FNCE 302, Investments H Guy Williams, Equilibrium Rates (how changes in world effect int rates)

Overview Real vs. Nominal Rate (consumable vs. financial) Equilibrium Rates (how changes in world effect int rates) Structure of the Yield Curve (will review 3 theories) Some of the following material comes from a variety of sources but especially Financial Markets and Institutions, Madura We need to understand interest rates, what drives them, what market conditions effect them, supply & demand, how. But most importantly we need to understand, how does the economy effect them. How do interest rates react to a change in the marketplace? We need a theory of interest rates and the structure of the yield curve. Real vs. Nominal Rate Suppose I purchase a one-year zero-coupon bond Face value $1,000 Price $930 What is the RATE OF RETURN on this investment? Invest $930 Receive $1,000 in one year if the NOMINAL RETURN is R then: investment Nominal Return, R = 1 return 930 x (1 + R) = 1,000 solve for R = (1000/930) 1 = 7.5% Real Rates are returned in the form of Consumption Goods. (returns you can eat) A Nominal Rate is a return in Dollars. (returns you can't eat) Real Rate of return is measured in terms of things you can buy. Nominal Rate only measures financial return, dollars. But now consider the effects of inflation. Say inflation is increasing the cost of living 3% per year FNCE302: Investments Lecture 3 Page 1

Real vs. Nominal Rate Suppose now that INFLATION is working against us making my cost of living increase by 3% over the same period Now, my $1,000 does not purchase as much as it could compared to the beginning of the period Think about it in concrete terms Imagine all I consume is pizzas At the beginning they cost $8 each Their price increases at the rate of inflation The $1000 return has been eroded. What is my return in pizzas? Pizza prices will be $8 x (1 + inflation) = $8 x 1.03 = $8.24 in one year $930 8 So at the beginning my $930 would buy 116.25 pizzas And at the end my $1,000 will buy $1000 8.24 121.36 pizzas What is the rate of return on the investment in pizzas? I invest 116.25 pizzas and receive 121.36 pizzas in one year, so if the real return is r then: 116.25 x (1 + r) = 121.36, r is the RETURN measured in REAL terms. Algebraically, if we define I as the inflation rate then: investment Nominal Return, R = 1 return r Closing Return 1 Opening Return r 121.36 1 4.395% 116.25 1 + r = (1 + R)/(1 + i) restated r = (R i)/(1 + i) Approximately, r = R i real = Nominal - Inflation (1+i) approx. = 1 because i is small. FNCE302: Investments Lecture 3 Page 2

Fisher Effect: interest rates are dependent on the level of inflation in the economy. Fisher Effect says the REAL rates stay roughly constant over time. Therefore, the NOMINAL rate moves in lockstep with inflation. This is just one theory of how interest rates change. This can be expressed as r = R expectation of Inflation (or expected inflation). An Interest Rate is the price of money, the price of credit. The price I pay or extract in the process of barrowing. It is the price of money! As such the interest rate is a factor of the supply and demand of money. The more people are willing to lend the lower interest rates should be. The more people want to barrow the higher interest rates should be. Supply of credit are those people who are supplying funds, deman for credit are those people who want to barrow funds. So we will look at different things which effect supply and demand of credit and consider what effect these things have on EQUILIBRIUM RATES Equilibrium Rates Interest rate levels are a factor of the supply and demand of credit The supply of credit is increased by an increase in the amount of money made available to borrowers. For example, The more banks can lend, the more credit there is available to the economy: As the supply of credit increases, the price of borrowing (interest) decreases If households decide to save more than 1% or their income and there will be a greater supply of credit. The more banks can lend the more credit there is available to the economy. This is the basis of the loanable funds theory What If Questions, if this happens in the real world what is likely to happen to interest rates? Say the FED lowers the reserve rate (percentage banks must keep on hand). Now more money is available to the banks to loan, but the question is, will they loan it out? Chances are they will find other ways to make money with it. Will put the money to work in some way. FNCE302: Investments Lecture 3 Page 3

Loanable Funds Theory Loanable funds theory suggests that the market interest rate is determined by the factors that affect the supply of and demand for loanable funds Can be used to explain movements in the general level of interest rates of a particular country Can be used to explain why interest rates among debt securities of a given country vary (why interest rates are different among different countries). LOANABLE FUNDS THEORY CAN BE USED TO EXPLAIN MOVEMENTS IN THE INTEREST RATE. IT IS NOT USED TO EXPLAIN WHAT INTEREST RATES SHOULD BE, ONLY TO TRY AND EXPLAIN THE REACTION OF INTEREST RATES TO MARKET CIRCUMSTANCES. THIS IS A DYNAMIC TOOL, IF SOMETHING CHANGES, HOW DO INTEREST RATES REACT? IT IS ALSO A COMPARITIVE TOOL. BUT YOU DO NOT USE IT TO PREDICT AN INTEREST RATE! Look at the factors in one country and look at the factors in another country, then you should be able to say "interest rates should be higher in this economy than they are in this economy" Now, who are the participants in the credit markets? Who are the suppliers of funds and who are the users of funds? Loanable Funds Theory Household demand for loanable funds Households demand loanable funds to finance what? mortgages, automobiles, consumer purchases, education, go on vacation There is an inverse relationship between the interest rate and the quantity of loanable funds demanded Wherever you see LOANABLE FUNDS think of CREDIT. Households have a demand for credit and capital. There is an inverse relationship between interest rates and the demand for loanable funds. Higher the interest rates the less households will barrow. Low int rates, more barrowing! FNCE302: Investments Lecture 3 Page 4

