Kenneth Singleton: Risk Premiums in Sovereign Debt Markets

Unspanned Macro Risks Financial Frictions Early Warning System References Risk Premiums in Sovereign Debt Markets 2012 Barcelona Lecture Kenneth J. Singleton Graduate School of Business Stanford University Based on joint research with Anh Le, Scott Joslin, Francis Longstaﬀ, Jun Pan, and Lasse Pedersen May 10, 2012

Unspanned Macro Risks Financial Frictions Early Warning System References “In-2-For-1” Year Forward Term Premiums Joslin, Priebsch, and Singleton (2011) 12% Forward Rate Expected Yield 10% Forward Term Premium 8% 6% 4% 2% 0% 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 ‐2%

Unspanned Macro Risks Financial Frictions Early Warning System References The Ingredients of Risk Premiums in Sovereign Bond Markets 1 Which risks are priced in sovereign bond markets? Macro-ﬁnance models used at many central bank explicitly include macro risks factors as determinants of bond yields. Most models used by ﬁnancial institutions focus on factors that capture the changing shapes of yield curves.

Unspanned Macro Risks Financial Frictions Early Warning System References The Ingredients of Risk Premiums in Sovereign Bond Markets 1 Which risks are priced in sovereign bond markets? Macro-ﬁnance models used at many central bank explicitly include macro risks factors as determinants of bond yields. Most models used by ﬁnancial institutions focus on factors that capture the changing shapes of yield curves. 2 Measuring the compensation that investors require for bearing these risks? The role of the macroeconomy? The role of indigenous yield-curve factors?

Unspanned Macro Risks Financial Frictions Early Warning System References The Ingredients of Risk Premiums in Sovereign Bond Markets 1 Which risks are priced in sovereign bond markets? Macro-finance models used at many central bank explicitly include macro risks factors as determinants of bond yields. Most models used by financial institutions focus on factors that capture the changing shapes of yield curves. 2 Measuring the compensation that investors require for bearing these risks? The role of the macroeconomy? The role of indigenous yield-curve factors? 3 How do financial “frictions,” limits to arbitrage, liquidity, etc. affect the quantities of risk and their market prices?

Unspanned Macro Risks Financial Frictions Early Warning System References The Ingredients of Risk Premiums in Sovereign Bond Markets ert (n): the expected return over one period on a bond with f initial maturity n, over and above the riskfree yield rt . n−1 n f ert (n) = −Et (n − 1)yt+1 + nyt − rt expected return riskfree rate ≈ B(n) · Σt · Λt Factor Loadings Quantities of Risk “Prices” of Risks What are the sources of risks in sovereign bond markets, and how are they “priced”?

Unspanned Macro Risks Financial Frictions Early Warning System References Parsimony in Modeling Sovereign Risks I Looking inside ﬁnancial institutions, bond yields are assumed to follow a low-dimensional factor structure: yt ≈ an + bn Levelt + bn Slopet + bn Curvaturet , n L S C where the sources of risk are: 10yr Level: yt (1st P C of yields) 10yr 1yr Slope: (yt − yt ) (2nd P C of yields) 10yr 1yr 5yr Curvature: (0.5yt + 0.5yt − yt ) (3rd P C of yields) These three principal components (P Cs) are “portfolios” of yields that explain over 95% of the variation in bond yields.

Unspanned Macro Risks Financial Frictions Early Warning System Referencesmethods used in computing the zero-coupon yields are consistent across the countriesconsideredLoadings on in this paper. P Cs of US Bond Yields: 1961-2010 European Central Bank Research WP1276 !"#$%&()*+,-".#/+0 "! 1 #! ,.- $! 12)3)4564768(9497( !"& ,-./0123 4565, ,-./0123 7,-85 !"% ,-./0123 9:;6.<:;5 !"$ !"# ! ( ) * + # #( #) ** *+ $ $( $) (* (+ % %( %) +* ++ & &( &) )* )+ ! !( !) * + # Note: The figure shows the loading of each latent factor at each maturity, expressed in months.

Unspanned Macro Risks Financial Frictions Early Warning System References Where’s the Macro? How can we understand risk premiums in bond markets without any reference to the macroeconomy? True, this approach prices bonds almost perfectly!

Unspanned Macro Risks Financial Frictions Early Warning System References Where’s the Macro? How can we understand risk premiums in bond markets without any reference to the macroeconomy? True, this approach prices bonds almost perfectly! However, the compensations that investors require for bearing these risks depend on global macroeconomic conditions. These macro links are missing, so this “internal” approach does a poor job of capturing investors’ risk premiums.

Unspanned Macro Risks Financial Frictions Early Warning System References “In-2-For-1” Year Forward Term Premiums Fitting with the Yield Curve (SP) 7% FTP 2,1 FTP2,1x SPP S 6% OM OM 5% 4% 3% 2% 1% 0% 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 ‐1% ‐2%

Unspanned Macro Risks Financial Frictions Early Warning System References Macro-Finance Approach to Modeling Risk in Bond Markets Start with the recognition that the policy rate rt is set by a monetary authority according to a Taylor-style rule rt = ρ0 + ρπ πt + ρg gt +ρ t . inf lation output gap policy surprise Price bonds of all maturities using a term structure model that rules out arbitrage opportunities. Now the factors are directly linked to macroeconomic activity! However, does this model accurately price bonds?

