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Econ notes after mid-term.docx

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ECON 330
John Shea

Patrick Dooley 11/1/13 After midterm notes Econ notes #2 Supply and Demand in the Bond Market (chapters 5 + 6) • Chapter 4: was all about formulas showing how bond prices and yields (i) related • NOW: we want to understand HOW are bond prices and yields determined? Chapter 5: applies supply/ demand framework to understand how economic shocks can cause yields/bond prices to vary over time This chapter will explain Why interest rates go up and down all the time Chapter 6:Applies framework to understand why different bonds pay different yields at any point in time • Risk and term structure of interest rates START: The demand for Bonds: • What factors influence the quantity of (Q) of a particular bond that investors/ savers want to hold in their portfolio? o Why would a investor want to hold one bond instead of another- what makes it more favorable 1. Bond price or Bond yield (nominal yield) a. Holding expected inflation and future interest rate FIXED (and other factors) a higher current nominal yield (i) on a bond implies a higher expected rate of return on that bond • All else equal, higher interest rate  higher ROR o More desirable for savers o Higher demand Holding a Bonds face value, coupon and maturity fixed, there is an inverse relationship between bonds price and its interest (yield) • All else equal, demand for a bond should be higher when bonds price is lower • All else equal: • Lower bond price  higher yield (interest) 2. Expected Inflation: Holding (i) interest, a higher expected inflation implies lower expected real return on holding a bond: a. Ex post: r = (i) – π b. Ex-ante: r = (i) – eπ (expected inflation) i. All else equal, higher expected inflation reduces benefit to holding a bond and demand goes down Investors should care about real yields ( r) , not nominal yield (i) o Because they want goods and services, not $ money • All else equal: bond demand should fall as expected inflation increases 3. Risk: investors are risk adverse they would prefer to hold assets whose returns are stable/ predictable o Holding nominal yields and other factors fixed, demand for particular bonds should be higher if the bonds return is less risky • Types of Risk: A. Default Risk – (credit risk/ repayment risk): risk that issuer won’t make promised repayments to  Example: when a company goes bankruptcy o Lowest default risk: o Treasury securities of stable, well-functioning prosperous countries: U.S., Germany, Japan, Canada and UK o More default risk: Municipal bonds, higher rated corporate bonds (corporations that are stable, profitable, and not too highly leveraged—AtoAAArated) o Highest default risk: Junk corporate bonds(rated B,C or D), bonds issued by less stable governments B. Inflation Risk: Holding expected inflation fixed, ex-post real returns on conventional bonds will be higher or lower than expected if ex-post inflation is lower or higher than expected inflation o If ex-post inflation < ex ante: expected inflation (bond holders will get windfall excess returns… lenders) o If ex post inflation > ex ante: expected inflation (bond holders suffer unexpected losses in real terms) All conventional bonds (Bonds with pre specified coupon, face value repayments), vulnerable to inflation risk • Only way to avoid inflation risk is to hold INDEXED bonds (example: TIPS) where coupon payments and face value are linked o Ex post: to measure of ex- post inflation C. Interest Rate Risk: holding current (i) interest rates fixed, long-term bond holders will suffer capital losses if interest rise unexpectedly ex-post(bond holders earn returns less than initial interest), and will enjoy capital gains if interest rate fall unexpectedly ex- pot (bondholders earn returns great than initial interest) o Rate of Return to holding long term bonds is risky, even if no default risk or inflations risk, because ex-post changes in interest rates can cause fluctuations in bond prices  Opportunity cost loss – when interest rates go up and you hold your bond o Extent of interest rate risk depends on maturity of bonds: Short term (money market) bonds with maturity = 1 year or less: no interest rate risk  Maximum interest rate risk: Consol bonds, 100 year bonds, 30 year bonds, 20 year bonds, 10 year bonds, 5 year etc…. the risk keeps going down with the amount of years is on the bond All else equal: bond demand should be higher the less risky the bonds return o All else equal: demand should be higher for US treasuries than for corporate bonds because of default rate risk o All else equal: demand should be higher for TIPS than for conventional US Treasuries because of inflation risk o All else equal: demand should be higher for T- Bills than for conventional 20 year T - bonds because of interest rate risk 4. Holding current interest rates fixed, Expected future interest rates affect demand for long-term bonds today a. Reason: given current yield(interest): i. If interest expected to rise in the future the bondholders will expect bond prices to fall in the future and expect capital losses on long-term bonds. 