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INTEREST RATE VOLATILITY DOES MATTER

The variability of interest rates directly influences how the public saves and invests, thus having a large impact on the standard of living. As fluctuations of the rate occurs, return on assets become less predictable forcing investors to re-evaluate their original investment decisions, or face the possibility of drastic loss. Those investors with low income are more likely to hold investments with relatively low volatility, ensuring a steady level of consumption. In contrast, investors with a steady level of income and a diverse portfolio can hold much more volatile investments. Any losses can easily be absorbed while holding the high risk/return investments.

Said volatility affects the business firm in a similar fashion as it does the investor. To manage risk firms must watch the changes in the interest rate in relation to the composition of their portfolios.

The Bank of Canada describes interest rates as "represent[ing] the cost of borrowing money over a period of time � the price that lenders charge borrowers for the use of the lenders money." As the rate fluctuates the amount of payment to the lenders varies therefore changing the total cost of borrowing by the public which, in a domino affect, affects their purchases, investing strategies and overall the health of the economy.

INTEREST RATES, BOND PRICES, AND THE TERM STRUCTURE

Typically, the price of a bond and the interest rate attached to it has a negative relationship. The term structure of interest rates is the relationship between the maturity of the bond and the interest rates implied by the bond prices. The yield curve, which is a graphical depiction of the relationship between interest rates and bond maturity, can take a variety of shapes because the U.S government offers securities with a variety of maturities. Usually interest rates on short term bonds are lower than interest rates on long term bonds which make the yield curve upward sloping. Based on the same logic, one might think that the volatility of interest rates varies with maturity. Since interest rates and bond prices have a defined relationship, when considering bond prices the interest rates can be found.

When considering a bond its clear whether it will fit into a conservative portfolio or a riskier one based on the derivation of its interest rate, the term structure is related basing the previous relationship to its maturity.

As seen in figure 1 the interest rates on the year bonds are constantly higher than those of the month bonds. The term structure of the interest rates is shown through the higher rate for long term bonds and lower rate for short term bonds. Based on the data, the longer the term to maturity the higher the rate will be. Since the price of the bond and the interest rate has a negative relationship, that prices of bonds between 1 and 00 would have been lower in the mid 10's and higher at the turn of the century.

Trends that are evident in the cycles of interest rates are long term variability is seen in long trends in interest rates. Short term variability fluctuates around these long term trends.

MEASURING THE VOLATILITY OF INTEREST RATES

Interest rate volatility is measured by a statistic called standard deviation, how dispersed a variable is around its average value. As the standard deviation increases it is probable there will be large changes in the value of the variable. The interest rate is the variable. A higher volatility is evidence of rates that jump far around the average and results in a higher standard deviation, thus standard deviation and volatility have a positive relationship. The correlation coefficient measures the strength of the co-variation between two variables, and can only be a number between negative one and one. If the correlation is close to positive one, the two variables are said to be moving in the same direction. If one is high so is the other. If the correlation is close to negative one, the two variables are said to be moving in opposite directions. If one is high the other is low. The correlation coefficient is useful in identifying the possible causes of interest rate fluctuations by plotting the interest rate directly against another variable to see if a relationship exists.

Based on previous data the following correlations are evident.

• Increases in current output are associated with increases in future interest rates.

• When current output rises the yield curve flattens. When output declines yield curve becomes steeper.

• Interest rates on bonds with different maturities are highly correlated with each other, specifically between bonds of similar maturity dates.

DETERMINANTS OF INTEREST RATE VOLATILITY

Determining short term interest rates. Current short term interest rates have a positive relationship with current output. If current output is low the current short term interest rates will fall at the same pace. The yield curve (interest rates vs. bond maturity) has the tendency to flatten when output is high and steepen when output is low. Such information derived from the slope of the yield curve does help to track and predict the different turns in the business cycle. For example, if the curve has a steeper shape, interest rates will be more varied signifying a change in the cycle, possibly the peak of an expansionary period. Expected inflation also determines short term interest rates. As inflation rises consumers expect a higher return from their investments, thus bond prices will fall and interest rates will rise. Since the direct relationship between inflation and interest rates, and determinate of inflation can be used in determining short term interest rates.

Determining long term interest rates. Long term rates are linked to short term rates. According to the expectations theory of the term structure long term interest rates are equal to an average of expected short term interest rates plus a risk premium. The expectations theory also links long term discount bond prices to expected short term discount bond prices over the life of the long term bond. Although like short term determinants, long term bond prices can be derived from include expected income growth and expected inflation; long term rates do not have a high co-variation with output.

Determining interest rate volatility. The economic variables that influence long and short term rates also affect the volatility of these rates- expected inflation and expected real income growth. Large changes in real expected real income growth are associated with large changes in interest rates. Large changes in expected inflation spark large changes in current bond prices and current interest rates, thus, the more volatile inflation is the more volatile bond prices and interest rates will be.

Inflation and income growth are factors that determine long term rates, short term rates and volatility, yet monetary policy is a factor that influences all of them. When the money supply grows to an excessive amount inflation is likely to be high. If monetary policies are volatile so is inflation. Its affect on real income is not as direct, only through certain circumstances of inflation leading to layoffs of workers could monetary policy affect the money supply.

Other factors that have an effect on interest rate volatility can vary from weather to changes in technology to a variety of economic models. These factors do not have a large effect and are only directly applicable in specific cases.

Economic models and interest rate volatility. One economic model suggests that investor's expectations of future real income growth and inflation are main determinants and interest rates.

Although economic models are useful in predicting some economic variables, when used as a tool in determining such a volatile variable such as interest rates, it may not be the most reliable. Predicting involves setting up identical economic circumstances within the model, but with the variety of factors on the economy, they are rarely identical.

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