Unspanned Macro Risks Financial Frictions Early Warning System References Actual Minus Model-Implied Yields from Macro-Finance Model 200 1−yr 5−yr 10−yr 150 100 50 Basis points 0 −50 −100 −150 1970 1975 1980 1985 1990 1995 2000 2005

Unspanned Macro Risks Financial Frictions Early Warning System References Why Do Macro-Finance Models Fail to Price Bonds? An implication of including macro variables as risk factors, rt = ρ0 + ρπ πt + ρg gt +ρ t , inf lation output gap policy surprise is that output growth and inﬂation are perfectly predictable given information in the current yield curve. Why? Because bond yields are linearly related to (πt , gt ) and, therefore, we can invert these relationships to express (πt , gt ) in terms of bond yields. (A weaker version: some models used by the FRB and ECB replace (gt , πt ) with survey forecasts.)

Unspanned Macro Risks Financial Frictions Early Warning System References How Large Are Unspanned Macro Risks? Real economic activity (GRO) and inﬂation (IN F ): IN F is the expected one-year expected inﬂation rate as measured by Blue Chip Economics. GRO is the Chicago Fed National Activity Index (GRO), a measure of current real economic conditions. There is substantial variation in (GRO, IN F ) that is unrelated to sovereign yields. 15% (85%) of the variation in GRO (IN F ) is explained by changes in Level, Slope, and Curvature.

Unspanned Macro Risks Financial Frictions Early Warning System References How Large Are Unspanned Macro Risks? Real economic activity (GRO) and inﬂation (IN F ): IN F is the expected one-year expected inﬂation rate as measured by Blue Chip Economics. GRO is the Chicago Fed National Activity Index (GRO), a measure of current real economic conditions. There is substantial variation in (GRO, IN F ) that is unrelated to sovereign yields. 15% (85%) of the variation in GRO (IN F ) is explained by changes in Level, Slope, and Curvature. The part of (g, π) that is uncorrelated with bond yields has substantial predictive power for risk premiums! Explained variation in realized excess returns increases from 28% to 46% when unspanned macro information is added!

Unspanned Macro Risks Financial Frictions Early Warning System References Forward Term Premiums With Spanned Macro Risks (CMM ) 7% CME 0 JPS CME0 0 S-CME JPS spanned 6% M CM CM KW 5% 4% 3% 2% 1% 0% 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 ‐1%

Unspanned Macro Risks Financial Frictions Early Warning System References Bringing Policy Analysis and Market Pricing Together If we focus on bond-market factors, we miss the impact of the macroeconomy of risk premiums in ﬁnancial markets. If we introduce macroeconomic variables (output, inﬂation) as risk factors, we fail to accurately price bonds.

Unspanned Macro Risks Financial Frictions Early Warning System References Bringing Policy Analysis and Market Pricing Together If we focus on bond-market factors, we miss the impact of the macroeconomy of risk premiums in financial markets. If we introduce macroeconomic variables (output, inflation) as risk factors, we fail to accurately price bonds. Can we build an economic framework for pricing bonds and measuring risk premiums in which: Bond yields follow a low-dimensional factor model (say with level, slope, and curvature as risk factors); Profitable riskless arbitrage opportunities are ruled out; Macroeconomic information influences investors’ attitudes towards risks

Unspanned Macro Risks Financial Frictions Early Warning System References Risk Premium Accounting with Unspanned Macro Risks Joslin, Priebsch, and Singleton (2011) Bond yields have a low dimensional factor structure: summarize underlying risks as (Level, Slope, Curvature): yt ≈ an + bn Levelt + bn Slopet + bn Curvaturet , n L S C Risk premiums (expected excess returns) also depend on the state of the macroeconomy– GRO and IN F . Intuitively, there are a small number or risks underlying each bond market, but investors’ attitudes towards these risks depend on the state of the global economy.

Unspanned Macro Risks Financial Frictions Early Warning System References Forward Term Premiums in the US 7% CME 0 JPS CME0 0 S-CME JPS spanned 6% M CM CM KW 5% 4% 3% 2% 1% 0% 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 ‐1%

Unspanned Macro Risks Financial Frictions Early Warning System References Forward Term Premiums Versus FRB Fed Funds Target 7% 0 18% CME JPS CME0 0 6% S-CME JPS spanned 16% FF r (right) FF Target 14% 5% 13% 12% 4% 10% 3% 8% 8% 2% 6% 1% 3% 4% 0% 2% 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 ‐1% ‐2% 0%

Unspanned Macro Risks Financial Frictions Early Warning System References Do Financial Frictions Matter for Risk Premiums? [With hindsight!] What should we look for? 1 Liquidity and the balance sheets of ﬁnancial institutions: Shin (2008), Adrian and Shin (2009). 2 Funding and Hedging pressures from GSEs: slope of the term structure of GSE spreads, GSE2. Massive growth in balance sheets of GSEs, indicative of funding conditions. GSEs hedge the interest rate risk of their mortgage positions with swaps. 3 Conditions in bank-loan market: senior loan oﬃcer survey of demand for C&I loans by large and medium size companies.