1. Expected ROR < initial interest ii. If interest expected to rise in the future: should lower demand for long- term bonds today iii.If interest expected to fall in future: should increase current demand for long-term bonds because investors would anticipate future capital gains and returns > initial yield All else equal: todays demands for long-term bonds should rise if interest rates are expected to fall in the future All else equal: Bonds demand should fall if interest rate expected to rise in future NOTE: this affects long term bonds demand only: short term bond demand doesn’t depend on expected future interest rates because for short term bonds, Rate of return = initial yield 5. Liquidity (ease of reselling at a fair price) a. Maximum liquid: U.S. treasuries (conventional) b. Less Liquid: TIPS, corporate bonds • All else equal: greater liquidity means demand is high 6. Tax Treatment: interest earned on municipal bonds exempts from federal, state and local taxes • All else equal: bond demand should be higher if tax treatment favorable 7. Demand for any particular bond will depend on the attractiveness of other securities or saving opportunities • If stocks more attractive (example: during a bull market)  Then all else equal: demand for bonds will fall as investors substitute portfolios away from bonds, and then put it towards stocks • During bear market: stocks are less attractive: and this will increase peoples demand for bonds • During recession: corporate bonds become less attractive due to higher default risk: therefore demand for treasuries goes up (Flight to quality) Bond Demand Curve: shows relationship between bonds price (P) and amount (Q) that investors want to hold in their portfolio, all else equal All else equal: bond slopes down because a lower bond price and higher interest rate makes the bond more desirable to saver/ investor Shifted by: changes in all other factors besides Price or nominal interest that affect the desirability of holding a bond Example: • Expected inflation rises should shift the demand(less desirable) for a bond left on graph o Given prices or interest, higher expected inflation reduces r • Bond less risky should shift the demand (more desirable) for the bond to the right/ out • Nominal (i) interest rates are expected to rise in the future should shift the demand (left for long term bonds) and no change for or no shift in demand curve for short term bonds • Bear Market (stocks are doing badly): should shift the demand (more desirable) for bonds to the right • Higher Price in bonds (and lower interest rate): Demand does NOT shift but you will have movement up to the left along bond demand curve Bond supply: what factors influence the amount (quantity) of bonds that borrowers (corporations, governments) want to issue? Key distinctions: US Treasury, (corporations/ municipalities – will have different supply curves) First: supply of corporate/ munis: 1. Bond price/ nominal yield (i) All else equal: lower price and higher interest, implies that issuing bond is more expensive to borrowers: higher cost of borrowing If the issuer has any control over when/ whether to borrow, more likely to issue bonds when price is high (equivalently, when interest is lower) because borrowing is cheaper • All else equal: corporate and municipal bond supply should be higher when bond Prices higher • Corporate borrowing mostly to finance new investments in plant/ equipment or innovation or to restructure corporate financing • Munis issued to finance public works o In all these cases the issuer have some discretion about when or whether to borrower o So that if the interest rate is too high, issuer can choose to borrow less or not at all U.S. Treasury has little to no discretion about whether/ when to borrow as a result its bond supply should be insensitive to prices and nominal yields • This is because the treasury has to borrow whenever receipts is less than expenditures Secondly: Expected inflation: affects supply of corporate/ munis: • Holding interest rate (or bond price) fixed, real cost of borrowing is lower if expected inflation is higher o Given interest, higher expected inflation rates should increase supply of corporate/ munis bonds Again: supply of treasuries insensitive to expected inflation: treasury has little to no discretion about when/ whether to borrow Thirdly: Supply of corporate and municipal bonds depends on availability of profitable (or socially worthy) Real investment opportunities in plan/ equipment/ innovations and public works Bonds (corporate or munis) issued largely to finance projects • If lots of good projects are out there then corporate/ munis bond supply will go up all else equal Example: All else equal: the supply of corporate bonds should be higher during business cycle booms than during recessions • Reason: investments in plants, equipment, innovation more likely to look profitable during a boom (economy doing well) Example: Corporate bond supply should be higher during periods of rapid technological change because of a lot of profitable investments opportunities Fourth: • Supply of US Treasuries is mostly dependent on fiscal policy (refers to the tax and spending policy, adapted by the President and congress) o Main thing that affects US treasuries is FISCAL policy Definitions: Budget deficit (BD)- refers to current short fall of tax revenues relative to