Trends and cycles Business Cycles Start by looking at quarterly US real Chris Edmond NYU Stern Spring 2007 1 3 Overview Trends and cycles Business cycle properties does not grow smoothly: booms and recessions categorize other variables relative to look at correlation, volatility, leads and lags, etc Business cycle indicators statistical forecasts market forecasts 9.25 8.75 8.25 US log real 7.75 7.25 2 4
Trends and cycles Business cycles Start by looking at quarterly US real want to isolate trend from cycle many ways to do this filtering we use something called the Hodrick-Prescott (HP) filter has the effect of drawing a smooth curve through the data percent deviation from trend - standard deviation at business cycle frequencies = 1.69-5 7 Trends and cycles Business cycle jargon US log real percent deviation from trend 9.25 peak peak peak 8.75 peak peak 8.25 smooth red line is the trend given by an HP filter trough 7.75 trough trough trough - trough standard deviation at business cycle frequencies = 1.69 7.25-6 8
Business cycle jargon NBER recessions percent deviation from trend contraction contraction contraction - - standard deviation at business cycle frequencies = 1.69 - - 9 Source: National Bureau of Economic Research, 2006 11 Business cycle jargon Co-movement and volatility percent deviation from trend Many macro variables comove with which are positively correlated with? which are volatile? which are smooth? Variables to look at expansion national income accounts: consumption, investment, etc labor markets: hours, earnings, unemployment financial markets: stock prices, interest rates expansion expansion - standard deviation at business cycle frequencies = 1.69-10 12
Nondurables consumption Durables consumption correlation at business cycle frequencies = 0.73 standard deviation relative to = 0.65 3 correlation at business cycle frequencies = 0.59 standard deviation relative to = 3.10 2 1-1 - -2 - -3 13 15 Services consumption Investment correlation at business cycle frequencies = 0.71 standard deviation relative to = 0.42 3 2 correlation at business cycle frequencies = 0.87 standard deviation relative to = 4.70 1-1 - -2 - -3 14 16
Co-movement and volatility Hours worked Consumption nondurables and services: pro-cyclical, relatively smooth durables: a bit less pro-cyclical, but much more volatile Investment extremely pro-cyclical and volatile similar to durables consumption correlation at business cycle frequencies = 0.74 standard deviation relative to = 0.27 - - Source: Bureau of Labor Statistics, 2006 17 19 Labor markets Earnings per hour Examples hours worked earnings per hour unemployment employment Cyclical properties correlation at business cycle frequencies = 0.58 standard deviation relative to = 0.45 positively correlated with? smooth or volatile? leads or lags? - - Source: Bureau of Labor Statistics, 2006 18 20
Unemployment Labor markets Hours worked correlation at business cycle frequencies = 0.76 standard deviation relative to = 11.88 6 4 pro-cyclical, relatively smooth Earnings per hour 2 pro-cyclical, relatively smooth Unemployment counter-cyclical and extremely volatile -2 Employment - - -4-6 pro-cyclical, somewhat volatile a lagging indicator? Source: Bureau of Labor Statistics, 2006 21 23 Employment Financial markets Examples correlation at business cycle frequencies = 0.71 standard deviation relative to = 1.48 6 4 S&P 500 index term spread (long return short return) credit spread (risky return safe return) 2 Cyclical properties positively correlated with? -2 smooth or volatile? leads or lags? - -4 What do you think? - -6 Source: Bureau of Labor Statistics, 2006 22 24
S&P 500 Credit spread 3 2 correlation at business cycle frequencies = 0.40 standard deviation relative to = 5.50 correlation at business cycle frequencies = 0.43 standard deviation relative to = 0.45 1-1 -2-3 - - credit spread = moody s BAA 10-year treasury Source: Standard and Poor s, 2006 25 Source: Federal Reserve Board of Governors, 2006 27 Term spread Financial markets S&P 500 index correlation at business cycle frequencies = 0.40 standard deviation relative to = 1.01 weakly pro-cyclical, massively volatile Term spread (long return short return) weakly counter-cyclical, same volatility as a leading indicator? Credit spread (risky return safe return) weakly counter-cyclical, smooth - term spread = 10-year treasury fed funds - Source: Federal Reserve Board of Governors, 2006 26 28