Loanable Funds Theory Business demand for loanable funds Businesses demand loanable funds to invest in fixed assets and short-term assets Businesses evaluate projects using NET PRESENT VALUE (NPV): NPV INV CFt 1 (1 k) Projects with a positive NPV are accepted There is an inverse relationship between interest rates and business demand for loanable funds Businesses use loanable funds to invest in fixed assets and short term assets. Of course they will also use it to retire debt or buy back shares but fundamentally businesses are using loanable funds to invest in projects (such as building a new plant overseas or upgrade their computer system). n t t Businesses use some form of the NPV rule to evaluate projects. k in the NPV equation is COST OF CAPITAL and it will be linked to interest rates at some level. This may be through a risk-free rate using CAP-M, a yield to maturity on bonds, it will be linked in some way. Of course, the HIGHER THE COST OF CAPITAL THE LOWER THE NPV FOR A PROJECT. Given a list of projects, with the cost of capital at one level some of them will be viable. As the cost of capital goes up the projects fall off of the NPV map. Once you get to a certain cost of capital no projects will have a positive NPV. The higher the cost of capital the less businesses invest. When the economy has high interest rates there are less positive NPV projects. This creates less of a demand from the business sector to invest in projects. FNCE302: Investments Lecture 3 Page 5

Loanable Funds Theory Government demand for loanable funds Governments demand funds when planned expenditures are not covered by incoming revenues Municipalities issue municipal bonds The federal government issues Treasury securities and federal agency securities Government demand for loanable funds is INTEREST-INELASTIC The government uses credit markets to barrow money because their budgets rarely balance. The inelastic effect is unique to governments. Regardless of the interest rate, if the government needs money it will barrow. Not so with households or businesses. Government really has no choice. Government also has to pay interest on its existing debt. This is even worse than being inelastic. In a high interest rate environment the budget deficit is likely to be higher because of financing costs. So in actual fact when interest rates go up governments actually barrow more! This is necessary to pay its increasing financing debt. This can lead to a crowding out effect. if government has a need for capital and barrows no matter what, iit will drive up interest rates and this will crowd out the business sector. Business will not barrow because the government is driving interest rates up. The governments rate curve is vertical! This is shown a little further in the notes. We will see more on this as well. Loanable Funds Theory Foreign Demand for loanable funds Foreign demand for U.S. funds is influenced by the interest rate differential between countries The quantity of U.S. loanable funds demanded by foreign governments or firms is inversely related to U.S. interest rates The foreign demand schedule will shift in response to economic conditions Foreigners barrow from the US markets. Foreign corporations barrow from US markets and foreign households can indirectly barrow from US markets. Foreign governments can barrow from US markets. But the main barrower of loanable funds from foreign entities is businesses. Their demand has an inverse relationship just as US businesses do. Their demand will also be driven between the competitive interest rates in the domestic market for these foreign funds and the US market. If they can barrow more cheaply in the US market then they will barrow funds here. If the US funds are more expensive they will not demand US funds. Inverse relationship between US interest rates and the demand of foreign entities for US funds. Loanable Funds Theory FNCE302: Investments Lecture 3 Page 6

Interest Rates FNCE 302, Investments H Guy Williams, 2008 Aggregate demand for loanable funds The sum of the quantities demanded by the separate sectors at any given interest rate is the aggregate demand for loanable funds government inelastic demand This demand curve represents the overall demand from households, businesses, government, and foreign entities to barrow money in the US. Downward sloping. High interest rates, low demand. Low interest rates, high demand inelastic is vertical, this is because the gov will barrow the same amount no matter what the interest rate is Capital FNCE302: Investments Lecture 3 Page 7