government expenditure • BD = government spending – tax receipts • If the budget deficit is equal to 0 then you have a balanced budget • If the budget deficit is equal to less than 0 then you have a deficit • If the BD is = to more than 0 then you have a surplus The National Debt (ND) – is total stock of what US government owes to investors Roughly speaking: BD = amount by which National Debt changes in a given year If BD = 0 then government “roles over” expiring National Debt (issues new ND with Face value = expiring debt) But issues no new net debt: ND unchanged to the supply of treasuries unchanged If BD is greater than 0 then government rolls over expiring debt and issue net new securities to cover shortfall of receipts relative to expenditures • Therefore the National Debt is rising and the supply of of treasuries is increasing If BD is less than then government uses surplus to retire some expiring national debt without rolling it over • National Debt decreases and supply of treasuries decreases Bond supply curve (treasuries) will be showing a VERTICAL LINE Quantity depends mostly on US fiscal policy • If taxes increase or spending is decreased then Budget deficit will fall or become negative shifts supply left • If taxes decrease or spending rises then budget deficit will rise and national debt will increase and the supply of treasuries to the right or out Supply of Treasuries independent of Price or Interest on treasuries (no discretion) Bond supply curve (corporate/ munis) : this shows the relation between the quantity of bonds that borrowers want to issue and the Price of these bonds, all else equal It slopes up because all else equal, a higher bond price translates to a lower interest on bonds and that translates to cheaper to borrow • Corporations/ munis have discretion about whether or when to borrow (more borrow when cheaper) • Shifted by: changes in other factors besides price/ nominal yield • Higher expected inflation means borrowing cheaper in real terms as a result the supply shifts out EXAMPLE: • Business cycle recession: means fewer profitable projects so the supply of bonds should shift in or to the left Patrick Dooley 11/8/13 Review: Bond Mark Supply and Demand (Chapter 5) • Slopes Down: Holding FV, C and T fixed, lower bond P  higher yield (i)  bond more attractive to savers • Shifted by: changes in other factors besides price or yield that affect desirability of holding to investors Examples: r = i - eTT • Higher expected inflation: Reduces expected real yield, shifts D to the left • Higher expected future interest rates: reduce expected for form holding long term bonds o Shift todays D for long term bonds left • Lower risk (default risk, inflation risk, interest rate risk) shifts Bond D right • Appeal of alternative assets o Demand for particular bond will shift (out or in) as other assets become less or more attractive Monetary Policy (Federal Reserve): • Federal Reserve: holds large portfolio of treasury securities, other securities- (just recently)- (like buying bonds from fanny mae and Freddie mac) • Fed can conduct open market purchases of treasury or other bonds  shifts demand for bonds out (to stimulate economy) --- it pays for this stuff by just printing more money for these purchases when they are conducting open market purchases Supply of Bonds: • Corporate/ muni’s bond supply curve shows relationship between bond P and Q of bonds corporations (or municipalities) want to issue, all else equal • Slopes up: all else equal, a higher bond price means a lower yield on a bond meaning borrowing is cheaper and when that happens corporations, municipalities borrow more (assuming corporations and municipalities have discretion about when/ whether to borrow) o When borrowing is cheap(interest rates are low) people and corporations, borrow more • Shifted by: changes in other factors besides bond prices or yields that affect eagerness to borrow Examples: • Higher expected inflation: holding interest fixed, o Higher expected inflation reduces real expected cost of borrowing- bond S shifts out. (The supply of corporate and municipal) --- (this would make it easier to pay back the set price of the borrowing because of inflation) • Availability of Profitable real investment opportunities (plant, equipment, research and development) is when corps would increase the supply of bonds to raise money • Recession: good real investment opportunities become scarce: Corporate bond S shifts in Treasury BONDS: • Treasury supply curve shows Q of treasury bonds issued by US Government: equals National Debt o Treasury Supply curve is Vertical because it is unaffected by prices/ nominal yields on treasuries:  US Treasury has no discretion about whether/ when to borrow.  Evolution of National Debt depends on fiscal Policies adopted by President/ congress: (tax/ spending) • If taxes are cut without cuts in spending: budget deficit will rise and the national debt will increase as a result the Supply of Treasuries shifts out to the right  Whenever federal tax revenue is less than federal spending in a given fiscal year: Budget Deficit means National Debt will increase as treasuries issues more bonds to covers its deficit.  