### The yield curve

The interest rate that lenders require of any borrower will depend on the term of the borrowing. The yield curve depicts the various rates at which the same borrower is able to borrow for different periods of time. The most closely watched yield curve in any country is that of the national government, which is the closest approximation to a risk-free yield. Other yield curves, such as the one for corporate borrowers, are best understood in comparison with the risk-free yield. The yield curve is drawn against two axes, the vertical showing yield (expressed in percentage points) and the horizontal giving the term in years. Most of the time the yield curve is positively sloped, going from the lower left corner of the chart to the upper right. In this case, very short-term borrowings would have the lowest yield, with the yield increasing as the term lengthens. The reasons for this shape are readily understandable, as lenders and investors wish to be compensated for the greater risk that i…

### Interest rates and bond prices

Interest-rate changes within the economy are the single most important factor affecting bond prices. This is because investors can profit from interest-rate arbitrage, selling certain bonds and buying others to take advantage of small price differences. Arbitrage will quickly drive the prices of similar bonds to the same level. Bond prices move inversely to interest rates. The precise impact of an interest-rate change depends upon the duration of the bond, using the basic formula:
Price change duration value change in yield Assume that an investor has just paid C\$1,000 for a bond priced at 100, denominated in Canadian dollars with a 6% coupon and a term of ten years to maturity. This bond might initially have a duration of 7.66 years. If Canadian interest rates for ten year borrowings suddenly decline, investors will flock to the bond with a 6% coupon and bid up the price. Suppose that the market rate for ten-year borrowings in Canada drops to 5.9% immediately after the bond is issued. So this bond would now have a market value of C\$1,007.66 and a price of 100.77. Conversely, if Canadian interest rates for ten-year borrowings rise, the value of the bond will decline until the current yield is in line with the market.

As this example illustrates, the prices of long-term bonds can be much more volatile than the prices of short-term bonds because of their longer duration. In the face of the same interest-rate change, the price of a bond with a duration of 12.5 years would have risen by 1.25%, and the price of a bond with a duration of 2.3 years would have risen by 0.23%. This relationship can be visualised using price/yield curves, drawn on a graph with the vertical axis denoting bond prices and the horizontal axis representing interest rates. As Figure 4.1 on the next page shows, a given increase in yield will cause the price of a bond with long duration to fall much more than the price of a bond with shorter duration, and a given decrease in yield will cause its price to rise more. This graphical relationship is known to bond investors as convexity.

Inflation and returns on bonds

Interest rates can be thought of as having two separate components. The first is recompense for inflation, the change in prices that is expected to  occur during the term of a borrowing. The second is the payment the bond investor exacts for the use of its money after taking inflation into account. The sum of these components is the nominal interest rate. Bond coupons and bond yields are both nominal interest rates. The payment to the investor beyond expected inflation is the real interest rate. The real interest rate cannot be known precisely, but there are ways to estimate it. For example, the current yield on a bond that is indexed for inflation could be compared with the yield on a bond with the same maturity date not indexed for inflation. The difference between these two rates can be understood as the inflation premium investors demand for buying bonds that are not indexed. If the expected inflation rate increases, the yield on such bonds will have to increase for the investor to receive the same real return, which means that the price of the bond must fall. Thus the bond markets are closely attuned to economic data concerning employment, wage increases, industrial capacity utilisation and commodity prices, all of which may be indicators of future inflation.

Exchange rates and bond prices and returns

Many bond buyers invest internationally. To purchase bonds denominated in foreign currencies, they must convert their home currency into the relevant foreign currency. After eventually selling the bonds, they  must convert the foreign-currency proceeds back into their home cur-rency. Their return is thus highly sensitive to exchange-rate movements. For example, consider a Japanese investor that spent \$10,000 to purchase a US bond at a time when ¥1 was worth 0.0083 cents (an exchange rate of ¥120 to \$1). The bond would therefore have cost ¥120,000. Assume that by the time the investor wishes to sell the bond, the yen has depreciated against the dollar by 10%, so that ¥1 is now worth 0.0075 cents (an exchange rate of ¥133.33 to \$1). Even if the price of the bond is unchanged, the value of the investment would be ¥133,330, a gain of 11.11%. The effects of currency movements can overwhelm the returns on the bonds themselves. It compares average bond-market returns
in local currency and in dollars for 1995, a year in which falling interest rates everywhere led to much higher bond prices. The dollar strengthened against the Japanese yen and the pound sterling but weakened against other currencies, which dramatically affected returns for international investors.

Thus the strengthening of a country’s currency can increase the demand for its bonds and raise prices, other things remaining the same. However, other things rarely remain the same.  the main reason for a change in the exchange rate between two countries is a change in their relative interest rates. Why this occurs will determine the effect on bond prices. In the example above, if the yen is weaker against the dollar because Japanese interest rates have fallen, bond prices in the United States might strengthen. If, however, the yen is weaker against the dollar because US interest rates have risen, bond prices in the United States might fall. In summary, the relationship between exchange-rate changes and bond prices is not always predictable.