Loanable Funds Theory Supply of loanable funds Funds are provided to financial markets by Households (net suppliers of funds) Suppliers of loanable funds supply more funds at higher interest rates Foreign households, Governments, and Corporations supply funds by purchasing Treasury securities Foreign households have a high savings rate The supply is influenced by monetary policy implemented by the Federal Reserve System The Fed controls the amount of reserves held by depository institutions The supply curve can shift in response to economic conditions Households would save more funds during a strong economy Households are the main group who supply funds to the market. The higher the interest rate the more likely it is for a household to save, this makes more funds available to the market. Foreign households supply capital in the same way that domestic households supply capital, they buy gov securities, they invest in T-Bills, they buy corporate bonds, treasurer notes But foreign households are also comparing rates around the world and going to the place which is most competitive. Foreign governments are also supplying capital to the US market (saving). They do this because they run surpluses and in turn buy US securities. Japanese and Chinese for instance, they are running surpluses and need somewhere to invest that money. They invest in government securities as in doing so are suppliers of credit to the US market. Some people argue that the reason US interest rates are so low right now is due to foreign governments buying US government securities (China). But recently the Euro is competing effectively. Part of the reason is the supply of US securities is so large (bonds) which creates liquidity. When any entity buys a US government bond they are supplying capital to the market. The more people buy government bonds the lower interest rates should go. As the Chinese buy large amount of US securities, US interest rates go down. Foreign corporations will also, to some extent, buy US government securities and in doing so supply credit to the US market. Federal Reserve also influence the amount of capital in the US market. They control the amount of reserves held by depository institutions. If they lower the reserve rate there is more capital available in the marketplace. If they increase that reserve rate the money will be dead sitting in some bank, not invested in a productive way. Supply curve will shift according to economic conditions. FNCE302: Investments Lecture 3 Page 8

Interest Rates Interest Rates FNCE 302, Investments H Guy Williams, 2008 Loanable Funds Theory AGGREGATE SUPPLY CURVE: interest rates vs. the amount of capital supplied in the marketplace. Supply increases as interest rates increase. Higher the rate of interest the more households will save and the more that foreign entities will invest in US markets. High interest rate means more capital flows into the marketplace. Capital Where supply meets demand, that is, when the supply of goods equates to the demand of goods, this is where the price is set. This is the price which clears the market. Where supply of funds meets demand for funds is called the Equilibrium Interest Rate. Again, keep in mind, we are interested in how these things move given different events. We are interested in the dynamic setting not the static setting. Capital Economic Forces That Affect Interest Rates FNCE302: Investments Lecture 3 Page 9

ECONOMIC GROWTH Shifts the demand schedule outward (to the right) There is no obvious impact on the supply schedule Supply could increase if income increases as a result of the expansion The combined effect is an increase in the equilibrium interest rate What are some of the things which can change interest rates? These are all within the loanable funds theory. Economic growth, economy is doing well, growing. In this case the demand schedule will be shifted out to the right (D A1 moves to D A2 ). Why? If economy is doing well are households more of less likely to barrow? More likely, this means some of their money is no longer in savings. If economy is doing poorly people are more likely to hold on to their money, worried about future. They are saving so this puts money into the economy in terms of making it available for lending. The same is true for businesses. If the economy is doing well businesses are more likely to invest because they anticipate demand increasing in the future. They want to be ready, will build a new factory so they have product to sell. If the economy is doing poorly businesses do not invest. And it takes a long time to convince a CEO that a recession is over and they should start investing in assets again. Government: if the economy who knows. Some would argue that the government should run a surplus and not demand funds from the market. But in reality when the economy is doing well governments will often cut taxes and still run the same budget deficits. Tend to spend more. It is inconclusive what happens to the government when the economy is doing well. In all these cases the net effect tends to be that the demand schedule moves outwards. But we can only say "tends to be." This will often be the case, there are no hard and fast rules in economics. You will be able to find circumstances where this outward shift does not happen. But usually when the economy is expanding the demand for funds increases. Empirically there is no net effect on the supply side. Supply does not seem to increase very much. The supply tends to stay static. Can makes arguments for either many cases but the empirical evidence says the supply schedule remains relatively fixed. Now, what is the net effect? Supply remains fixed, demand shifts outwards, therefore interest rates should increase. When the economy grows interest rates tend to go up. (do not confuse a movement of the curve with a shift along the curve) Economic Forces That Affect Interest Rates FNCE302: Investments Lecture 3 Page 10

INFLATION SHIFTS THE SUPPLY SCHEDULE INWARD (to the left) Households increase consumption now if inflation is expected to increase Shifts the demand schedule outward (to the right) Households and businesses borrow more to purchase products before prices rise Lenders will demand higher interest rates as compensation for the decrease in the purchasing power of the money they will be repaid in the future DA1 to DA2 causes a Price shift INWARDS! Why does inflation shift the supply curve inward? If people believe that inflation is going to increase in the future they will make their big purchases today! They SPEND, no save! They believe their money is not going to be worth as much in the future I am going to do my spending now! In a hyper-inflation environment money is becoming worthless. People will not save, will just buy REAL GOODS. In general, if inflation is expected to increase people do not save as much, they spend more. Net Effect: Supply Schedule Shifts Inwards Less credit available in the market because households are saving less. Generally inflation will tend to shift the demand curve outward. Why? Not only do households not save so much, they want to barrow money today so that they can buy the real goods they seek immediately (rather than wait for the price to go up). Households will save less and barrow more! This is the main reason for the demand shift outward. Lenders will demand a higher interest rate to compensate them for the loss of purchase power. This goes back to the relationship between real and nominal interest rates. If interest rates are expected to go up people still need the same real return. Therefore, if I am lending money and inflation is going up, I tend to charge a higher rate for it. The better way to think about it is by looking what happens to supply and demand. The DEMAND schedule moves outwards, the SUPPLY schedule moves inwards. Double-Effect: not only do interest rates go up (because the demand schedule slips outwards) but because the supply schedule moves inwards they go up even further. INFLATION LEADS TO HIGHER INTEREST RATES, even without the FED acting to slow down the economy. Economic Forces That Affect Interest Rates The GOVERNMENT, through the Federal Reserve, affects interest rates FNCE302: Investments Lecture 3 Page 11

