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Integer Factorization
, 2005
"... Many public key cryptosystems depend on the difficulty of factoring large integers. This thesis serves as a source for the history and development of integer factorization algorithms through time from trial division to the number field sieve. It is the first description of the number field sieve fro ..."
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Cited by 123 (8 self)
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Many public key cryptosystems depend on the difficulty of factoring large integers. This thesis serves as a source for the history and development of integer factorization algorithms through time from trial division to the number field sieve. It is the first description of the number field sieve from an algorithmic point of view making it available to computer scientists for implementation. I have implemented the general number field sieve from this description and it is made publicly available from the Internet. This means that a reference implementation is made available for future developers which also can be used as a framework where some of the sub
Risk Premiums in Dynamic Term Structure Models with . . .
, 2010
"... This paper quantifies how variation in real economic activity and inflation in the U.S. influenced the market prices of level, slope, and curvature risks in U.S. Treasury markets. To accomplish this we develop a novel arbitragefree DT SM in which macroeconomic risks – in particular, real output and ..."
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Cited by 66 (10 self)
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This paper quantifies how variation in real economic activity and inflation in the U.S. influenced the market prices of level, slope, and curvature risks in U.S. Treasury markets. To accomplish this we develop a novel arbitragefree DT SM in which macroeconomic risks – in particular, real output and inflation risks – impact bond investment decisions separately from information about the shape of the yield curve. Estimates of our preferred macroDT SM over the twentythree year period from 1985 through 2007 reveal that unspanned macro risks explained a substantial proportion of the variation in forward terms premiums. Unspanned macro risks accounted for nearly 90 % of the conditional variation in shortdated forward term premiums, with unspanned real economic growth being the key driving factor. Over horizons beyond three years, these effects were entirely attributable to unspanned inflation. Using our model, we also reassess some of Chairman Bernanke’s remarks on the interplay between term premiums, the shape of the yield curve, and macroeconomic activity.
Information in (and not in) the term structure.
 Review of Financial Studies,
, 2011
"... ABSTRACT Standard approaches to building and estimating dynamic term structure models rely on the assumption that yields can serve as the factors. However, the assumption is neither theoretically necessary nor empirically supported. This paper documents that almost half of the variation in bond ris ..."
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Cited by 34 (3 self)
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ABSTRACT Standard approaches to building and estimating dynamic term structure models rely on the assumption that yields can serve as the factors. However, the assumption is neither theoretically necessary nor empirically supported. This paper documents that almost half of the variation in bond risk premia cannot be detected using the cross section of yields. Fluctuations in this hidden component have strong forecast power for both future shortterm interest rates and excess bond returns. They are also negatively correlated with aggregate economic activity, but macroeconomic variables explain only a small fraction of variation in the hidden factor.
The CrossSection and TimeSeries of Stock and Bond Returns. Unpublished Working Paper.
, 2010
"... Abstract We propose an arbitragefree stochastic discount factor (SDF) model that jointly prices the crosssection of returns on portfolios of stocks sorted on booktomarket dimension, the crosssection of government bonds sorted by maturity, the dynamics of bond yields, and time series variation ..."
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Cited by 22 (3 self)
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Abstract We propose an arbitragefree stochastic discount factor (SDF) model that jointly prices the crosssection of returns on portfolios of stocks sorted on booktomarket dimension, the crosssection of government bonds sorted by maturity, the dynamics of bond yields, and time series variation in expected stock and bond returns. Its pricing factors are motivated by a decomposition of the pricing kernel into a permanent and a transitory component. Shocks to the transitory component govern the level of the term structure of interest rates and price the crosssection of bond returns. Shocks to the permanent component govern the dividend yield and price the average equity returns. Third, shocks to the relative contribution of the transitory component to the conditional variance of the SDF govern the CochranePiazzesi (2005, CP) factor, a strong predictor of future bond returns. These shocks price the crosssection of booktomarket sorted stock portfolios. Because the CP factor is a strong predictor of economic activity oneto twoyears ahead, shocks to the importance of the transitory component signal improving economic conditions. Value stocks are riskier and carry a return premium because they are more exposed to such shocks.