Unspanned Macro Risks Financial Frictions Early Warning System References Repo Positions and Mean Leverage of Primary Dealers 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 0.5 24 GRepo LevPD 23 0.4 22 0.3 21 Annual Growth Rate Leverage Ratio 0.2 20 0.1 19 0 18 −0.1 17 −0.2 16 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08

Unspanned Macro Risks Financial Frictions Early Warning System References Senior Loan Oﬃcer Survey And BBB Corporate Spreads 0.6 0.015 Survey Strong C&I Demand --Survey Tighter C&I Terms 0.4 0.01 BBB PC1 0.005 0.2 0 0 -0.005 -0.2 -0.01 -0.4 -0.015 -0.6 -0.02 -0.8 -0.025

Unspanned Macro Risks Financial Frictions Early Warning System References Projections of xrLevelt+1yr and xrSlopet+1yr Excess Returns on U.S. Dollar Swap Portfolios PP LHS PP xrP C1t+1yr xrP C2t+1yr RHS PP PP ∗ P C1 −.441 .309 P C2 .997∗ −.353 P C3 −.957 1.06∗ IN F −5.89∗ 2.60 .101 1.97 −2.12 −.020 GIP 1.65∗ 2.13∗ 2.82 −.868 −1.16† −1.59 GP ay −9.48 −9.66 −9.96 1.35∗ −1.88 .945 M bsED .003 .016 .016 −.013 GSE2 −.0004 −.0003 −.0001 −.0002 C&ILT .002 .038 −.010∗ −.003 GRepo .034 .043∗ −.010∗ −.013 R2 0.75 0.47 0.70 0.91 0.52 0.86 Signiﬁcance: 1%; ∗ 5%; † 10%.

Unspanned Macro Risks Financial Frictions Early Warning System References Forward Term Premiums in the US 7% CME 0 JPS CME0 0 S-CME JPS spanned 6% M CM CM KW 5% 4% 3% 2% 1% 0% 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 ‐1%

Unspanned Macro Risks Financial Frictions Early Warning System References Risk Premiums as Early Warning Signals Singleton and Tamarisa (2012) Is there information in sovereign bond markets about “abnormal” conditions that regulators should be monitoring? Did investors fail to adequately price sovereign risks in Europe? Or where risk premiums the natural outcome of economic and regulatory policies? Will risk premiums signal the next ﬁnancial crisis?

-2.5 -2 -1.5 -1 ‐0.5 0 0.5 1 1.5 29/29/1989 Unspanned Macro Risks3/30/19909/28/19903/29/19919/30/19913/31/19929/30/19923/31/19939/30/19933/31/1994 Data ending in 2011 Data ending in 20069/30/19943/31/19959/29/19953/29/19969/30/19963/31/19979/30/19973/31/19989/30/1998 Financial Frictions3/31/19999/30/19993/31/20009/29/20003/30/20019/28/2001 United States3/29/20029/30/20023/31/20039/30/20033/31/20049/30/20043/31/20059/30/20053/31/20069/29/20063/30/20079/28/20073/31/20089/30/2008 Early Warning System3/31/20099/30/20093/31/20109/30/20103/31/20119/30/2011 Early Warning: Risk Premiums for US Market References

-2 -1.5 -1 -0.5 0 0.5 1 1.5 15 2 2.5 31/1/20015/1/2001 Unspanned Macro Risks9/1/20011/1/20025/1/20029/1/20021/1/2003 Data ending in 2009 Data ending in 20075/1/20039/1/20031/1/20045/1/20049/1/20041/1/20055/1/20059/1/2005 Financial Frictions1/1/20065/1/20069/1/2006 Greece1/1/20075/1/20079/1/20071/1/20085/1/20089/1/20081/1/20095/1/20099/1/20091/1/20105/1/2010 Early Warning System9/1/20101/1/20115/1/20119/1/2011 Early Warning: Risk Premiums for Greek Market References

Unspanned Macro Risks Financial Frictions Early Warning System References Adrian, T., and H. Shin, 2009, “Liquidity and Leverage,” Journal of Financial Intermediation, 17, 315–329. Joslin, S., M. Priebsch, and K. Singleton, 2011, “Risk Premiums in Dynamic Term Structure Models with Unspanned Macro Risks,” working paper, Stanford University. Kim, D., and J. Wright, 2005, “An Arbitrage-Free Three-Factor Term Structure Model and the Recent Behavior of Long-term Yields and Distant-Horizon Forward Rates,” working paper, Discussion Series 2005-33, Federal Reserve Board. Shin, H., 2008, “Risk and Liquidity in a System Context,” Journal of Financial Intermediation, 17, 315–329.

Kenneth Singleton: Risk Premiums in Sovereign Debt Markets

by Barcelona Graduate School of Economics (GSE)

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