Question

Long-term government bonds now pay approximately 3 percent nominal interest. Would you prefer to trade yours in for an indexed bond that paid a 1 percent real rate of interest? What if the real interest rate offered were zeroed? What if it were negatioe 1 percent? What do your answers to these questions reveal about your personal beliefs about future inflation?

Short answer

Answer: When deciding whether to trade a non-indexed bond for an indexed bond with different real interest rate offerings, an individual should consider their beliefs about future inflation and compare the effective real interest rates of each option. This will help them determine which trade, if any, would make the most sense based on their expectations about future inflation.

Step-by-step solution

Understanding Nominal and Real Interest Rates

To make a decision about the trade, first, we have to understand the difference between nominal and real interest rates. The nominal interest rate is the percentage increase in the value of an investment without considering inflation. The real interest rate is the percentage increase in the value of an investment considering inflation. The real interest rate can be calculated using the following formula: \(real\:interest\:rate=\frac{(1+nominal\:interest\:rate)}{(1+inflation\:rate)}-1\)

Determine the Current Real Interest Rate on the 3% Nominal Bond

We don't know the actual inflation rate, but we can denote it with \(i\). We can calculate the current real interest rate on the 3% nominal bond using the above formula: \(real\:interest=\frac{(1+0.03)}{(1+i)}-1\)

Compare the Offered Indexed Bond Real Interest Rates to the Current Real Interest Rate

Now we will consider three different cases, where indexed bonds pay a real interest rate of 1%, 0%, or -1%. Case 1: Indexed bond pays a real interest rate of 1%: In this case, we need to compare the current real interest rate on the 3% nominal bond to the 1% real interest rate offered by the indexed bond. If the current real interest rate is lower than 1%, it justifies trading in the bond. Case 2: Indexed bond pays a real interest rate of 0%: Similarly, in this case, we need to compare the current real interest rate on the 3% nominal bond to the 0% real interest rate offered by the indexed bond. If the current real interest rate is lower than 0%, it justifies trading in the bond. Case 3: Indexed bond pays a real interest rate of -1%: In this case, too, we need to compare the current real interest rate on the 3% nominal bond to the -1% real interest rate offered by the indexed bond. If the current real interest rate is lower than -1%, it justifies trading in the bond.

Evaluate the Beliefs about Future Inflation

Analyzing our answers to the three cases will reveal our beliefs about future inflation. If we decide to trade in the bond for an indexed bond that offers 1% real interest rate, it shows that we believe future inflation will be higher than 2%. If we opt to trade for an indexed bond that offers 0% real interest rate, it reveals our belief that future inflation will be higher than 3%. And lastly, if we choose to exchange for an indexed bond that offers -1% real interest rate, it indicates a belief that future inflation will be higher than 4%. In conclusion, the decision to trade a non-indexed bond paying a 3% nominal interest rate for an indexed bond with different real interest rate offerings depends on the individual's beliefs about future inflation. By analyzing each case and comparing the effective real interest rates, it is possible to determine which trade, if any, would make the most sense based on the individual's expectations.

Key concepts

Inflation Rate

When discussing financial matters, the term 'inflation rate' frequently pops up, referring to the percentage at which the general level of prices for goods and services is rising. But why does it matter? Well, inflation can erode the purchasing power of money over time. For students grappling with finance, this means that the money you have today will likely buy less in the future due to inflation.

To gauge the real increase in wealth, investors need to look at the real interest rate, which adjusts the nominal interest rate for inflation. The formula provided in the exercise is the cornerstone for this adjustment:
\[real\:interest\:rate=\frac{(1+nominal\:interest\:rate)}{(1+inflation\:rate)}-1\]
This equation bridges the gap between the sticker price increase of your investments (nominal interest rate) and what you can actually buy with that increase after adjusting for rising prices (real interest rate).

Indexed Bonds

Imagine owning a shield that protects your money from the invisible monster of inflation. That shield is known as 'indexed bonds'. These are a type of bond designed to help investors maintain their purchasing power. They do this by having their principal amount and interest payments adjusted according to the inflation rate.

How are they different from regular bonds?

Regular bonds pay a fixed nominal interest rate which doesn’t change, regardless of the economy's inflation rate. This means that if inflation is high, your real rate of return can be significantly lowered. Indexed bonds, however, are structured to be inflation-proof to an extent, making them particularly attractive during periods of high or unpredictable inflation. If you're contemplating the switch from a fixed-rate bond to an indexed bond, as in the textbook exercise, you're essentially opting for security against the eroding effects of rising prices.

Future Inflation Expectations

Looking at financial options is very much like trying to predict the weather for an outdoor party weeks in advance. It involves future inflation expectations, which are your projections or guesses about the rate of inflation in the future. These expectations can significantly influence your decision-making process.

For instance, if you believe inflation will rise, as suggested in the exercise scenarios, you might opt for an indexed bond offering a real interest rate that compensates for higher inflation. Basically, the higher your expectations of future inflation, the more attractive indexed bonds may become, as they promise to adjust your earnings in line with increasing prices. Making decisions based on these expectations demonstrates how your views about the economy's future can shape where you put your money for safekeeping and growth.