Chicago Booth BUSF 35150 - Term structure I Expectations Hypothesis and Bond Risk Premia — Overheads

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23 Week 9 Term structure I Expectations Hypothesis and Bond Risk Premia Overheads 23 0 1 Definitions 1 Discount zero coupon bond Promise to pay 1 at time 2 Price price of year discount bond at time t 2 Example 0 9 10 interest rate log price of year discount bond at time Example ln 0 9 0 10536 0 1 or 10 discount 3 Yield For discount bonds 2 Example 1 h i 2 0 1 h i 1 1 0 1 0 05 5 discount per year 2 4 Forward rate a Definition The rate at which you can contract today to borrow from time 1 and pay back at time b Fact 1 1 c Example 3 2 0 15 2 3 0 10 0 05 5 5 Holding period return a Definition words Buy an year bond at time and sell it now an 1 year bond at time 1 b Definition equations 1 1 1 1 1 1 c Excess log returns over the risk free rate 1 1 1 485 6 Summary log 1 1 1 1 1 1 1 7 Notation maturity time when observed To be clear 1 1 1 23 1 Expectations hypothesis Question Why does the yield curve sometimes slope up sometimes slope down 1 Yield curves15 15 It s a lot of fun to play with the website http www treasury gov resource center data chart center interest rates Pages Historic Yield DataVisualization aspx 486 Treasury yield curve 8 16 2013 4 5 4 3 5 Percent 3 2 5 2 1 5 1 0 5 Yield forward 0 0 5 10 15 Maturity years 20 25 30 2 Why are yields di erent for bonds with di erent maturity Three equivalent statements a Long maturity yield average of expected future short rates plus risk premium b Forward rate expected future spot rate plus risk premium c Expected holding period returns should be equal across maturities plus risk premium 3 Big picture Hold long term for one period Forward rate Hold N period zero 0 1 2 N 1 Roll over 1 period bonds Short rate N Spot rate a 0 to N Long yield average of expected future short rates Buy N year zero 0 0 Rollover 1 1 1 1 0 1 2 1 1 1 1 1 1 0 1 2 1 risk premium 487 b N 1 to N Forward rate expected future spot rate lock in E wait and use spot risk premium h i 1 1 risk premium c 0 to 1 Expected returns are the same at all maturities hold N period bond 1 year h 1 h 1 1 4 Example 1 a 2 b c d 2 5 2 0 05 i i hold 1 period bond for 1 year h 1 1 h i 1 i risk premium 1 0 risk premium 10 Find and understand 0 20 15 2 1 1 1 1 5 15 e Yield forward and return statements of the EH are all equivalent f This is a hypothesis about expectations not a truth about how things will come out or about actual expectations 0 5 yeld log price 0 05 10 yield 0 1 15 forward 15 yield 0 15 5 return 0 2 0 1 time 2 5 Exchange rates and interest spreads a Realized return to US investor foreign interest exchange rate depreciation log 1 1 1 488 b Expectations hypothesis 1 1 1 1 c For one period rates 1 so 1 1 1 1 Interest rate spread expected depreciation of the euro 6 Exchange rates and forward rates a Arbitrage Covered interest parity ft st 1 it it st 0 b Uncovered interest parity expectations hypothesis 1 23 2 Risk premia 1 What risk premium do we expect Which end of these ways to get money from x to y is riskier Summary The sign of risk premium can go either way it depends on investor s horizon relative to supply of bonds and whether real interest rates or inflation are the source of interest rate risk 2 Theory II as always 1 1 1 1 1 1 1 489 Do interest rate surprises come in good times or bad times Typically we think higher rates come with higher consumption growth so the covariance is positive and the risk premium should be negative 3 US We ll just look at it empirically 4 Terminology The strict expectations hypothesis means no risk premium The expectations hypothesis alone means that the risk premium is small and constant over time 23 3 Empirical evaluation of yield curves and risk premia 1 Facts Yields of 1 5 year zeros and fed funds 15 10 5 1960 1970 1980 1990 2000 2010 2000 2010 Yield spreads y n y 1 2 1 0 1 2 1960 1970 1980 490 1990 1 5 year forwards 16 14 12 10 8 6 4 2 1960 1970 1980 1990 2000 2010 2000 2010 forward spreads f n y 1 4 2 0 2 4 1960 1970 1980 491 1990 Annual returns on 1 5 year bonds 30 25 20 15 10 5 0 5 1960 1970 1980 1990 2000 2010 2000 2010 Annual excess returns on 2 5 yerar bonds 15 10 5 0 5 10 15 1960 1970 1980 1990 a EH does not seem awful When the curve slopes up yields subsequently rise b Risk premium on average h Interest rate data 1964 01 2012 12 1 2 3 4 Maturity i h 5 68 5 90 6 08 6 23 1 h i i 1 h t statistici 1 Sharpe 5 6 34 0 21 0 39 0 54 0 65 0 50 1 94 1 80 0 28 0 91 1 91 3 31 0 28 1 24 1 86 4 60 0 27 1 36 1 66 5 67 0 24 Slight upward slope Long bonds seem terrible by one period measures Why hold them A you don t care about one period 492 2 Expectations failures Fama Bliss Updated 1964 2012 n 2 3 4 5 1 1 1 1 2 0 83 0 27 0 11 1 14 0 35 0 13 1 38 0 43 0 15 1 05 0 49 0 07 forecasting one year returns on n year bonds 1 1 1 1 2 0 17 0 27 0 01 0 53 0 33 0 05 0 84 0 26 0 14 0 92 0 17 0 17 forecasting one year rates n years from now a Two year forward spot spread translates 0 83 almost 1 1 to expected return The EH is exactly wrong b Two year forward spot spread does not forecast one year rate change at all 0 17 c The EH does start to work well at 4 5 year horizon 5 does forecast that 1 will be higher in 4 years d First row adds to 1 Higher rows do not add up to 1 Why Time safe 1 year return Higher 1 year rate in year 1 2 Price lower return of 2 year bond in 0 1 Time Time Higher …


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Chicago Booth BUSF 35150 - Term structure I Expectations Hypothesis and Bond Risk Premia — Overheads

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