The Mathematics of Fixed Interest securities pinpoints the risks
Working through each of these:
- if you buy a bond for $100 paying a 3.5% coupon p.a. for 5 years with a promise to repay $100 at the end of 5 years what is the price today if rates immediately fall to 2.5% p.a.? $104.70 according to the fixed rate bond formula. What if rates rise to 4.5% p.a.? $95.50.
- if I change the maturity to 20 years and again rates fall to 2.5% p.a immediately, then the price rises from $100 to $115.70, a lot more than the rise for a 5 year bond. If yields rise by 1% p.a. to 4.5% p.a. the price falls to $86.90 again a lot more than for the 5 year bond.
- if I change the maturity to 1 year the price becomes $101 if rates fall to 2.5% p.a. and $99 if rates rise to 4.5% p.a.. This is much less volatile and why a low risk fixed interest portfolio needs to contain securities with short term maturities.
The larger the rate movements and the longer the term the greater the price volatility.
Of course, if you buy and hold your 5 year bond having paid $100, earning 3.5% p.a. for 5 years and regaining your $100 after 5 years, the secondary market movements pre maturity become irrelevant. Your return will be 3.5% p.a. on the $100 over 5 years, provided the issuer doesn't default of course.
In the global financial crisis, rising interest rates caused by widening credit spreads saw many long term securities lose a lot of value. Ultimately many regained their value as time went by and repaid their principal at maturity. It is good to be a buyer in a crisis but that is only possible when you understand the mathematics. Many companies and fund managers were unfortunately forced sellers as prices fell. They didn't understand the maths.
Floating rate notes have a different pricing formula and therefore different scenarios.
| 1 year | 2 year | 5 year | 10 year | 20 year | ||
| Coupon | 3.5% | 3.5% | 3.5% | 3.5% | 3.5% | |
| Yield | ||||||
| 1.5% | 102 | 104 | 109.6 | 118.5 | 134.5 | |
| 2.5% | 101 | 102 | 104.7 | 108.8 | 115.7 | |
| 3.5% | 100 | 100 | 100 | 100 | 100 | |
| 4.5% | 99 | 98 | 95.5 | 92 | 86.9 | |
| 6.5% | 97 | 94.4 | 87.3 | 78 | 66.5 | |
| 10.5% | 93 | 87.5 | 73 | 57 | 41.7 |
Frequently Asked Questions about this Article…
The price of a fixed interest bond will increase if interest rates fall and decrease if interest rates rise. For example, a bond priced at $100 with a 3.5% coupon will rise to $104.70 if rates fall to 2.5% and drop to $95.50 if rates rise to 4.5%.
The longer the maturity of a bond, the more volatile its price will be in response to interest rate changes. A 20-year bond will experience larger price swings compared to a 5-year bond when interest rates change.
Short-term bonds are less risky because their prices are less volatile in response to interest rate changes. For instance, a 1-year bond will have minimal price fluctuations compared to longer-term bonds.
If you hold a bond to maturity, the secondary market price fluctuations become irrelevant. You will receive the bond's face value and the agreed coupon payments, assuming the issuer does not default.
During the global financial crisis, rising interest rates and widening credit spreads caused many long-term securities to lose value. However, many regained their value over time and repaid their principal at maturity.
Fixed interest bonds have a set coupon rate, while floating rate notes have a variable rate that adjusts with market interest rates. This results in different pricing formulas and scenarios for each.
Understanding bond mathematics can help investors identify buying opportunities during a financial crisis, as they can anticipate price movements and make informed decisions rather than being forced sellers.
Credit spreads can affect bond pricing by influencing interest rates. Wider credit spreads typically lead to higher interest rates, which can decrease bond prices, especially for long-term securities.
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