# Buying Bonds When Interest Rates Are Low

Extending maturity is a simple way of increasing yield. But is it safe at a time of near zero interest rates?

Bonds are said to carry lower risk than stocks, which justifies their greater presence in more conservative portfolios. That’s the case with pension funds, for example. But, when central banks around the world have their printing machines turned on, investors need to squeeze bonds to get some yield. They then jump off to equities and to longer maturity bonds. But what happens if interest rates start rising again?

## The Relation Between Bond Prices and Interest Rates

Interest rates and bond prices are inversely related. If the central bank hikes its key rate, the yields on all bonds are expected to rise as well. The mechanism works as follows: central bank hikes its key rate > short-term rates rise > demand for money market products increases > demand for longer maturity products like bonds declines > bond prices decline > bond yields increase.

Bond prices and yields are inversely related. If coupon payments are fixed, as is the case with a plain vanilla bond, the only way for the yield to increase is by means of a price decline.

**The above relation tells a simple story for bond investors: if interest rates rise, their bond holdings lose value; and if interest rates decline, their bond holdings gain value.**

**What about if a bondholder keeps the bond until maturity?**

Nothing changes in the above observation. The bondholder would still miss the higher yield. If he keeps the bond until maturity instead of selling it, he gets something near the initial yield. If he opts for selling the bond, he immediately loses on the price difference, but he can purchase another bond at a lower price and earn a higher yield for the remaining time. There’s no material difference between the two options, in particular when the coupons received are reinvested at market rates. **No matter what the decision is, an increase in yields results in an opportunity cost. In the end, the bondholder is worse off than he would if yields remained unchanged.**

**Let’s use an example,… or maybe two**

An investor purchases a 10-year bond paying coupons at a rate of 3% per year for €1,000 (bond A). The implied yield on the bond is 3%, which means it is trading at par value. One year later and due to a series of interest rate hikes by the central bank, the yield on the bond rises to 4%. By then, the bond should trade at €925.65, reflecting a price loss of 7.4% (check the results using this simple bond price calculator).

Another investor opts for a 30-year bond, which pays coupons at a rate of 4.5% per year, and trades at par value. The purchase price is €1,000 and the implied yield is 4.5% (bond B). The yield is higher than in the previous case to reflect a time premium that is often included in longer maturity bonds. So, bond B is pretty similar to bond A but has a longer maturity. Again, one year later, there is a 1% increase in the yield of this bond. To reflect the increase the bond should trade at €856.67, which represents a 14.3% price loss.

The table below summarises the change in prices for bonds A and B due to a 1% increase in yields:

Characteristics | Bond A | Bond A* | Bond B | Bond B* |
---|---|---|---|---|

Coupon Rate | 3.00% | 3.00% | 4.50% | 4.50% |

Face value | 1,000 | 1,000 | 1,000 | 1,000 |

Frequency | 1 | 1 | 1 | 1 |

Maturity | 10 | 9 | 30 | 29 |

Yield / Discount Rate | 3.00% | 4.00% | 4.50% | 5.50% |

Price | 1,000.000 | 925.647 | 1,000.000 | 856.669 |

## Interest Rate Risk and Bond Duration

**The above example pinpoints two important bond features:**

- A bond loses value when interest rates rise, and
- The loss is greater for longer maturity bonds.

Time left to maturity is an important source of risk. By one side, bondholders benefit from buying longer maturity bonds, as they offer higher yields to compensate for higher risks. By the other side, longer maturity bonds are more sensitive to yield rises, and consequently to interest rate hikes. This is a key point to consider for someone willing to manage bond risk. Investing in bonds requires a serious look at interest rates and at their expected future path.

The U.S. financial crisis of 2007-2009 and the subsequent sovereign crisis in Europe forced central banks around the globe to cut their key rates to near zero or even to negative levels. As a result, bond prices rose and yields declined. In certain cases, 10-year bonds were trading with negative yields. Central banks were forcing investors to abandon bonds and embrace stocks. But such a trade is never open to all investors…

Many bond portfolio managers and pension funds just don’t have a mandate to increase the proportion of equities oi their portfolio. Many times, they’re also unable to buy high yield bonds. When this is the case, the only option available to them is to extend the maturity of the bond portfolio. Longer maturities pay higher yields. But, as explained above, longer maturities also carry higher interest rate risk, or in jargon, they havehigher duration.

**Duration is a measure of interest rate risk. It measures the expected change in bond prices due to a change in interest rates (or yields).** There are several ways of measuring it. One common measure is the **Macaulay Duration which is a weighted average of the bond cash flows.** The output from the formula is in years. Another measure is the **Modified Duration which measures the expected percent change in a bond’s price due to a 1% change in yield**.

Bonds with higher coupons and shorter maturities have lower duration. For the same yield, a bond with higher coupons releases more money in the form of coupons than in the form of facial value repayment. As coupon payment occurs before facial value repayment, duration should be lower. Following the same reasoning, it’s easy to see that for the same yield a bond with a longer maturity spreads its payments over a longer period and then should carry a higher duration.

## Implications for Bond Investment

With all of the above in mind, investors may be willing to ask a couple of questions before jumping into the bond market:

- What’s the current level for interest rates?
- What’s the expected path for interest rates?
- What are the risks involved in different bonds?

When interest rates and yields are so low as they currently are, bonds become particularly sensitive to any changes (due to convexity). At the same time, when interest rates are near zero, it seems there’s not much room for anything other than rate hikes. As bond prices suffer from rate increases, investors looking for opportunities in fixed income markets should keep the duration of their portfolios at low levels. Extending maturities to get higher yields is a high risk strategy. Bonds offering higher coupon rates and shorter maturities are eventually the best option at this point.