As a result Treasury Supply of bonds shifts out to the right o If Government raises taxes or cuts spending: it may run a Budget Surplus meaning tax revenue is great than the spending the government does and then that surplus goes into paying off some of the National Debt and Supply of Treasuries shift to the left • Treasury supply curve is vertical: o Shifted by fiscal Policy (tax income versus government spending) o Can also be shifted by monetary policy of federal reserve  If the fed conducts open market sales it sells large quantities of Treasuries and as a result this shifts the Supply of Treasuries Out to the right (Fed collects money from its sales, that money is removed from circulation- money supply falls) • The Fed creates open market sales to slow down the economy Putting Supply and Demand together we can talk about equilibrium interest rates in the bond market • Bond Market Equilibrium: occurs at price (or equilibrium, interest) at which quantity supplied and quantity demand of bond are equal o In equilibrium: Savers will hold the quantity of bonds that the borrowers want to issue: (interest rate or price) on the bond will adjust to make Supply and Demand equal • What if P = Pa?At that low price, interest rate on that bond will be very high. Bond in this case would be very attractive to savers (Quantity demanded Da will be high) but borrowers will not want to issue many bonds that rate so ( quantity supplied Sa will be low) o Means borrowing is expensive (and borrower do not want to borrow when borrowing is expensive) • If Price = Pa means excess demand for bond o This will push bond prices up meaning Pa is NOT an equilibrium • If P= Pb means excess supply of bonds means high price or low interest o This will drive bond price down and Pb would not be an equilibrium • The only equilibrium is when P= Peq because at that point, supply and demand is equal Shocks that shift the demand or supply of bonds will cause changes in the equilibrium price (and therefore, the equilibrium interest rate) CHAPTER 5: applies bond supply and demand framework to study factors that cause interest rates to change over time Example: (from handout in class) • Fisher effect  see handout figure 5 o Plots nominal interest rate on US 3-month T-Bills versus a measure of expected inflation over time o Over time we see movements in expected inflation are tacked very closely by movements by nominal interest rates. (correlation not perfect but very close)  During 1960/1970s: there was a rise in expected inflation, and a rise in interest rates  During 1980’s and 1990’s there was a steady decline in expected inflation and in interest rates • This is consistent with the Fisher equation: i= r + eTT o Holding real interest rates fixed, nominal interest rates should move one to one to offset changes in expected inflation Can we explain Fisher effect using Bond market supply and demand framework? • Market for US Treasuries o Initially, equilibrium P=Po (implies initial interest = io) • Now suppose that expected inflation rises, all else equal: treasuries less attractive to savers at any given interest means Demand for Treasuries will shift in to the left • The supply for treasuries will be unchanged assuming that there is no Direct effect of expected inflation on current budget deficit or monetary policy Equilibrium Price falls to P1 < Po • Since Price falls, then interest rates will rise and interest greater than i0 • Expected inflation increases means interest rates increase on treasuries o In equilibrium the quantity of treasuries held by savers will be unchanged: Price will fall enough at the same time (interest will rise enough) to fully compensate savers for higher expected inflation CORPORATE BONDS Initial Price = Po (initial interest = io) When expected inflation is high then the demand for corporate bonds will shift in to the left • Also: Supply will shift out to the right because corporations will be more eager to borrow if real yield is lower • New equilibrium P = P1 < P0 and New interest i1 > i0 o Fisher effect holds for corporate rates too Example: • Cyclical behavior of interest rates (chapter 5 handout: Figure 7) o Plots 3 months T-Bills interest rates over time and should also plot Vertical lines during recessions:  Recessions: 1975 -76 , 1982-1983, 1990-1992, 2001- 2002 and most recent 2008- 2010  you will notice that Treasuries interest rates fall systematically fall during recessions • Treasuries interest rates are strongly procyccical o Corporate bond interest rates are NOT as strongly procyccical as treasury interest rates MARKET FOR CORPORATE BONDS: Initially P = P0 (i = i0) Recession Happens: • Two effects on corporate bond market: o 1 Number of good real investments opportunities will fall: so corporate bond Supply will shift in to the left o 2 Corporate bond become riskier during a recession in particular the default risk increases during a recession  Corporate bonds Demand should shift in to the left • On balance: effect on bond Price and interest rates are ambiguous( no clear prediction about what happens to corporate interest rates during a recession) o Prices could rise or fall depending on which curve shifts more, etc… MARKET FOR TREASURIES: Initial P= P0 and initial interest = i0 During a recession: • 1 Savers will find corporate bonds less appealing due to elevated risk o Demand for treasuries will shift out to the