Interest rates and default risk premiums

Last week’s lesson noted that the Fed’s control over the federal funds rate, in effect gave it a very high degree of control over yields and interest rates in financial markets where maturities are short and default risk is low. This is because federal funds market lending also possesses these same two properties of short maturity and low default risk. If yields on assets with similar properties diverged noticeably from each other, every investor would start to sell off the lower yielding asset (driving its price down & its yield up) and pour the funds released into the higher yielding asset (driving its price up and its yield down). This activity would quickly drive the assets’ yields back together. Thus, as long as the markets believe that the Fed is committed to maintaining a given interest rate target in the fed funds market for the short run, relatively low risk short run yields throughout the financial system will remain in the near neighborhood of the federal funds rate.
However when we turn to markets or categories of bank loans that have longer maturities or that have varying degrees of non-negligible default risk, the situation is more complex. In this week’s lesson we will see that the Fed’s control over longer term yields and interest rates in markets with default risk is far less tight than its control over rates in short term markets with very low default risk. We will argue that to attain its interest rate objectives in longer term markets, the Fed must influence not just current short term rates, but also expectations of future short term rates. In this set of notes, we will briefly discuss the default risk structure of interest rates (yields). In a second set of notes we will discuss the long-term/short-term structure of rates.
Default Risk and the Structure of Interest Rates
Default risk exists in loan markets or markets for financial instruments whenever there is some possibility that the borrower or the issuer of the financial asset will not deliver contractual payments on time and in full amount. The greater the probability of default, the higher must be the interest rate or yield to compensate the lender or asset buyer. Lets run through a simple example to illustrate this point.
Assume a 1 yr Treasury Bill is currently priced to yield 6%. This security has no default risk.
Assume a 1 yr Loan to the “” internet start-up has a 40% chance of defaulting, and that in the event of default the bank will receive back only 20% of it’s initial investment from sale of the loan’s collateral. How high a rate of interest would the bank have to charge to obtain an expected rate of return = 6%? (i.e. If the bank had lots of such risky lending opportunities, how high a rate of interest would have to be charged in order to earn a 6% return overall, even after allowing for the losses on the non-performing loans?)
Solution: Let the rate that solves this question be designated “z.” Then 60% of the time the bank earns (z) on this category of risky investment and 40% of the time it earns only -80%.Therefore the weighted “average” or expected rate of return overall if this category of loan were made repeatedly would be:[.6(z) +.4(-80)]
The expected return = 6% when .6z +.4(-80) = 6 or when .6z = 38 or when z = 63.3%!
Thus a lender would have to charge borrowers with this default rate probability 63.3% just to have an expected return equivalent to the certain return of 6% on the treasury security!
Therefore, higher default risk necessarily implies higher interest rates or yields simply to equalize the expected rate of return across assets. However, investors generally dislike bearing risk and therefore will not be willing to buy or hold risky assets unless yields on those risky assets are high enough to permit the investors to receive an expected return higher than the return on less risky assets. Therefore, in practice, the interest rate charged to risky borrowers such as Zits-R-Us would be even higher than indicated by the calculations in the above example. The greater the degree of risk aversion on the part of investors, the greater the yield differentials between assets with different degrees of default risk.
Changes in the Default Risk Structure of Yields or Interest Rates
The previous few paragraphs have argued that the interest rate differentials between assets that are similar except for differences in their degree of exposure to default risk, will depend on: a)investor estimates of the probability of default; b)degree of investor aversion to bearing risk. If any development in the economy altered either investor perceptions of or attitudes towards default risk, then yields on assets subject to default risk could change even if the Fed had not altered its federal funds rate target. For example, several years ago the default by Russian banks on some large loans to western money center banks triggered an increase in both perceptions of and attitudes towards default risk throughout the world financial system. Yields on “junk” bonds and even on moderate grade corporate bonds rose sharply in the US., even though the Fed had not changed its target rate in the federal funds market. In this case, the Fed realized that it would have to reduce its federal funds rate target to alleviate market fears of a global slowdown. While this move and two subsequent reductions in the federal funds rate by the fed did help to prevent full blown panic in the markets, it was several months before corporate borrowing rates and yields on corporate bonds returned to levels seen before the Russian default.
Generally, investor perceptions that the economy will slide into a recession will raise yields on financial instruments subject to default risk , while perceptions that strong economic growth will resume or continue lower yields on instruments subject to default risk. If the investing public lost confidence in the ability of the Fed to halt an economic slide by reducing its federal funds target, corporate borrowing rates might not decline even if the Fed were reducing its federal funds rate target. Such a situation would seriously undermine the ability of the Fed to fight recessions with expansionary monetary policy!
In the next set of notes we will discuss more broadly the relationship between long term and short term rates, even where default risk is not an issue. (For example, the relationship between yields on short term treasury and long term treasury securities, none of which are subject to default risk.) We will see that expectations of changes in the future prices of longer term securities can cause their yields to behave differently than short term yields, complicating the role of the fed in managing long term interest rates. Just as we have noted in the paragraph above, we will see that the success of Fed policies will depend critically on the credibility which the Fed has with investors!
The file attached in PDF.
Long Term interest rates and expectations of future interest rates

