FNCE 3020Financial Markets and Institutions Fall Semester 2006

Lecture 5: Part 2

Forecasting Interest Rates with the Yield Curve

Forecasting Interest Rates with the Term Structure (Yield Curve) In the previous lecture (Lecture 5: Part 1), we

discussed the term structure of interest rates, i.e., the yield curve.

The previous lecture introduced you to three major theories which are used to explain why the yield curve takes the shape it does.

In this lecture, we will see how we can apply these three theories forecasting interest rates.

Why is Forecasting Important? Interest rate forecasts are important to a

variety of possible organizations. These include: Lenders of funds.

A lender of funds could use an interest rate forecast to set lending rates today. This is especially important in committing to longer term loans.

Asset managers. The future direction of interest rates will have an impact

on the financial asset holdings of these organizations. A forecast will help establish appropriate portfolio allocations.

Why is Forecasting Important? Other organizations interested in interest rate

forecast would include: Investment bankers.

Interest rate forecasts would assist these organizations in determining the timing of issues which they intend to bring to market for their clients.

Corporations. Decisions about when to borrow, and the method of

borrowing, to invest in possible projects might depend upon interest rate forecasts.

Economic forecasters. Given the possible impact of interest rate changes on key

sectors of the economy, forecasters need to utilize interest rate forecasts in their macro-economic forecasts.

Theories to Explain the Shape of the Yield Curve Recall, that there are three main theories or

explanations of the yield curve. These theories which attempt to explain why a yield

curve has the shape that it does, are: (Pure) Expectations Theory Liquidity Premium Theory Market Segmentations Theory

The question for this lecture is whether or not these, theories may be used to forecast (i.e., predict) future moves and levels of interest rates!

Forecasting Interest Rates Using the Expectations Model The Expectations Model may be used to forecast

“expected” future spot interest rates. This model assume that the long term spot interest

rate is an average of short term (both spot and forward) rates.

Thus, if we observe a: Short term spot rate and A long term spot rate We can calculate what the forward rate must be to produce the

observed long term spot rate.

Formula for Forecasting Interest Rates Using the Expectations Model The formula we use to derive the Expectations

Model “expected” forward rate (ie), on a one-period bond for some future time period (n-t) is as follows, where: Ils = the observed long term rate. Iss = the observed short term rate.

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Expectations Forecasting Example #1 Assume current 1 year short term spot interest rate

(iss1) and current 2 year long-term spot interest rate (ils2) as follows: iss1 = 5.0% and ils2 = 5.5%

Then, in equilibrium, the expected 1 year forward rate, 1 year from now (ien-t) must be:

Note: A 6% forward rate is the only rate which will produce the two observed spot rates.

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Yield Curve Example #1

i rate

6.0 oie This is the forecast (forward rate)

5.5 o

5.0 o This is the observed yield curve

1y 2y

Term to Maturity →

Expectations Forecasting Example #2 Assume current 1 year short term spot (iss1) and

current 2 year long-term spot (ils2) rates are as follows: iss1 = 7.0% and ils2 = 5.0%

Then, in equilibrium, the expected 1 year forward rate, 1 year from now (ien-t) must be:

Note: A 3% forward rate is the only rate which will produce the two observed spot rates.

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Yield Curve Example #2

i rate

7.0 o

5.0 o This is the observed yield curve

3.0 oie This is the forecast (forward rate)

1y 2y

Term to Maturity →

Liquidity Premium Theory The Liquidity Premium Theory assumes that long

term bonds carry greater risks and therefore investors require greater premiums (i.e., returns) to commit funds for longer periods of time.

Therefore, if we use the Liquidity Premium Theory to forecast future interest rates, we need to observe the follow: We need to make some estimate as to the liquidity

premium per maturity. We then subtract our estimated liquidity premium out of the

forecast (i.e., forward) rate.

Forecasting Interest Rates Using the Liquidity Premium Theory We can use the Liquidity Premium Theory to

forecast future interest rates. But to do so: We need to make some estimate as to the liquidity

premium per maturity. We then subtract our estimated liquidity premium out of

the forecast rate. Start with the Pure Expectations Forecast formula:

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Forecasting Interest Rates Using the Liquidity Premium Theory We can use the Liquidity Premium Theory to

forecast future interest rates. But to do so:

(1) We need to make some estimate as to the liquidity premium per maturity, and

(2) We then subtract our estimated liquidity premium out of the forecast forward rate.

Formula for Forecasting Interest Rates Using the Liquidity Premium Model The formula we use to derive the Liquidity Premium “expected”

forward rate (ie), on a one-period bond for some future time period (n-t), is a follows, where: Ils = the observed long term rate. Iss = the observed short term rate. lp = the assumed liquidity premium in the long term rate.

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Liquidity Premium Forecasting Example #1 Assume current 1 year short term spot interest rate

(iss1) and current 2 year long-term spot interest rate (ils2) as follows: iss1 = 5.0% and ils2 = 5.75%

Also assume the liquidity premium on the two year bond is .25%.