The federal funds rate, or the rate that institutions charge each other for extremely short-term loans, affects the interest rate that banks set on the money they lend (bonds = government securities) The FED affects interest rates by changing the targeted federal funds rate (overnight lending rate). Physically this is done by the FED bank in New York which works with brokers and dealers in the government securities market, to buy and sell bonds. To INCREASE INTEREST RATES they sell bonds, by selling the security they take cash out of the economy. This reduces supply. To DECREASE INTEREST RATES they buy bonds, this puts cash back into the marketplace. It adds supply. Increase Interest Rates by Selling Bonds / Decrease Interest Rates by Buying Bonds How does targeted FED funds rate compare to actual. Well, they are not always the same. In the above graphic we can see that at the end of 2007 the TARGETED fed funds rate was 4.25% but the ACTUAL fed funds rate went almost as low as 3.0%! If you look at the press during that period you will find that the government flooded the market with capital during that period, pumped money into the economy which dropped interest rates due to the increased supply. Why did they do this? Difficult to say, there is no official explanation. Some would say that they knew there was a problem with banks, a crisis with sub-prime loans. Pumping money into the economy allowed the banks to show more cash on their balance sheets at year end. Purely a window dressing exercise by the government. Some analyst believe this, that it was a ploy to make the economy look stronger. Government bought bonds aggressively which put a massive amount of funds in the market which dropped the interest rates. We can see that the effect rebounded quickly making us believe it was a completely artificial manipulation. The government is wanting the world to feel better about the banking system in the US yet there was nothing fundamentally different in the banking system between Dec 2007 and Jan 2008. FNCE302: Investments Lecture 3 Page 12

Economic Forces That Affect Interest Rates MONEY SUPPLY If the Fed increases the money supply, the supply of loanable funds increases If inflationary expectations are affected, the demand for loanable funds may also increase If the Fed reduces the money supply, the supply of loanable funds decreases. This is how they affect interest rates. During 2001, the Fed increased the growth of the money supply several times. After 9/11 they flooded the market with capital because they wanted interest rates to be lower. They drastically pushed the supply curve out. Same is true end of 2007 and beginning of 2008 (chart last page) MARKET REACTION TO VARIOUS EVENTS September 11 Firms cut back on expansion plans Households cut back on borrowing plans The demand of loanable funds declined At the same time the federal reserve was throwing cash into the market. Interest rates in the market place declined almost to 1% due to these two events. The weak economy in 2001 2002 (this was a recession) Reduced demand for loanable funds The Fed increased the money supply growth Interest rates reached very low levels This was an example of a "double-effect" from a few pages ago. Question: if inflation were negative would the principle be adjusted lower? Answer, YES! In inflation is positive principle is increased, if inflation is negative principal is decreased. FNCE302: Investments Lecture 3 Page 13

1962 1967 1972 1977 1982 1987 1992 1997 2002 2007 FNCE 302, Investments H Guy Williams, 2008 Economic Forces That Affect Interest Rates BUDGET DEFICIT A high deficit means a high demand for loanable funds by the government Shifts the demand schedule outward (to the right) because the government needs to barrow more. Interest rates increase, less supply. Gov using it all. Government is INELASTIC The government may be willing to pay whatever is necessary to borrow funds, but the private sector may not CROWDING-OUT EFFECT The supply schedule may shift outward if the government creates more jobs by spending more funds than it collects from the public In this way, crowding out effect, government budget deficits can reduce economic activity. It is not often that the gov uses deficit spending to create jobs. 16.0% 14.0% 12.0% 10.0% 8.0% 6.0% 4.0% 2.0% 0.0% -2.0% -4.0% Deficit 10-Year recession Darker line is the US Gov budget deficit (relative government barrowing) divided by the GDP (which measures the size of the economy) and the lighter line is the yield on 10 year bonds. We have used 10 year bond because it is the yield which correlates most closely to mortgages. Mortgages are priced off of 10 year gov bonds. So the question is, do budget deficits tend to drive interest rates up? We could argue yes, they tend to track pretty well. There is a disconnect around 2000 but other things were going on in the economy. FNCE302: Investments Lecture 3 Page 14