In the last set of notes we discussed how investor perceptions of, and attitudes towards, default risk could create situations where the interest rates that corporate borrowers paid to obtain funds might not move in completely parallel fashion to changes in the fed funds interest rate and other short term interest rates. In this set of notes we discuss a second important reason why the behavior of long-term rates does not always follow the behavior of short-term rates. We will see that if investors expect future short-term interest rates to behave differently than current short-term rates, the behavior of long-term rates may diverge from the behavior of short-term rates even if investor perceptions of default risk are not an issue. Investors often look at the relationship between yields on short-term treasury bills vs. yields on long-term treasury notes and bonds (none of which are subject to default risk) to gain clues about investor expectations of future interest rates. Information on the relationship between treasury yields and maturities is published every day in the Wall Street Journal’s “Credit Markets” page and on popular financial websites such as Bloomberg.

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Interest Rate Risk

If interest rates changed by a small amount and, therefore, the yields required by investors to willingly absorb treasury securities into their portfolios also changed, the market prices of treasury securities would change. (Recall that we have already seen that the prices of bonds necessarily move in the opposite direction from changes in bond yields.) However, the key point here is that the % change in the market price of longer-term securities is much greater than the % change in the price of short-term securities for any given small change in required yields. Thus if interest rates across the board were all to rise by a small amount such as .5%, the prices of 10-year treasury notes would fall substantially more than the prices of 1- year treasury bills. Existing holders of the 10-year notes would suffer a larger proportionate loss than holders of the 1-year T-bills. This phenomenon is called “interest rate risk.”

It is possible to develop a formula to predict the % change in a security’s price for a given small change in required yields, but that is beyond the scope of this class. Instead, we’ll just give a simple numerical example involving a 1-year and a 2-year treasury security. To keep the math even simpler, we’ll assume that the 2-year security has no coupon payments during its lifetime but simply pays a face value payment on its maturity date. (Such securities are known as ‘0-coupon’ securities.)


Let’s assume that both the 1 and 2-year securities have a face value of $100,000 and that both are initially priced to yield 5% but subsequently decline in price as the yields required to clear the market rise by .5% to 5.5% for both.

For the 1 year security: P0(1.05) = $100000 before the change and P1(1.055) = $100000 after the change. The percent change in P = (P1-P0)/P0
= [100000/1.055 -100000/1.05]/(100000/1.05) = -.0047 = -.47%

For the 2 year security: P0(1.052) = $100000 before the change and P1(1.0552) = $100000 after the change. The percent change in P = (P1-P0)/P0
=[100000/(1.0552)-100000/(1.052)]/100000/(1.052) = -.0094 =-.94%

Thus, the % loss on a portfolio of 2-year securities as interest rates rose would be twice as great as the % loss on a portfolio of 1-year securities. Of course, if interest rates and required yields on securities fell, the market price of 2-year securities would rise twice as far proportionately as the prices of one-year securities. But, investors still dislike the greater price volatility of longer-term securities, given that they can seldom be certain of the direction of future interest rate movements.Therefore, normally, longer-term securities must be priced to yield investors a higher rate of return than shorter-term securities to compensate them for the greater exposure to unforeseen increases in interest rates.