Calculate the Liquidity Premium model’s forecast (forward rate) for the 1 year interest rate, one year from now.

Liquidity Premium Forecasting Example #1 The expected 1 year forward rate, 1 year from

now without a liquidity premium (ien-t) is:

The expected 1 year forward rate, 1 year from now with a 25 basis point liquidity premium is:

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Liquidity Premium Forecasting Example #2 Assume current 1 year short term spot interest rate

(iss1) and current 2 year long-term spot interest rate (ils2) as follows: iss1 = 5.0% and ils2 = 5.75%

Also assume the liquidity premium on a two year bond is .75%.

Calculate the Liquidity Premium model’s forecast (forward rate) for the 1 year rate, one year from now.

Liquidity Premium Forecasting Example #2 The expected 1 year forward rate, 1 year from

now without a liquidity premium (ien-t) is:

The expected 1 year forward rate, 1 year from now with a 75 basis point liquidity premium is:

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Liquidity Premium Forecasting Example #3 Assume current 1 year short term spot interest rate

(iss1) and current 2 year long-term spot interest rate (ils2) as follows: iss1 = 5.0% and ils2 = 5.75%

Also assume the liquidity premium on a two year bond is 1.00%.

Calculate the Liquidity Premium model’s forecast (forward rate) for the 1 year rate, one year from now.

Liquidity Premium Forecasting Example #3 The expected 1 year rate, 1 year from now

without a liquidity premium (ien-t) is:

The expected 1 year rate, 1 year from now with a 100 basis point liquidity premium is:

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Differences in 3 Forecasts Note: Observed short term rate = 5.0% and long term

rate = 5.75% Then Assuming Forecasted Forecasted

Spot Rate Change in 1 yr from Now Spot

Rate* No Liquidity Premium 6.5% +150bps LP of .25% 6.0% +100bps LP of .75% 5.0% no change LP of 1.00% 4.5% - 50 bps

*In basis points over current 1 year spot rate of 5.0%

Yield Curve and Differences in Liquidity Premium and Expectations Forecasts (Oie) i rate

6.756.50 oie (No Liquidity Premium) = 6.5%6.256.0 oie (.25% LP) = 6.0%5.75 o5.55.25 Observed Yield Curve5.0 o oie (.75% LP) = 5.0%4.754.5 oie (1.00% LP) = 4.5%

1yr 2yr Years to Maturity

Liquidity Premium Forecasting Issues If there are liquidity premiums in longer term

spot interest rates, NOT subtracting them out will result in “over” forecasting errors. That is, the Expectations forecast will have a

upward bias. Questions (or problems for forecasting):

First, Is there a liquidity premium, and if so SECOND, HOW MUCH IS IT?

Market Segmentations Theory The Market Segmentations Theory explains how the

yield curve might respond over the course of a business cycle.

Essentially, this theory suggests that: (1) the yield curve may become downward sloping just

before the economy enters into a recession (or slowdown), and

(2) the yield curve may become upward sweeping near the end of a recession, or beginning of an expansion.

This model is based observing yield curve patterns and assuming borrowers and lenders will move away from their neutral positions in financial markets and interest rates change.

Yield Curves Prior to a Recession Near the end of a business expansion (period before

shaded areas) short term rates exceed long term rates. Thus, during this period we would observe a

downward sloping yield curve.

Yield Curves Near the Beginning of an Expansion Into a recession (shaded area), short term rates come

down faster than long term and eventually, near the end of the recession or beginning of the expansion, short term rates fall below long rates. Thus, during this period we would observe an upward

sweeping yield curve.

Near the End of a Business Recession or Early Expansion Short term rates below long term. (Severe) Upward sweeping yield curve. Why this shape?

Interest rates have fallen during the recessionary period and are now “relatively” low.

Borrowers realizing that rates are relatively low, finance in the long term (wanting to lock in long term liabilities at low interest rates).

Lenders realizing that rates are relatively low, lend in the short term (not wanting to lock in long term assets at low interest rates)

Note: Both borrowers and lenders accentuate their natural tendencies.

Forecasting with Market Segmentations Theory The Market Segmentations Theory CANNOT be used to

forecast future spot rate (forward rates). The Market Segmentations Theory can be used perhaps

to identify (signal) turning points in the movement of interest rates (and in the economy itself) based on the shape of the curve. Downward sweeping curve suggests a fall in interest rates,

the end of an economic expansion, and a future economic (business) recession.

Severe upward sweeping curve suggests a rise in interest rates, the end of an economic recession, and a future economic (business) expansion.

But there are problems: Lags (see next slide) And some forecasters think the model no longer works.

Upward Sweeping Yield Curve in Early 2002; Recession Ended in Early 2003

What Does the Yield Curve Look Like Today and What Would the Market Segmentations Theory Tells Us About Future Business Activity?U.S. Yield Curve: September 6, 2006

http://www.bloomberg.com/markets/rates/index.html