Economic Forces That Affect Interest Rates FOREIGN FLOWS OF FUNDS The interest rate for a currency is determined by the supply and demand of that currency, ie, what is going on in that economy. Impacted by the economic forces that affect the equilibrium interest rate in a given country, such as: Economic growth Inflation can drive up interest rates in one country. This will cause a global flow of funds into the highest interest rate economy. Shifts in the flows of funds between countries cause adjustments in the supply of funds available in each country Must be warry of the effect of currency movements on that return. May look at the effect of interest rates on currency levels later in course. Economic Forces That Affect Interest Rates INTEREST RATE VARIATION OVER TIME Late 1970s: high interest rates as a result of strong economy and inflationary expectations (oil shock) Early 1980s: recession led to a decline in interest rates government lower interest rates because inflation was going down and they wanted to stimulate the economy (they supplied capital to the markets) Late 1980s: interest rates increased in response to a strong economy. Economic growth meant there was a demand for funds. Also government was trying to curb possible inflation. Early 1990s: interest rates declined as a result of a weak economy (mild recession in early 1990s). decline in interest rate due to low economic activity. FED wanted to stimulate. 1994: interest rates increased as economic growth increased, result was higher interest rates. Drifted lower for next several years despite strong economic growth, partly due to the U.S. budget surplus FNCE302: Investments Lecture 3 Page 15

FNCE 302, Investments YIELD CURVE shows NOMINAL INTEREST H Guy Williams, RATES, 2008 not real interest rates. INFLATION WILL ERODE EARNINGS! Term Structure The relationship between yield to maturity and maturity Information on expected future short term rates can be implied from yield curve The yield curve is a graph that displays the relationship between yield and maturity We will consider three major theories to explain the observed yield curve Term structure is a picture of what the yield is on 10 vs 20 vs 30 year debt (bond). How much it cost for the gov to barrow money overnight vs 1 year vs 2 years vs 30 years. Term Structure is the picture of yields vs maturity. It is interesting because it may predict recession or inflation. Many reasons why investors and economist follow the structure of the yield curve. Gives important indications about what the future holds. We will look at 3 different theories to explain yield curve. Treasury Yield Curves We usually expect to see a rising curve in the marketplace. Inverted is the same as declining. Yield Curves are annualized rate, they are per year return. What do they tell us? Generally speaking, historically, most yield curves are upward sloping. Why? Consider, if investing in a 3 month T-Bill I earn 2%, if I invest in a 30 year bond I earn 4.25% (per year). I expect to earn a higher yield on a longer term bond because duration is higher and there is more risk if int rates go up. Also, there is more liquidity for short term maturities (which requires a higher rate). FNCE302: Investments Lecture 3 Page 16

Consider the inverted curve. It returns 6.25% for a 6 month bond and roughly 5.8% for 30 years. Long term is less return! What economic circumstances would bring this about? People think the economy is slowing down and interest rates are going down. Downward sloping yield curve says people are predicting that yields will decline. People interpret an inverted yield curve as a signal that recession is coming. During recession the FED will cut interest rates. So the curve is predicting that future interest rates are coming down due to recession. It is a pretty good indicator. A sharply upward sloping yield curve means investors expect an economic boom. US yield curve was recently flat. People interpret this as a sign of impending recession. See it as a strong sign of recession coming. Why a dip in the yield curve? Lets say our dip is at roughly 2 years. The FED controls near term interest rates. Technically they only effect the very beginning of the curve but they can keep on effecting it until the near term does what they want (?). So this dip is a signal that people think over the next 2 years the FED is going to be aggressively cutting interest rates. So therefore the rate will come down as the short term rates are cut by the FED. After two years the market is back on course. FNCE302: Investments Lecture 3 Page 17

How can we make money off the yield curve? Obvious that if the yield curve is upward sloping I want to invest long term and barrow short term: long term rates are up good for investor, short term rates are down good for barrower. We will see this later in course. Comments on the Yield Curve It shows NOMINAL INTEREST RATES Inflation will erode the value of future coupon dollars and principal repayments The Federal Reserve directly manipulates only the short-term interest rate at the very start of the curve The Fed s main tool is the FEDERAL FUNDS RATE The rest of the curve is determined by supply and demand (FED has little effect on parts of the curve beyond a few months) If you were able to remove expectations of future inflation from yield curve it would look very different. You can actually do this with inflation adjusted bonds, some using them to construct a yield curve would take out future expectations of interest rates. Now we look a 3 theories which try to explain the yield curve PURE EXPECTATIONS THEORY (aka Expectations Hypothesis) Pure expectations theory suggests that the shape of the yield curve is determined solely by expectations of future interest rates (particularly short term interest rates) Assuming an initially flat yield curve: The yield curve will become upward sloping if interest rates are expected to rise The yield curve will become downward sloping if interest rates are expected to decline The yield curve is made up of short term investments over time. Therefore the path of short term bond yields is predicted by the shape of the yield curve. Jan 2006, yield curve is flat. If int rates are expected to rise the slope will go up, if int rates are expected to go down the slope will go down. We will look at some mechanics as to why this should happen. FNCE302: Investments Lecture 3 Page 18