right when corporate bonds are less attractive (flight to quality) • 2 Stock market less appealing also during a recession: so Demand for Treasuries shift out to the right more o Massive shift in demand for treasuries in a recession Result: • Prices will go up and P1> P0 and interest rates will fall during a recession for treasuries i1 Interest rates on ‘AAA’ corporate bonds > interest rates on US treasuries and munis Figure 4: plots interest on treasuries at various maturities: 3 months (t-bill), 3-5 year, 20 year • At any given point in time: these yields are different: (term Structure) Both figures show, interest rates on different bonds tend to move up and down together over time (bond yields among different bonds are highly correlated over time) but at any point in time different bonds will pay different interest rates STARTING point: If two bonds have exactly the same maturity, risk, liquidity and other characteristics then they should pay the same interest rates at all times Reason: otherwise there will be arbitrage opportunity EXAMPLE: 2 companies, Aand B: regarded bonds identically by market Suppose at some point in time: PriceA> Price B  InterestA< Interest B • What should happen: investors should sell bondA, use proceeds to buy bond B because B offers higher interest rates, should be strictly more attractive thanA • Demand Curve for bondA should shift in to the left (demand goes down), so the price of bond Awill fall and interest rate will rise • Demand curve for bond B should shift out to the right (higher demand), so the price of bond B will rise and interest rate will fall o This will continue until PriceA = Price B and InterestA= Interest B  This process is called ARBITRAGE- buy low, sell high • Is why any given asset will trade for almost exact price in different places (US NYC, Chicago, London, China, etc.) • This process applies to any tradable security not just bonds( like stocks)  Therefore if 2 bonds paid different yields at a point in time, it must be because they differ along some dimension, such as maturity or default risk, etc. Risk structure of interest rates: refers to differences in interest across bonds of same maturity (e.g. 20 years), due to differences in liquidity, tax treatment, risk, etc. o Most important difference across bonds of same maturity is default risk Government bonds have lower default risk than corporate bonds – so interest rates will always be higher on corporate bonds than government bonds Within corporate bonds—different corporate bonds have different rating assigned by Moody’s, Fitch and standard and poor • These ratings reflect analyst views of bonds default risk o AAAbond: companies with stable, high profits and low leverage (low debt burden relative to revenue stream) – least likely to default • If revenue/ Profits less stable and/or you have a higher debt already: then the bonds will be rates lower and analyst will perceive your default risk higher o Ratings on a given company can change overtime to reflect changes in default risk Why is default risk reflected in yields? Back to supply and demand model • 2 companies:A, B  they issue bonds with identical face value, coupon payments and maturity. Supply curves identical o Let’s suppose thatAhas a higher default risk than B (otherwise bonds identical- same liquidity) • All else equal: savers/investors will prefer/ want to hold bonds of company B in portfolio (lower default risk) • All else equal: demand curve for BondAwill be located to the left of the demand curve of B (snap shot at any point and time) o The Price of Abe lower than Price of B o Interest rate will be greater on BondAthan bond B • In Equilibrium: Investors will hold some of both bonds in their portfolios o QB > QA> 0 o Investors are motivated to hold some of bonds A, due to opportunity to earn a higher interest rate/ yield  Ahigher yield on bondA, compensates savers/investor for a higher default risk in equilibrium Risk spreads between Baa andAaa corporate bonds: the spread is highest during recessions: • 1930’s (depression) there was a big spread • 2008 (great recession) Situation: Explain using supply/ demand framework (assume that bonds issued by 2 companies (x and y) are identical except for default risk) • Boom economy: default risk for both companies is low (but higher default risk for company Y) o During Boom: Price of Y will be less than the Price of X company bond  Interest rate of Y will be higher than interest rate of X (but not by much) o Demand curve for Y will be at the left of the demand curve of company X o Booms: investors are not worried to much about default risk because every company does better during booms • Recession: o Demand for Y will be far to the left of Demand for X curve  Price for Y will be lower than Price for X  interest rates for Y will be higher than interest rates for X o Recession: investors worry more about default risk  Weak companies more likely to default in recession, due to lower revenues • Default risk will rise for all companies but more so for weaker companies like Y This is an EXAMPLE: of Flight to Quality during recessions Risk Spreads—are the difference between (interest rates of Baa and interest rates ofAaa) rise during recessions because saver/investor needs more compensation in form of higher yields to