently have a higher yield. Our bond would therefore be overpriced in real terms. The value of the bond will therefore have to fall till it is fairly valued with other bonds in terms of its real value.