What have we learned so far? does not grow smoothly: booms and recessions investment and durables consumption are even more volatile than ; nondurables and services consumption are less volatile consumption, investment, employment, and stock market all pro-cyclical unemployment, term and credit spreads counter-cyclical some indicators seem to lead the cycle (term spread?) while others lag the cycle (employment?) Business cycle indicators and forecasting Statistical forecasts properties of good leading indicators regression methods Market forecasts leading example: yield curve other examples? Lead/lag relationships might help with forecasting 29 31 Business cycle indicators and forecasting Some variables seem to lead the business cycle can we exploit these indicator variables to forecast movements? Market prices aggregate information/beliefs of market participants can we use prices/returns to infer market forecasts? Correlated with variable of interest strength of correlation important sign of correlation not important Leads variable of interest Timely What s a good indicator Stable available quickly no significant revisions that would make in-sample assessments unreliable 30 32
Index of leading indicators Regression-based forecasting Regression INDICATOR WEIGHT Average weekly hours, manufacturing 0.1946 Average weekly initial claims for unemployment insurance 0.0268 Manufacturers new orders, consumer goods and materials 0.0504 Vendor performance, slower deliveries diffusion index 0.0296 Manufacturers new orders, non-defense capital goods 0.0139 Building permits, new private housing units 0.0205 Stock prices, 500 common stocks 0.0309 Money supply, M2 0.2775 Interest rate spread, 10-year Treasury bonds less fed funds 0.3364 Index of consumer expectations 0.0193 γ Y,t+k = α + βx t + ε t Sources of forecast error large residual error (low R 2 ) imprecise estimates of α or β (large standard errors) unstable relationship between γ Y and X unstable data, revisions Source: Conference Board 33 35 Regression-based forecasting Information aggregation Example k-period ahead growth γ Y,t+k vector of indicator variables observed at time t X t How do we combine information from many sources? adjust for differing degrees of quality or reliability? Market data basic idea: prices aggregate information of market participants regression γ Y,t+k = α + βx t + ε t (gives estimates of α and β coefficients) 34 36
Reading the yield curve: overview Euro yield curve Long bond yields contain information about expected future bond market conditions Why? If you buy a 10-year Treasury bond 6 annual percentage the yield should compensate you for expected changes in short rates over time if we expect short rates to rise, long yield should be higher Insight can try to reverse engineer this process infer expected future short rates from yield curve Difficulty separating risk premia on long bonds from expected future short rates 5 4 3 2 1 0 yields ym maturity m (in years) 1 2 3 4 5 6 7 8 9 10 Source: Euro zero-coupon yield curve, Feb 2006 37 39 Look at zero-coupon bonds ( zeros ) Bond yields Notation Convert yields to forward rates Notation p m = price of $100 in m-periods y m = yield on m-period bond (maturity m) Price and yield related by present value formula p m = 100 (1 + y m ) m (since prices are in dollars, yields are nominal) Yield curve ( term structure of interest rates ) is a plot of y m against m f m = 1-period return on investment made in m periods (forward rate) Yields apply to all periods until maturity, so $100 = p m (1 + y m ) m Forwards apply one period at a time, so $100 = p m (1 + f 0 )(1 + f 1 )... (1 + f m 1 ) Compute forwards from yields by comparing these relations, leads to 1 + f 0 = 1 + y 1 1 + f m = p m p m+1 38 40