Sudden Expectation of Higher Interest Rates Suppose we have a flat yield curve today and tomorrow morning we wake up, there has been some economic event and the market believes that interest rates are going to go up. They believe that the federal reserve is going to act. Suddenly the expectation of inflation goes up, say because some consumer price index comes out. At that point the whole market suddenly thinks that inflation is going to be higher than we thought yesterday. What impact will this have on interest rates? SHORT TERM INTEREST RATES The supply of short term rates will increase. If I believe that interest rates are going to go up, would I invest my money in a 1 month bond or in a 5 year bond? Of course I would buy short term investments so that I do not lock myself in to long term investments if I believe rates are going to go up. So at the short end of the yield curve the supply (of money?) increases. The amount of money invested in short term securities goes up (making the money available to the marketplace). What about the demand? Demand for short term securities is going to decline. Why? If I am a corporation do I want to barrow money on 1 month commercial paper or do I want to barrow money on a 10 year bond if I believe interest rates are going to go up? I, the corporation, would want to barrow money on a 10 year bond because I want to take advantage of the low interest rates I see today. This says that businesses do not barrow short term money if they believe interest rates are going to rise. Impact: Demand Increases, Supply Decreases, Interest Rates Increase LONG TERM INTEREST RATES The flip side of this is to look at the long term securities. Supply declines. People do not buy the 5 year CD they buy the 1 month CD. People invest less long term. Demand increases (?). A company wants to barrow long term because rates are low right now and they want to lock in a low rate. Impact: Demand Decreases, Supply Increases, Interest Rates Decrease FNCE302: Investments Lecture 3 Page 19

Sudden Expectation of Higher Interest Rates The expectation that interest rates are going to increase will push the yield curve up. And short term rates will go down. Long term rates are going to go up. Sudden Expectation of Lower Interest Rates People will invest less in short term funds. If I believe interest rates are going to fall I will buy the 5 year CD and not buy the 1 month CD. Because I want to lock into the high interest rate which is in place today. I do not want to invest short term because interest rates are going to fall. If interest rates are expected to fall businesses barrow short term. They sell one month commercial paper. Why? Because they think interest rates are going to fall they do not want to barrow money long term. Net Impact: Short term Interest Rates go up Here people are wanting to invest long term. They want to lock in their money at the high rate available today. In this case businesses will not demand money. They demand less long term. They do not want to lock into long term barrowing at what they believe are high rates (available today). Therefore long term rates decline. Net Effect: Short term rates go up, long term rates come down, slope of yield curve flattens or goes inverted. FNCE302: Investments Lecture 3 Page 20

Yield to Maturity and Prices and Prices on Zero-Coupon Bonds ($1,000 Face Value) How are yield curves constructed? If we had a sequence of zero-coupon bonds with maturities at different dates, then we can calculate the yield at different maturities based on the price of these zero-coupon bonds. Note: the yield curves we have here are not, strictly speaking, are not true yield curves. Why? Take for example the 10 year note. A 10 year note is 20 coupon payments plus the principle payment at the end. It is actually a note of a mixture of different maturities. It's not a pure 20 year zero-coupon bond. It has a duration of less than 20 years. Therefore, it really is just a combination of many bonds across the yield curve. So strictly speaking, when you calculate the yield to maturity on a 10 year bond, that is not truly a 10 year yield. Because it's a mixture of different things. Really, we should use zero-coupon bonds. When you see a published yield curve it isn't calculated from zero-coupon bonds, it's calculated from coupons. So if we make our own yield curve we should use zero-coupon bonds. A published yield curve lets us know what the interest rates are in the economy because it looks at coupon bonds. But if you are using it to predict the path of short term interest rates, it doesn't quit work. Close but not quite. So the published yield curves are going to be pretty close to the true pure zero-coupon bond yield curve but it is not going to be exactly the same. In the old days they did not have zero-coupon bonds for long term securities so you would have to use an iterative process to break apart bonds. These days we have strip bonds that go all the way up to the 30 year maturity. Easy to find these zero-coupon bonds. So what we would do to construct a yield curve is if you know the price of different zero-coupon bonds of different maturities you can infer the yield to maturity on those bonds. The yield to maturity can then be used to construct the yield curve. This thought process will push us toward an understanding of how the yield curve predicts the path of short term interest rates. Consider these two strategies: FNCE302: Investments Lecture 3 Page 21

Two 2-Year Investment Programs Suppose I wanted to invest for a 2 year period. Imagine I have 2 choices; 1. I can invest in a 2 year zero-coupon bond. Done, no interest rate risk, no reinvestment risk, I know what I am getting in terms of the coupon rate. 2. I invest in 2 one year zero-coupon bonds. I know what the return is over the first year because if I invest in a one year coupon bond, I am getting a certain known percent. I know the one year payout. But I do not know what the payout will be over the second year. It depends on many things such as economic conditions, what the fed is doing, what happens with inflation, the foreign flow of funds I do not know for a fact what the 1 year bond will be yielding one year from today. But I can calculate a forward rate. The way I do this is this. if I invest $890 today I can infer the 1 year rate one year from today by making the return from this strategy equal to the return from that strategy. So if the return of alternative 1 (straight 2 year investment) is $1000 and I set that return equal to the second year return of alternative 2, I can calculate what the projection is for the 1 year rate is one year from today. The (spot rate) 1 year rate 1 year from today. Short Rates versus Spot Rates So we make the two strategies payoff the same and can use the result to infer what the short term 1 year rate will be in the future. We know from our zero-coupon bond that the 1 year rate today is 5%. The solution for r 2 is the predicted 1 year rate a year from today. 934.50(1 r2 ) 1000 1000 r2 1 7.01% 934.50 This is not the same as the yield on the 2 year bond. The 1 year bond of alt 1 pays 5% whereas the 2 year bond pays 6% for two years. This means the second year of alt 2 must pay more than 6% to catch the investment up to alt 1. The "Spot Rate" graph is calculating the 1 year rate 4 years from today. Notice that it has an upward sloping yield curve, 5% 6% 7% 8%. If I believe that these strategies of investments should pay the same, then this is predicting that future short term interest rates are expected to go up. The upward sloping yield curve are predicting that short term rates are expected to go up in the future (according to PURE EXPECTATIONS THEORY). PET is saying that the yield curve predicts the path of short term interest rates. FNCE302: Investments Lecture 3 Page 22

