Question

Can you explain intuitively why the interest-rate risk is positively associated with maturity but negatively associated with coupon rate of the debt instrument that you hold?

How does the interest-rate risk vary with the level of interest rates? For example, during the recession when market interest rates are low, does the overall level of interest-rate risk become higher or lower?

Imagine that you’re managing a portfolio of long- and short-term bonds. If you predict a rise in interest rates, how would you adjust your portfolio composition? 

And how would you adjust your portfolio if you predict a fall in interest rates?

What is the relationship between interest rates and stock market?

How would you compare the degree of interest-rate risk and reinvestment risk between floating rate (variable rate or adjustable rate) bonds and fixed rate bonds? Floating rate bonds are bonds whose coupon payments are adjusted periodically according to market interest rates.

Can you explain intuitively how a bond ladder mitigates interest-rate risk and reinvestment risk?

Answer 1

Since you have asked multiple questions, I will address the first one and some of the other related questions.

Before answering the questions, let's try to understand the following concept:

• At any point in time, the value of a bond is present value of all the future coupon payments and principal repayment.
• And interest rate prevailing in the market is the proxy for the discount rate.

Let's now look at the question one by one.

Can you explain intuitively why the interest-rate risk is positively associated with maturity but negatively associated with coupon rate of the debt instrument that you hold?

suppose I have two bonds one with 3 years maturity and another one with 8 year maturity. Suddenly interest rate increases, say at the end of two years from now. In the 3 year maturity bond, i will then have just one more year to go. I will be stuck with the bond for 1 more year and as soon as third year comes, i will get my principal back which i will reinvest at higher interest rate. In case of the 8 years maturity bond, I will be stuck for balance 6 years before i get my principal back to reinvest at a higher interest rate. Thus i have a higher interest rate risk in case of bond with a higher maturity. Thus, the interest-rate risk is positively associated with maturity.

Another way to look at it: For a bond with higher maturity, future coupon payments and principal repayments are relatively further away in future. When interest rate increases, these long distant coupon payments get discounted at a higher discount rate and they loses value significantly and thus result into lower value of the bond. The reduction in the bond price is sharper. It's true that increase in interest rate will have a similar impact on the price of a bond with lower maturity, but reduction in price there is not that sharp and abrupt. Thus, interest rate risk is prevalent in bonds of all kinds of maturities, but it's impact is more severe in case of bonds with higher maturity.

Negative relationship with Coupon

Assume I have two bonds, one paying a coupon of 10% and another one paying a coupon of 5%. Both have the same maturity of 10 years and face value of $ 100.

Total money that i am going to get in 10 years time from 10% coupon bond = 10 interest payments + principal repayment = 10% x 100 x 10 + 100 = 200

Total money that i am going to get in 10 years time from 5% coupon bond = 10 interest payments + principal repayment = 5% x 100 x 10 + 100 = 150

Let's say at the end of five years, interest rate rises.

At the end of five years' i would have already received five coupons.

In case of 10% coupon bond i would have received = 10% x 100 x 5 = 50. So the pending cash flows on 10% coupon bond = 200 - 50 = 150. Proportion of pending cash flows = 150 / 200 = 75%.

In case of 5% coupon bond i would have received = 5% x 100 x 5 = 25. So the pending cash flows on 5% coupon bond = 150 - 25 = 125. Proportion of pending cash flows = 125 / 150 = 83.33%.

In case of a higher coupon bond, i have a relatively lower proportion of my total cash flows pending that will be subjected to a higher discount rate due to increase in interest rate. In case of lower coupon rate, i have a relatively higher proportion of my total cash flows pending that will be subjected to a higher discount rate. Clearly, the risk is more in case of lower coupon bond. Hence, interest rate risk is negatively correlated with coupon rate.

Imagine that you’re managing a portfolio of long- and short-term bonds. If you predict a rise in interest rates, how would you adjust your portfolio composition?

The answer follows from the arguments above. The increase in interest rate will lead to a sharper and more abrupt decline in the value of long term bonds than in the case of short term bonds. Hence i will try to get rid of long term bonds. So, i will increase the proportion of short term bonds in my portfolio.

And how would you adjust your portfolio if you predict a fall in interest rates?

I will try to realign my portfolio in favour of long term bonds. I will try to get rid of short term bonds and increase my allocation to the long term bonds.