Choice of Sample Split in OutofSample Forecast Evaluation
, 2011
"... Outofsample tests of forecast performance depend on how a given data set is split into estimation and evaluation periods, yet no guidance exists on how to choose the split point. Empirical forecast evaluation results can therefore be di ¢ cult to interpret, particularly when several values of the ..."
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Cited by 22 (2 self)
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Outofsample tests of forecast performance depend on how a given data set is split into estimation and evaluation periods, yet no guidance exists on how to choose the split point. Empirical forecast evaluation results can therefore be di ¢ cult to interpret, particularly when several values of the split point might have been considered. While the probability of spurious rejections is highest when a short outofsample period is used, conversely the power of outofsample forecast evaluation tests is strongest when the sample split occurs early in the sample. We show that very large size distortions can occur, more than tripling the rejection rates of conventional tests of predictive accuracy, when the sample split is viewed as a choice variable, rather than being …xed ex ante. To deal with this issue, we propose a test statistic that is robust to the e¤ect of mining over the start of the outofsample period. Empirical applications to predictability of stock returns and in‡ation demonstrate that outofsample forecast evaluation results can critically depend on how the sample split is determined. Keywords: Outofsample forecast evaluation; data mining; recursive estimation; predictability of stock returns; in‡ation forecasting. JEL Classi…cation: C12, C53, G17. 1 1
Why Gaussian MacroFinance Term Structure Models are (Nearly) Unconstrained FactorVARs.” Discussion paper,
, 2011
"... ABSTRACT This article develops a new family of Gaussian macrodynamic term structure models (MTSMs) in which bond yields follow a lowdimensional factor structure and the historical distribution of bond yields and macroeconomic variables is characterized by a vectorautoregression with order p > 1 ..."
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Cited by 21 (7 self)
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ABSTRACT This article develops a new family of Gaussian macrodynamic term structure models (MTSMs) in which bond yields follow a lowdimensional factor structure and the historical distribution of bond yields and macroeconomic variables is characterized by a vectorautoregression with order p > 1. Most formulations of MTSMs with p > 1 are shown to imply a much higher dimensional factor structure for yields than what is called for by historical data. In contrast, our "asymmetric" arbitragefree MTSM gives modelers the flexibility to match historical lag distributions with p > 1 while maintaining a parsimonious factor representation of yields. Using our canonical family of MTSMs we revisit: (i) the impact of noarbitrage restrictions on the joint distribution of bond yields and macro risks, comparing models with and without the restriction that macro risks are spanned by yieldcurve information; and (ii) the identification of the policy parameters in Taylorstyle monetary policy rules within MTSMs with macro risk factors and lags. ( JEL: G12,E43, C58, E58) KEYWORDS: Macrofinance term structure model, Lags, Taylor Rule Identification Dynamic term structure models in which a subset of the pricing factors are macroeconomic variables (MTSMs) often have bond yields depending on lags of these factors. 1 As typically parameterized, such MTSMs imply that the crosssection
2012, ‘Bond Liquidity Premia
 Review of Financial Studies
"... Recent models of limits to arbitrage imply that the tightness of funding conditions faced by financial intermediaries is a component of the pricing kernel. In the US, the repo market is the key funding market for traders and arbitrageurs implying in turn that the ontherun premium shares a common c ..."