(1 f ) n n (1 y ) (1 y ) n 1 n 1 f one year forward rate for period n y Forward Rates from Observed Rates n yield for a security with a maturity of n n n 1 (1 y ) (1 y ) (1 f ) n n 1 n n n Solution is for n-1, if you pick n=4 you are solving for 1 year rate 3 years in future. f n is the forward rate. y n is the yield n periods in the future. We must know the yields at n and n-1 periods in the future. EXAMPLE using the rates in the spot rate graph on last pare: f (1 y ) (1.08) 1 1 11.06% 4 4 4 4 3 3 (1 y3) (1.07) This is our forward rate prediction of the 1 year rate for 3 years in the future. This result matches what the graph on last page shows if you are sitting at year 3 and looking at the next 1 year rate. SPOT RATE: an interest rate quoted today. FORWARD RATE: a prediction of the spot rate in the future based on the yield curve. Spot Rate and Forward Rates On Friday the yield on 1 year and 2 year treasury securities was 3.51% and 3.82%, respectively These are 1 and 2 year spot rates (rates available today) Thus if an investor bought $1 million of 1 year treasuries then he would have $1 mm x (1.0351) = $1,035,100 in one year (certain return) And if an investor bought $1 million of 2 year treasuries then he would have $1 mm x (1.0382) 2 = $1,077,859 in two years (also certain) What is the additional return earned over the second year? What is the forward 1 year rate? We must calculate f2 where I take the investment at the end of year 1, grow it by 1 plus the forward rate, and this gives me the two year return. Note that our yield curve is upward sloping (3.51% 3.82%). Solution is predicting that the 1 year arte 1 year from today is going to rise to 4.13% (if you believe PET). f (1 y ) (1. ) 1 1 4.13% 2 2 2 0382 2 1 1 (1 y1) (1. 0351) $1,035,100 1 $1, 077,859 FNCE302: Investments Lecture 3 Page 23

Forward Rates What is the additional return earned over the second year? It will be f 2 where $1,035,100 x (1 + f 2 ) = $1,077,859 So f 2 = 4.1% This is the forward rate for year two Relationship Forward and future spot rates EXAMPLE Suppose an investor has a two-year investing horizon He wishes to invest in treasury securities and has two strategies (if only one year and two bonds existed) STRATEGY I. Invest in a one year bond and at the end, roll over the proceeds in a new one year bond STRATEGY II. Invest in a two year bond Given the above data what is the 1 year spot rate going to be 1 year from today. In order to have an identical return it would have to be 4.13%. That is what I am expecting. Given the above data, what will the one-year spot rate need to be in one year to yield identical returns? It would be 4.13% since in the above calculation f 2 was calculated from the relationship: (1 + 3.51%) 1 x (1 + f 2 ) = (1 + 3.82%) 2 The only problem is, a future spot rate is prediction (no guarantee) Many things can change to affect the future rates. FNCE302: Investments Lecture 3 Page 24

Relationship Forward and Future Spot Rates If we believe that forward rates are set so as to equal the spot rate over the same period then we believe in the Expectations Hypothesis Generally this will only hold if investors are risk neutral Economists believe that investors need to be induced to hold riskier long-term bonds (because there is more interest rate risk, the duration is longer) (as opposed to holding smaller bonds and rolling over) thus expected spot rates are likely smaller than their corresponding forward rate Expectations Hypothesis camp believes that forward rates are set so as to equal the spot rate over the same period. If we believe that forward rates are good predictors of future spot rates then we follow the Expectations Hypothesis. If investors are risk neutral they should be indifferent to investing in a sequence of one year bonds or investing in a longer term bond. Another way of saying this is If you believe the yield curve to be described by the path of future interest rates then you believe in the pure expectations theory (PET). but this is not the only theory LIQUIDITY PREMIUM THEORY According to the liquidity premium theory, the yield curve changes as the liquidity premium changes over time due to investor preferences Investors who prefer short-term securities will hold long-term securities only if compensated with a premium Short-term securities are typically more liquid than long-term securities The preference for short-term securities places upward pressure on the slope of the yield curve Basically this theory is saying: I need a higher yield to invest in longer term bonds because the markets tend to be less liquid in longer term bonds and, because of duration, there is greater interest rate risk in investing in longer term bonds. For these reasons the yield on a longer term bond should give me something extra. Thus the name, LIQUIDITY THEORY PREMIUM. Saying that an upward sloping yield curve may not be predicting what is happening to future interest rates, it may just simply be the fact that the longer I invest the higher return I need to compensate for the additional risk. FNCE302: Investments Lecture 3 Page 25