The chart above shows a picture of the treasury yield curve for February 8th and 9th. Notice that as maturities rise from 2 years to 30 years, yields rise from 4.6% to 5.35%. This is the pattern that our discussion in the paragraph above of interest rate risk would lead us to expect. Note however that at the short maturity end of the curve from maturities of 3 months out to maturities of 2 years, yields actually fall as maturities increase! This, phenomenon, known as “yield curve inversion,” is precisely the opposite of what our discussion thus far would lead us to expect. The explanation for this unusual pattern lies in investor expectations of future interest rate movements. An inverted yield curve over a 2-year time horizon means that investors strongly expect interest rates to fall over the next two years. We explain the relationship of expectations of future rates to the shape of the treasury yield curve in the paragraphs below.


Expectations of Future Interest Rates and the Shape of the Treasury Yield Curve.
If an investor sells a financial asset prior to its maturity date, the rate of return earned on that financial asset will not necessarily equal the yield the investor would have obtained if he or she had held the asset until maturity. For example, if an investor paid $87, 343.87 for a 2 year bank CD which had a maturity value of $100,000 and held that security to maturity, the annual rate of return would = 7%. ($87,343.87 [1.072] = $100,000) However, if interest rates on 1 year securities were only at the level of 5% one year after the investor bought the CD, it would be possible to sell the CD at a price which would allow 5% return over the following year. The price which allows a 5% rate of return is $95,238.10. ($95,238.10 [1.05] = $100,000) If the investor sold the security at that price of $95,238.10 he or she would earn a rate of return =
(95238.10-87,343.87)/87,343.87 = 9%!


In this example, the realized rate of return over one year on this asset rose above its yield to maturity when it was originally issued because interest rates fell. If interest rates during the year had risen, then the rate of return on the asset would have declined below its original yield to maturity. Since many investors who buy bonds or CD’s do not plan to hold those bonds or CD’s until maturity, the published yield to maturity will not be an accurate measure of their expected return whenever they expect a noticeable change in interest rates. That is, investors’ expectations of future interest rates are crucial to determining their expected rate of return on bonds and CD’s. Only if they do not expect any noticeable change in rates will the published yields to maturity at the point of purchase be an accurate reflection of their expected rate of return.


In the above numerical example, if investors expected 1-year interest rates to be only 5% one year from now and yields to maturity on 2-year CD’s were currently 7%, yields on 1-year securities would have to equal 9% in order for an investor to expect the same one year return on a 1-year and on a 2-year CD. Investors, as noted earlier, require a slightly higher rate of return on riskier long term securities and, therefore 1-year yields might not have to be quite as high as 9% to induce investors to buy 1 year CD’s, but they would certainly have to be above the 7% yield that 2-year securities were currently advertising. That is, with a steep decline in interest rates predicted over the coming year, the treasury yield curve will be inverted in the 0-2 year maturity range.

The situation described in this example is an exaggerated version of what we are witnessing with the current downward slope of the yield curve for early February 2001 pictured above. At this point in time, investors widely anticipate a recession and believe that the Fed will be placing further downward pressure on interest rates over the coming year. Thus the expected return on 2-year securities if held for only 6 months or a year is well above the published yields to maturity on those securities. Hence, investors are eager to buy them even though their yields are below those on 6-month or 1-year securities.


By a similar process of reasoning we can establish that if investors believed that interest rates were going to rise in the future, then the treasury yield curve would slope upward more steeply than normal. If investors think interest rates will rise going forward, they assume that the prices of treasury securities will be falling. Thus, the expected return on securities which they anticipate selling prior to maturity is less than the published yield to maturity. This means that the published yield to maturity on longer term securities must be substantially higher than short term yields in order to raise investors’ expected rate of return on long term securities sufficiently above the expected return on short term securities to compensate investors for the greater risks of longer term securities. Historically, the typical yield difference between 3-month yields and 10-year yields has been about 1.2%. So if (i10 yr-i3 month) >> 1.2% it is a sign that investors expect rising interest rates!


