The Bond Market Chapter 22

Students Should Be Able to: Use the price and face value of a bond to calculate the yield or the face and the yield to calculate the price. Use the expectations theory of the term structure to identify expectations of future short-term interest rates by looking at yields on short and long-term bonds. Distinguish between the ex ante yield and the ex post return. Use the rule of thumb to find the impact of an increase in yield on ex post returns. Qualitatively identify the effects of monetary policy on the yield curve. Use average inflation rates and average interest rates to calculate real returns.

Bond Investment An Indian investor decided to invest Rp.1,000,000 in Indian bonds in 1970. The strategy will be to buy bonds in 1970 and roll over all payments of principal and interest back into a bond fund. The average return on Indian bonds during this period was 6% In 1990, the Indian investor would have Rp. 3,253,992.04 in savings, tripling his money in twenty years.

Real Returns However, the average Indian inflation rate during this period was 8.3%. Thus, in 1990, the pay-off of the savers bond investment would only buy the same amount of goods as Rp.$622,394 would have bought in 1970. Investing in Indian bonds has cut the purchasing power of savings nearly in half!

What is a Bond Bonds are a promise to repay certain amounts of money at specific dates in future. Most bonds specify specific amounts of currency units that will be repaid (unlike stocks which entitle owner to a share of profits). Bonds unlike bank loans can be traded on securities markets. Since governments cannot issue equity, they rely on bonds for financing. Government bonds are a large share of world bond market.

Hong Kong Government Bonds Hong Kong government has not typically raised funds with bonds (though government owned companies like MTR, KCR, HKMC do). Instead, the central bank issues Exchange Fund bonds to increase the liquidity of the HK dollar bond market.

HK Dollar Bond Market

Domestic vs. Foreign vs. Euro Bonds specify a currency of denomination. Domestic bonds are bonds issued in a domestic market by domestic residents. Foreign bonds are local currency bonds issued in domestic market by non-residents (often have cute nicknames: a foreign bond in Japan is a Samurai, a foreign bond in USA is a Yankee, etc.) Eurobonds are foreign currency denominated bonds issued in any country by residents or non-residents

Yield to Maturity If you buy a bond today and hold it for its lifetime, then the average yearly interest rate that you would receive is called the yield to maturity. You pay a certain price for a bond in the bond market and you will receive certain pay-offs. The yield to maturity is defined as the interest rate that would set the present value of the pay-offs equal to the price.

Discount Bonds There are many types of bon’„The simplest type of bond is a discount bond. The issuer of a discount bond makes a single payment (called the face value) at some designated time T periods from now. The standard unit of bonds are in $100 of face value. So if a bond price is quoted at PB, this is the price per $100 worth of face value. Ex. If a bond had a face value of $10,000 and you were quoted a price of 90, you would have to pay $9000 for this bond.

Yield to Maturity: Discount Bond Since there is only 1 payment in T periods, the present value of the bond is the face value divided by the interest rate raised to the power T. The yield to maturity would be the interest rate that would set the in

Intuition If you put the initial bond price in a bank account that paid a constant interest rate equal to the yield to maturity, at the end of T periods you would have a total balance equal to the face value of the bond.

Implications There is an inverse relationship between the price of a bond and the interest yield on the bond. When a bond is relatively cheap, an investor can earn a high return by buying it and holding it until maturity. When interest rates rise, bond prices fall.

Yield Curve Bonds are sold with different maturities. For example, there are Hong Kong government bonds with maturities as long as 10 years. An expansion in money growth will have different effects on interest rates on long-term bonds and short-term bonds

Expectations Theory of Term Structure Consider two strategies which should have the same expected pay-off. Starting with $1. Buy a two year discount bond and hold it for two years. Payoff: Buy a 1 year bond. After 1 year, invest pay-off in another 1 year bond. Payoff: Equal pay-offs imply that yield on a two year bond is equal to the expected average yield of 1 year bonds over the next two years.

In general, if the pay-off for investing in an n period bond should be the same as the pay-off from rolling over 1 year bonds for n periods: Then a T period bond yield is (approximately) equal to the average expected yield on 1 period bonds between today and date n.

Today, the yield curve is very steep.

Monetary Policy and Interest Rates There is a close linkage between monetary policy and the interest rate. Consider the impact of a persistent increase in the money growth rate on interest rates. Short-term: An increase in liquidity will reduce the interest rate. Long-term: An increase in money growth rate will increase inflation and increase the nominal interest

Implications Long-term bond prices are more sensitive to a persistent increase in interest rates because they are held for many periods. The percentage change in discount bond prices are approximately equal to the negative maturity level. Example: Interest rates at all maturities change from 2% to 3%: Δi=.01 The % change in a two year bond price will be approximately -2%. The % change in a 3 year bond price will be approximately -3% The % change in a 10 year bond price will be approximately -10%.

Ex Ante Yields vs. Ex Post Returns Yields are the average returns that a bond holder can expect to earn in the future. Ex post returns are the returns that someone has earned by holding bonds over a past period. For discount bonds, the annual ex post bond return, Rt, will be the change in the price level over the period

Inflation: Enemy of Bondholders A surprise increase in money growth may reduce short-term interest rates through the liquidity effect, but it can be expected to increase long-term interest rates through the Fisher effect. Therefore, an increase in money growth is likely to increase long-term bond yields and reduce long-term bond prices. Bondholders must either sell at a low price or keep their bonds and receive a face value with low real value.

Inflation Risk Unexpected inflation is bad for long-term bond holders. Volatile inflation is a source of risk for bond buyers. Extra risk pushes up interest rates, pushes down bond prices. Inflation risk premium can lead to higher interest rates.

Floating Rate Bonds Bond holders who are sensitive to inflation risk often purchase floating rate bonds. If some benchmark interest rate rises, the holders of floating rate bonds receive an extra payment. Most mortgages are floating rate loans. Government debt is typically fixed rate.

Inflation Adjusted Bonds US Treasury (TIPS) whose face values are directly linked to the CPI. This can guarantee a real return. The calculated yield on inflation adjusted bonds can be interpreted as the ex ante real interest rate Japanese Ministry of Finance begins issuing these bonds this quarter.