According to PET: a flat yield curve means that you expect short term interest rates to remain the same over time. An upward sloping yield curve means that you believe that short term interest rates are going to increase over time. With Liquidity Premium Theory you can have an upward sloping yield curve, because of the extra premium it may mean that you expect interest rates are going to remain the same. There is an upward bias due to the additional return (premium). Now let's look again at the equation we used to predict spot rates in the future Estimation of the FORWARD RATE based on a LIQUIDITY PREMIUM The yield on a security will not necessarily be equal to the yield from consecutive investments in shorter-term securities: 2 1 y 2 1 y1 1 f2 LP2 0 LP LP 1 LP2 LP3... The relationship between the LIQUIDITY PREMIUM and the TERM TO MATURITY is: So what the liquidity premium is saying is: "to invest in the longer term bond I am going to need more than I would receive from two short term investments in order to compensate for the risk of investing in a longer term bond." So even if short term interest rates are expected to remain unchanged over time, the yield curve is still going to be upward sloping because of the extra return investors need to compensate for the longer term. Generally it is believed that this liquidity premium increases with maturity. I need extra return for investing in a 20 year bond compared to a 10 year bond because there is that much greater risk. So there is an upward bias to the yield curve. According to the liquidity premium theory a flat yield curve means that you are actually expecting short term interest rates to decline (slight decrease in rates). Likewise, a slightly upward sloping yield curve means no expected change in interest rates, it merely reflects the liquidity premium with no change in short term rates. 20 FNCE302: Investments Lecture 3 Page 26

SEGMENTED MARKET THEORY Investors and borrowers choose securities with maturities that satisfy their forecasted cash needs Pension funds and life insurance companies prefer long-term investments Commercial banks prefer short-term investments Shifting by investors or borrowers between maturity markets only occurs if the timing of their cash needs change Investors and barrowers choose to invest in a certain part of the yield curve and they have no flexibility to move around in the yield curve (to get more competitive rates). For instance, insurance company has obligations it must pay out over the next 20 years. They will invest in 20 year bonds. They have no ability to invest in a 10 year bond of a 2 year bond or any other term bond. They are locked into 20 years (due to their need). If we believe the segmented market theory then we believe that each part of the yield curve is driven by its own supply and demand and there is no connection between a 10 year yield, a 20 year yield, or a 1 year yield. SEGMENTED MARKET THEORY: PREFERRED HABITAT Some borrowers and savers have the flexibility to choose among various maturity markets e.g., Corporations may initially obtain short term funds if they expect long-term interest rates to decline If markets were segmented, an adjustment in the interest rate in one market would have no impact on other markets, but evidence shows this is not true Preferred Habitat variation says investors will not behave in the manor described by straight SMT (Part A). They will give themselves flexibility. There must be some ability to move in the yield curve according to needs. Example would be an insurance company which needs to barrow and invest over a 20 year period but they can do so over 10 or 25 year terms. They have wiggle-room along the yield curve. Investors will move along the curve, even if only a little, to optimize their return, the return for their situation. Example: homeowner wants to take out a mortgage, they will choose among the 25 and 30 year mortgages, will not try to squeeze themselves into a 5 year product. Implications The preference for particular maturities can affect the prices and yields of securities with different maturities and therefore the shape of the yield curve The preferred habitat theory is a more flexible perspective Investors and borrowers may wander from their markets given certain events. FNCE302: Investments Lecture 3 Page 27

Which of the three theories is true? People have done a lot of research on which holds true. Interest rate expectations do have a strong influence on term structure. RESEARCH ON TERM STRUCTURE THEORIES Interest rate expectations have a strong influence on the term structure. Peoples belief about the path of short term rates do explain the term structure of interest rates. The Pure Expectation Theory does go a long way in explaining the yield curve. The forward rate from the yield curve does not accurately predict future interest rates. It does an OK job, doesn't do a great job. Variation in the yield-maturity relationship cannot be explained by interest rate expectations or liquidity General research implications Some evidence for pure expectations, liquidity premium, and segmented markets theory So which of the 3 ½ theories is correct? They all seem to tell a partial story, it seems to be a mixture of the 3 theories at work. No one is correct, all 3 effect the structure of the yield curve. Prof: I don't think the liquidity premium really explains very much. I think the preferred habitat has a lot to say, large parts of the economy that are locked into a particular segment of the yield curve. (mortgage example) Corporations and savers do have particular needs they are looking to address in the market and will respond accordingly. So preferred habitat has a lot going for it in explaining yield curve structure but if you look at how short term interest rates change over time, the yield curve does a fairly good job of predicting the path of short term interest rates. So theories 1 and 3B seem to have the biggest impact. FNCE302: Investments Lecture 3 Page 28