induce them to hold riskier bonds due to higher bonds, due to higher perceived default risk during recessions • Besides default risk: difference in other characteristics can also cause differences in bond yields at a point in time across different bonds of same maturity EXAMPLE: US Treasuries have similar default risk to Canadian Treasuries • Main difference: US treasuries are more liquid than Canadian Treasuries • • Demand curve for Canadian treasuries will be to the left of the US treasuries demand curve of US treasuries o All else equal: savers will prefer to hold US treasuries due to higher liquidity  At any point in time likely to see the Price of US treasuries higher than Canada treasuries  Interest rates higher on Canada treasuries than US treasuries Municipal Bonds versus US Treasuries • Interest rates on munis are less than interest rates on treasuries (most of the time) o Occasionally: interest rates on munis will be higher than interest rates of treasuries  This would happen during periods of economic crisis (e.g. 1930 and today 2013) • Reason why?: Two differences between Municiapal bonds and treasuries o 1. Default risk is higher on Munis this difference be amplified during a crisis periods (This force would imply interest rate on munies will be higher than interest rates on US treasuries) o 2. Tax treatment: interest earned on Munis is exempt from federal tax (and often state/ local taxes) – this is not true for treasuries  This makes munis more appealing than treasuries, especially for high income people in high tax brackets (rich people hold lots of munis) • This force will make interest rates on munis lower than interest rate on US treasuries • This tax advantage makes more important during periods of higher tax rates on investments incomes The Term Structure of interest rates: Differences in yields across bonds of different maturity, holding default risk and other characteristics fixed (usually refers to US treasuries) • All treasuries have high liquidity, lower default risk: but can pay different yields at any point in time, according to maturity(term) Figure 4: Shows rates on 3 months, T-bills, 3-5 year notes, and 20 year treasury bonds over time • Interest rates at all maturities trended up 1950 – 1980 trended downward 1980 – present (mostly these trends track movement in inflation (fisher effect) • Also: short term fluctuations in interest rates also correlated across maturities but not identical (peaks) Figure 7: plots yield curves for US treasuries, at different dates Yield curve for a particular date just graphs interest rates on that date, by maturity of the bonds FACT: About Term Structure: • Treasury interest rates at different maturities tend to move up/down overtime (time- series movements in treasury yields highly correlated at different maturities) • Yield curves usually slope up: o Interest rates on long term treasuries(20 year) tend to be higher > than interest rates of short term treasuries(3- months) • Yield curves are usually steeper o 1. When short term interest rates are low relative to recent history (during valleys) o 2. When short term interest rates are high relative to recent history (during peaks), yield curve flatten (gap between long interest rate and short term bond interest rates shrinks)  Occasionally, can even see and inverted yield curve • Inverted yield curve: Downward sloping (are rare but can occur when short term interest rates are high relative to historical standards: 1981) o 3. If interest rates in a short term in a valley- you will tend to have steep yield curves (where the long term rate is relative to high term rate)  When current short term interest rates are low relative to recent history: steep yield curves (now)  Peak periods when short interest rates are high – you will get flatter yield curves and/or inverted yield curves Leading benchmark theory of the term structure: Expectations theory of term Structure • At any point in time: the current interest rate for a security with a T year maturity will equal the average current expectation of the one year interest rate expected to prevail over the next T years EXAMPLE: The current interest rate on a 5 year treasury note should equal 1/5(todays 1year interest rate on 1 year t- bill + todays expectation of the 1 year interest rate on 11/15/14 + todays expectation of 1 year interest rate on 11/15/15 + “ “11/15/16 + “ “ 11/15/16) – expectation of what a 1 year treasury rate will be 1 year out from today through 4 years from today • Current 5 year rate = average 1 year rate expected to prevail over the next 5 years • Current 2 year rate = average 1 year rate expected to prevail over the next 2 years o ½(current 1 year rate + current belief on what 1 year rate will be a year from today on 11/15/14) The long term rate according to expectation theory Long term interest rate = average of current short term interest rates and short interest rate expected to prevail in future Example: Suppose currently the 1 year interest rate = 5% and suppose currently we believe that on 11/15/13 date the 1 year interest rate will be Date 1 year interest rate will be 11/15/14 6% 11/15/15 7% 11/15/16 8% 11/15/17 9% We believe interests rates 1 year from now will rise by 1% per year
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