Bond prices p m = Forward rates 100 (1 + y m ) m Numerical example 1 + f 0 = 1 + y 1 then 1 + f m = p m p m+1 Expectations hypothesis Basic idea: forward rate includes market expectation of future short rates Notation y m,t = yield on m-period bond contract at t f m,t = 1-period return on investment at m agreed at t Expectations hypothesis m (years) ym (%) pm (per 100) fm 1 (%) 1 2 3 4 5 3.018 3.215 3.315 3.386 3.441 97.07 93.87 90.68 87.53 84.44 3.018 3.412 3.517 3.600 3.660 f m,t = E t {y 1,t+m } + risk premium m (E t { } means expectations of { } at date t ) Risk premium constant across time, varies across maturity m 41 43 Euro yield curve Intuition for expectations hypothesis Compare strategies for investing over two periods: 6 annual percentage rollover strategy: reinvesting in short bonds 5 rollover return = (1 + y 1,t )(1 + y 1,t+1 ) 4 3 2 1 0 forwards fm 1 yields ym maturity m (in years) 1 2 3 4 5 6 7 8 9 10 buy and hold strategy: buy a two-period bond buy and hold return = (1 + y 2,t )(1 + y 2,t ) = (1 + y 1,t )(1 + f 1,t ) If y 1,t+1 known at t, market forces should equalize returns (so, y 1,t+1 = f 1,t ) But y 1,t+1 not known at t, so weaker conclusion f 1,t = E t {y 1,t+1 } + risk premium Source: Euro zero-coupon yield curve, Feb 2006 42 44
Estimating risk premia Euro yield curve Expectations hypothesis f m,t = E t {y 1,t+m } + risk premium m 6 annual percentage historical average f m 1 5 Simple method to estimate risk premium terms forwards fm 1 T 4 risk premium m = 1 T t=1 {f m,t y 1,t } = f m f 0 3 yields ym (risk premium is average forward average short) 2 Calculate from historical data over long horizon T 1 0 maturity m (in years) 1 2 3 4 5 6 7 8 9 10 Source: Euro zero-coupon yield curve, Feb 2006 45 47 Numerical example Euro yield curve m (years) 0 1 2 3 4 6 5 annual percentage historical average f m 1 current data historical average f m f 0 f m,t (%) f m (%) risk premium 3.018 3.412 3.517 3.600 3.660 3.221 3.716 4.161 4.502 4.779 0 0.495 0.940 1.281 1.558 4 3 2 1 0 forwards fm 1 yields ym estimated risk premium f m 1 f 0 maturity m (in years) 1 2 3 4 5 6 7 8 9 10 Source: Euro zero-coupon yield curve, Feb 2006 46 48
Reverse engineering the yield curve Euro yield curve Expectations hypothesis forward rate = expected short rate + risk premium 6 annual percentage historical average f m 1 5 So if we have market forward rates plus estimates of risk premia, then we can compute forwards fm 1 expected short rate = forward rate risk premium 4 yields ym 3 estimated risk premium f m 1 f 0 2 expected future short Et{y1,t+m} 1 0 maturity m (in years) 1 2 3 4 5 6 7 8 9 10 Source: Euro zero-coupon yield curve, Feb 2006 49 51 Numerical example Comments Historical yield/forward curve is upward sloping, so current data f m f 0 m (years) f m,t (%) risk premium 0 1 2 3 4 3.018 3.412 3.517 3.600 3.660 0 0.495 0.940 1.281 1.558 risk premium increases with maturity so an inverted (downward sloping) yield/forward curve surely gives falling expected future short rates but also flat yield/forward curve also gives falling expected future short rates Consequences of falling expected future short rates? lower growth and/or lower inflation expected future short E t {y 1,t+m } 3.018 2.917 2.577 2.319 2.102 50 52
Recall: term spread Credit spreads and default probabilities Similarly, can use credit spreads to infer market default probabilities correlation at business cycle frequencies = 0.40 standard deviation relative to = 1.01 Basic idea borrower s default probability α lender gets zero if borrower defaults lender gets return R if borrower does not default risk free return R f Market forces R f = α0 + (1 α)r or - - term spread = 10-year treasury fed funds α = R Rf R Observe credit spreads R R f, so infer market α Source: Euro zero-coupon yield curve, Feb 2006 Example: R = 1.10, R f = 1.05 then α = 0.045 53 55 Reading the yield curve: recap Recall: credit spread Summary convert yields to forward rates use historical forward rates to estimate risk premium correlation at business cycle frequencies = 0.43 standard deviation relative to = 0.45 subtract estimate of risk premium result: market-based forecast of future short rate What can go wrong? bad/unstable estimates of risk premium market pricing based on non-risk factors - credit spread = moody s BAA 10-year treasury - Source: Euro zero-coupon yield curve, Feb 2006 54 56
Business cycle properties What have we learned today? does not grow smoothly: booms and recessions investment and durables more volatile than ; nondurables and services less volatile consumption, investment, employment, and stock market all pro-cyclical unemployment, term and credit spreads counter-cyclical Business cycle indicators regression-based forecasting yield curve reflects market forecasts of future rates inverted/flat yield curve implies falling growth (and/or lower inflation) 57