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Cited by 16 (1 self)
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Recent models of limits to arbitrage imply that the tightness of funding conditions faced by financial intermediaries is a component of the pricing kernel. In the US, the repo market is the key funding market for traders and arbitrageurs implying in turn that the ontherun premium shares a common component with the risk premia observed in other markets. This observation leads to the following identification strategy. We measure the value of liquidity from the crosssection of ontherun premia by adding a liquidity factor to an arbitragefree term structure model. As predicted, we find that liquidity value affects the crosssection of risk premia at quarterly and annual horizons. An increase in the value of liquidity predicts lower risk premia for ontherun and offtherun bonds but higher risk premia on Libor loans, swap contracts and corporate bonds. Moreover, the measured impact is pervasive through crisis and normal times. Finally, we find that liquidity value varies with changes in aggregate uncertainty, measured from S&P500 options, and with changes in monetary stance, measured from bank reserves and monetary aggregates. These linkages are consistent with the theory and suggest that different securities serve, in part, and to varying degrees, to fulfill investors ’ uncertain future needs for cash.
CoVar”, Federal Reserve Bank of New York Staff Reports, no 348.
, 2007
"... Abstract We reconsider the role of financial intermediaries in monetary economics. We explore the hypothesis that financial intermediaries drive the business cycle by way of their role in determining the price of risk. In this framework, balance sheet quantities emerge as a key indicator of risk ap ..."
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Cited by 13 (1 self)
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Abstract We reconsider the role of financial intermediaries in monetary economics. We explore the hypothesis that financial intermediaries drive the business cycle by way of their role in determining the price of risk. In this framework, balance sheet quantities emerge as a key indicator of risk appetite and hence of the "risktaking channel" of monetary policy. We document evidence that the balance sheets of financial intermediaries reflect the transmission of monetary policy through capital market conditions. Our findings suggest that the traditional focus on the money stock for the conduct of monetary policy may have more modern counterparts, and we suggest the importance of tracking balance sheet quantities for the conduct of monetary policy.
Improving the predictability of real economic activity and asset returns with forward variances inferred from option portfolios. SSRN Working Paper 1622088,
, 2010
"... a b s t r a c t This paper presents an option positioning that allows us to infer forward variances from option portfolios. The forward variances we construct from equity index options help to predict (i) growth in measures of real economic activity, (ii) Treasury bill returns, (iii) stock market r ..."
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Cited by 9 (3 self)
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a b s t r a c t This paper presents an option positioning that allows us to infer forward variances from option portfolios. The forward variances we construct from equity index options help to predict (i) growth in measures of real economic activity, (ii) Treasury bill returns, (iii) stock market returns, and (iv) changes in variance swap rates. Our yardstick for measuring predictive ability is both individual and joint parameter statistical significance within a market, as well as across a set of markets.
The Structure of Risks in Equilibrium Affine Models of Bond Yields ∗
, 2013
"... Many equilibrium term structure models (ETSMs) in which the state of the economy follows an affine process imply that the variation in expected excess returns on bond portfolio positions is fully spanned by the conditional variances of the state variables. We show that these two assumptions alone – ..."
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Cited by 6 (4 self)
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Many equilibrium term structure models (ETSMs) in which the state of the economy follows an affine process imply that the variation in expected excess returns on bond portfolio positions is fully spanned by the conditional variances of the state variables. We show that these two assumptions alone – an affine state process with conditional variances that span expected excess returns – are sufficient to econometrically identify the factors determining risk premiums in these ETSMs from data on the term structure of bond yields. Using this result we derive maximum likelihood estimates of the conditional variances of the state – the “quantities of risk” – and evaluate the goodnessoffit of a large family of affine ETSMs. These assessments of fit are fully robust to the values of the parameters governing preferences and the evolution of the state, and to whether or not the economy is arbitrage free. Our findings suggest that, to be consistent with U.S. macroeconomic and Treasury yield data, affine ETSMs should have the features that: (i) inflation risk, and not longrun risks or variation in risk premiums arising from habitbased preferences, is a significant (and perhaps the dominant) risk underlying risk premiums in U.S. Treasury markets; and (ii) risks that are unspanned by bond yields have substantial explanatory power for risk premiums consistent with timevarying market prices of risks.