Implications for Federal Reserve Policy
Because the behavior of long term bond prices and yields depends on investors’ expectations of future short term interest rates, the Fed can’t always assume that long term rates will move in tandem with short term rates when it announces changes in its federal funds interest rate target. For example, if the FED lowers its interest rate target in the federal funds market and short term rates decline, but investors believe that the lower rates will trigger a spending boom that will, in turn, generate increased inflation pressures, then long term rates may decline little if at all! Investors will be concerned that as the expected inflation materializes, interest rates will rise and bond prices will fall. Thus, even though short-term yields have declined, the prospect of capital loss may deter investors from purchasing longer-term securities. Prices of long-term securities under these circumstances do not rise and their yields do not fall.

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In next lesson we will discuss Federal Reserve policy in an AS/AD framework. We will incorporate in that discussion, where appropriate, comments on when short rates and long rates do not move in tandem and what the consequences are for the success or failure of FED policies.


Monetary Policy: Preventing/Fighting Recession
AS/AD View of Monetary Policy: The Recession Case

In the last few weeks we have discussed how the Fed uses open market operations to adjust the federal funds rate to its desired target, and how this influences other interest rates in the economy. In this week’s lesson we integrate that material into the AS/AD model of the economy that we developed earlier in the term. In this set of notes we will discuss monetary policy when the economy is in a recession or when the Fed believes a recession is imminent. A second set of notes will discuss monetary policy when the economy is at or near full employment.

In the diagram below, the black lines represent an economy in which AD is insufficiently large to absorb the output the economy can produce when at full employment. Assume that the Fed believes that these black lines represent the actual position of the economy in one year if the Fed does nothing…i.e. if the Fed simply maintains its existing Federal Funds rate target. In this case, the Fed’s policy objective is to shift AS and AD conditions such that AS = AD at full employment RGDP. The Fed will attempt to achieve this policy objective by reducing its Federal Funds rate target. Usually it reduces the target federal funds rate in a series of 1⁄4% and 1⁄2% steps. The red lines in the diagram below illustrate the resulting change in AS and AD if the Fed’s rate reductions are successful in achieving the Fed’s objectives. In the following paragraphs we will discuss the sequence of events that occurs when the Fed’s rate reductions work as hoped, and then we will discuss what can go wrong and lead to a failure of monetary policy. To combat the great recession of 2007-2011, the Fed actually has reduced the fed fund rate (the ST interest rate target to its lowest level (from .5 to zero%) in its history.


When the Fed reduces its Federal funds rate target in an effort to avoid a recession or help the economy emerge from a recession, it hopes that the following sequence of events occurs:

1) The Fed purchases Treasury securities in greater volumes in order to increase the rate at which it adds reserves to the banking system …this reduces the actual federal funds rate down to the Fed’s new lower target;

2) Other short term interest rates follow the federal funds rate down;

3) Investors revise downward their expectations for future interest rates as current short term interest rates decline; also fears of default lessen…these developments cause demand for longer term and riskier securities to rise, so that long term and corporate bond rates follow short term rates down;

4) The reduction in interest rates increases the demand for physical investment goods, including residential housing. This effect will be stronger if entrepreneurs’ expectations of the profitability of physical capital investments are increased by the decline in rates…i.e. if entrepreneurs believe that the Fed’s policy to stimulate the economy will work.

5) The resulting increase in I sets in motion a multiplier process that shifts AD to the right by a multiple of the increase in investment goods production.

6) The increase in I also increases labor productivity. This shifts AS and Qfull to the right and also shifts AS down.

7) The net result shown on the diagram above is that the economy ends up at point instead of at point 1…this represents a substantial gain in RGDP with little or no increase in the economy wide price level!

However, the rosy scenario sketched in the above paragraph may not always unfold. In particular, problems can arise at either step 3 or step 4 of the above chain of events which result in little or no overall increase in I and, therefore, little or no shift in either AS or AD. I.e.… It is completely possible that despite reductions in the fed funds interest rate, the economy stays stuck in recession at point 1! The key issue is the behavior of expectations among lenders and entrepreneurs following the Fed’s reductions in the federal funds rate. One possibility is that lenders and financial market investors believe that the short-term interest rate reductions are only temporary and that as soon as the economy starts to recover, inflation rates and interest rates will start to climb again. In this case, the demand for longer-term securities will not increase significantly because investors will fear capital losses on these securities as interest rates in the future rise. This will mean that longer-term interest rates decline little if at all. Since entrepreneurs prefer to finance physical capital goods with long term fixed rate loans or bonds, the failure of these rates to decline implies little or no stimulus to I. A second problem, particularly if an economy has already sunk deep into a recession and firms are operating with substantial excess capacity, is that entrepreneurs’ expectations of the profitability of new I are so depressed that even that even substantial reductions in borrowing costs are insufficient to motivate additional I. Why add additional machines and productive capacity when you can’t fully utilize your existing equipment and facilities?

The situations outlined in the above paragraph are not just theoretical possibilities. They have both been illustrated in the last 20 years. For example, in Japan the central bank in the latter half of the 90’s pushed short term interest rates under 1% without leading to any surge in I. In the US during the recession of 1990-1991, the Fed lowered its Fed funds target from 8% to 3%, but long-term interest rates only fell by 1.5%…not enough to ignite an investment boom. Eventually, by 1993, investors began to believe that lower rates were here to stay, bond markets rallied and the economy took off. But the economy suffered through two years of little or no growth waiting for this shift in investor expectations. (When expansionary monetary policy fails to ignite a stalled economy, expansionary fiscal policy may be needed to complement the expansionary monetary policy. We will discuss expansionary fiscal policy in a future lesson.) The Fed has lowered the federal fund rates significantly to less than 2% in late 2008 and beginning of 2009 in order ease out the credit market crisis, which froze the financial market since 2007. The fed again reduced it to its lowest level of .5% in 2010 to further stimulate the economy for quick recovery of the great recession of 2007. In this context, the role of the Fed has been further strengthened in controlling the current recession. We will discuss this important role of the Fed in coming weeks.

A final source of expansionary policy failure is prediction error. That is, the Fed’s forecast of future AD may be in error. For example, in the above diagram if AD growth were stronger than the FED believed, so that even without interest rate reductions aggregate demand would reach AD’, then there would be no need for an expansionary monetary policy. If the Fed did embark on such a policy because it underestimated AD, the result would be that the economy would be pushed beyond full employment into the zone of accelerating inflation. We will discuss the difficulties that occur when the economy is allowed to grow beyond full employment in the next set of notes in this week’s lesson.
Now Answer the quiz questions. I divided by 3 parts, answer all the parts properly.

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1) Assume that an investor is risk-neutral (i.e. assume that the investor always chooses the investment with the higher expected rate of return even if it is riskier). If the yield on 1-year marketable CD’s is 6% while the yield on 2-year marketable CD’s is 7% and this investor purchased the 1year T-bill, what must (s)he expect to happen to short term interest rates over the coming year?
2) In question # 1 above, what is the expected interest rate level one year from now that would equalize the expected rate of return on one year and two year CD’s if both were held for one year?
3) If the Fed lowers short term interest rates by 1/2% but investors believe this is just a temporary reduction which will only last a few months, and therefore their expectations of future short term interest rates remain unchanged, what will happen to the yield on 10 year Treasury bonds?
4) If at a point in time long term interest rates were below short term interest rates, what would this indicate about investors expectations of future short term interest rates? Explain your answer in a few sentences.
5) If investors thought that a reduction in the Fed’s Federal Funds market interest rate target would cause inflation rates to increase in the future, what would happen to the shape of the treasury yield curve? Draw a diagram to illustrate your answer.
6) If interest rates and required yields at all maturities unexpectedly fell by .5% in a month, would a portfolio of long term securities perform differently than a portfolio of short term securities? explain your answer and relate it to the concept of interest rate risk.
7) Bond rating agencies such as Moody’s publish rankings of the credit quality of corporate borrowers. AAA rated corporations have the lowest level of default risk followed by AA and A the Baa, etc. Under what circumstances would the spreads between yields on bonds issued by ‘B’ rated corporations and yields on AA rated corporate bonds widen noticeably?
8) Suppose 1 year Treasury-bills were currently yielding 5.5%. Also suppose that a bank estimated that a particular loan applicant had a 30% chance of defaulting on a one year loan and that in the event of default the bank would recover only 25% of its scheduled payment of principle (estimated net proceeds of the sale of collateral). What interest rate would the bank have to charge to earn an expected rate of return on its loan equal to the T-bill rate?
Second part
1) When the economy is close to or at full employment why is it difficult for the Fed to decide whether or not to change its interest rate target in the federal funds market?

2) Explain why monetary policy makers believe that it is important to start restraining growth in aggregate demand before there is a noticeable increase in the CPI.

3) Draw an AS-AD diagram to illustrate the effects of rising inflation expectations on an economy threatened by inflationary growth in aggregate demand. Explain your diagram clearly.

4) Explain why expansionary monetary policy may be relatively ineffective and slow in helping an economy recover from a serious recession

5) Draw an AS-AD diagram to illustrate the results of a successful expansionary monetary policy.

6) Assume that workers, employers and investors all believed that inflation in the coming year would equal the annualized rate of inflation experienced in the past 6 months. Also assume that workers had been receiving nominal wage gains of 5% during a several year period where the annual inflation rate was 2%. and worker productivity growth was 3% per year. Now assume that a decline in the unemployment rate below NAIRU creates conditions where workers push for an annual real wage increase of 4%. Also assume that labor productivity growth declines to 1% per year as unemployment is squeezed below normal frictional & structural levels.

a) what rate of nominal wage growth will workers seek at the new low unemployment rate?

b) how fast will firms have to raise prices given your answer in (a) in order to protect profit margins?

c) if the rate of inflation in (b) occurs and the Fed allows AD to grow fast enough to maintain the unemployment rate below NAIRU for another year, what rate of nominal wage growth will workers seek in the following year?

d) if the rate of inflation in (b) had persisted for 6 months or more, how large an increase in the federal funds rate would be needed to increase the level of real interest rates in the economy?

7) Is the Fed currently pursuing an expansionary, neutral, or contractionary monetary policy? What if any difficulties do you think may be encountered in implementing the current policy being pursued by Fed Chai Janet Yellen (who succeeded Ben Bernanke in Feb 2014) to cope with one of the worst financial crises in the US since the Great depression?
Third part
1) One cornerstone of President George W. Bush’s economic policy during his first term in office was tax cuts targeted towards high income and high net worth households. Under his proposals the marginal tax rate applied to capital gains taxes has been reduced, taxes on stock dividend have been eliminated and marginal tax rates on wage and interest income, particularly those applied to high income brackets have also been reduced. Please note that the Bush Tax Cut has been extended by Obama Admin for 2 more years, 2011 and 2012 (Expired on Dec 31, 2012) and further extended in 2013 with some modifications.

a) What would be the short-run effects of tax cuts on interest rates and growth in RGDP given that the economy was in recession at the time of Bush’s tax cuts? Contrast the Keynesian and crowding out perspectives on this question.

b) If in question (a) we were interested in the long run effects of the proposed tax cuts would a “supply side” economist give a different answer to this question than an economist who believed that federal budget deficits created significant “crowding out” effects? Explain.

2) “Market Slump Helps Sell Tax Cuts Now.” (Headline from fall 2000) Explain from the standpoint of Keynesian macroeconomic theory why the slump in the stock market that began in the spring of 2000 help build support for Bush’s tax cut proposal in his first year in office

3)The exchange rate of the $ has declined by 20% or more against the currencies of major US trading partners during the past year. Do you think the Fed welcomes continued weakness in the exchange value of the $ at this time? Explain your answer carefully.

4) What is the “crowding out” effect of budget deficits? What determines whether crowding out leads to a minor or major reduction in the impact of expansionary fiscal policies on Aggregate Demand?

5) Why do think the European Union countries decide to have a single central bank and a single currency, instead of just agreeing to maintain fixed exchange rates among their currencies?

6a)What fiscal policies are recommended by conservative “supply-side” economists?

6b) What assumptions about the behavior of savers and investors are required for conservative supply side theories of the benefits of tax cuts to be correct?

6c) Why did the experience of the 1980’s following the massive Reagan tax cuts discredit supply side theory in the eyes of many economists?
7) How can large government deficits lead to large trade deficits?
8) Although the monetary authorities are concerned that the high level of the $ exchange rate is holding back the economic recovery, (see e.g. question 3a), they are afraid of a sudden major negative shift in investor sentiment towards the $. Explain why.