The Relation Between Default-Free Interest Rates and Expected Economic Growth Is Stronger Than You Think

The relation between default-free interest rates and expected economic growth is substantially stronger than suggested by extant literature. Futures-implied Treasury bill yield spreads are more highly correlated with future real consumption, investment, and GNP growth than spot spreads. This stronger relation arises because using futures removes a component of the spot term structure that covaries negatively with real economic growth. Treasury forward rates from spot bills contain a premium for the risk that short-sellers will default. This risk premium is negatively related to expected economic growth.     

Time variation in the relationship between inflation and interest rates

This paper tests the propositions that the real rate of interest was constant from 1953 to 1971 and that Treasury bill yields included an efficient inflationary premium over the same period. Only the former hypothesis is rejected. Comparable results are obtained with both variable parameter regression and piecewise linear regression. Direct estimates of the real rate of interest are reported.     

A Required Yield Theory of Stock Market Valuation and Treasury Yield Determination

Stock market valuation and Treasury yield determination are consistent with the Fisher effect (1896) as generalized by Darby (1975) and Feldstein (1976) . The U.S. stock market (S&P 500) is priced to yield ex-ante a real after-tax return directly related to real long-term GDP/capita growth (the required yield ). Elements of our theory show that: (1) real after-tax Treasury and S&P 500 forward earnings yields are stationary processes around positive means; (2) the stock market is indeed priced as the present value of expected dividends with the proviso that investors are expecting fast mean reversion of the S&P 500 nominal growth opportunities to zero. Moreover, (3) the equity premium is mostly due to business cycle risk and is a direct function of below trend expected productivity, where productivity is measured by the growth in book value of S&P 500 equity per-share. Inflation and fear-based risk premia only have a secondary impact on the premium. The premium is always positive or zero with respect to long-term Treasuries. It may be negative for short-term Treasuries when short-term productivity outpaces medium and long run trends. Consequently: (4) Treasury yields are mostly determined in reference to the required yield and the business cycle risk premium; (5) the yield spread is largely explained by the differential of long-term book value per share growth vs. near term growth, with possible yield curve inversions. Finally, (6) the Fed model is partially validated since both the S&P 500 forward earnings yield and the ten-year Treasury yield are determined by a common factor: the required yield.     

The long-run equity risk premium

Based on a survey of US Chief Financial Officers (CFOs), we present expectations of the equity risk premium measured over a 10-year horizon relative to a 10-year US Treasury bond. This multi-year survey has been conducted each quarter from June 2000 to June 2005. Each quarter the survey also provides measures of cross-sectional disagreement about the risk premium, skewness, and a measure of individual uncertainty. The individual uncertainty is deduced from the 80% confidence interval that each respondent provides for his or her risk premium assessment. We also present evidence on the determinants of the long-run risk premium. Our analysis suggests there is a positive correlation between the ex ante risk premium and real interest rates as reflected in Treasury Inflation Indexed Notes.     

Treasury Safety,Liquidity, and Money Premium Dynamics: Evidence from Debt Limit Impasses

Treasury securities enjoy a “money premium” because they are ultra-safe and liquid. However, during debt limit impasses, the safety and liquidity of Treasury securities temporarily deteriorate, eroding the money premium. Using past impasses, we find the money premium eroded by roughly six basis points across all Treasury securities and up to 50 basis points for the shortest maturities at the greatest risk of a delayed principal payment. Safety and liquidity each accounted for about half of the erosion. The deterioration of safety and liquidity also appears to interact, consistent with theories of default-driven liquidity risk and the information sensitivity of debt.     

Estimating Portfolio and Consumption Choice: A Conditional Euler Equations Approach

This paper develops a nonparametric approach to examine how portfolio and consumption choice depends on variables that forecast time-varying investment opportunities. I estimate single-period and multiperiod portfolio and consumption rules of an investor with constant relative risk aversion and a one-month to 20-year horizon. The investor allocates wealth to the NYSE index and a 30-day Treasury bill. I find that the portfolio choice varies significantly with the dividend yield, default premium, term premium, and lagged excess return. Furthermore, the optimal decisions depend on the investor's horizon and rebalancing frequency.     

INFLUENCE OF TREASURY BILL FUTURES TRADING ON THE PRIMARY SALE OF THE DELIVERABLE TREASURY BILL

This paper investigates the impact of the presence of Treasury bill (T-bill) futures market contracts on the primary auction price of deliverable T-bills. Of the 52 weekly three- and six-month T-bill auctions, only four are deliverable against the T-bill futures market contract. This unique ability to deliver may command a premium price in the primary market. The results of this study support this hypothesis with regard to the six-month auction but are inconclusive with regard to the three-month auction. Furthermore, there is some evidence that the 1983 rule change making the one-year T-bill a deliverable instrument reduced the size of the premium in the six-month bill auction.     

RECENT EVIDENCE ON THE ACCURACY AND RATIONALITY OF POPULAR INFLATION FORECASTS

This paper compares the accuracy and examines the rationality of inflation forecasts extracted from U.S. Treasury bill yields, the mean forecast of surveys conducted by the Institute for Social Research, and the predictions from a rolling time-series model. Measures of realized inflation include both the Consumer Price Index reported during the period and a revised CPI series (CPIX) that replaces the mortgage interest rate with the recently adopted “rental equivalence” component. Inferences about accuracy and rationality depend upon both the measure of inflation and the period studied. The findings suggest that survey forecasts should be used when turbulent variation in the unobservable expected real rate of interest obscures the measurement of the market's expectation of inflation.     

The realized forward term premium in the repo market

Repurchase agreements for general-collateral government debt measure the short-term cost of riskless borrowing, thus avoiding issues relating to specialness of Treasury offerings or irregular term-to-maturity in the Treasury bill market. The spread between reverse and repo rates has previously been ignored by researchers who find that the pure expectation hypothesis either holds at this extremely short end of the term structure or that observed deviations from the expectations hypothesis are not economically significant. This paper shows that the time-varying realized forward premium at the short-end of the yield curve is consistently positive when accounting for the spread between repurchase and reverse repurchase agreement rates.     

STOCK MARKET SIGNALS OF CHANGES IN EXPECTED INFLATION

This paper examines the relationship between stock returns and several measures of expected inflation. The proxies include the inflation forecasts extracted from U.S. Treasury bill yields, the mean forecast of surveys conducted by the Institute for Social Research, and the predictions from a rolling time-series model. Unlike recent studies, there does not appear to be a significant negative relationship between stock returns and expected inflation at the beginning of the period. The results are consistent with the hypothesis that stock returns signal changes in expected inflation.     

ESTIMATING THE EQUITY RISK PREMIUM AND EQUITY COSTS: NEW WAYS OF LOOKING AT OLD DATA

This article examines three alternative ways of estimating the expected return on the equity market in using the CAPM or some other risk premium model. The three techniques are (1) direct estimation of the average nominal equity return for use as a forecast nominal equity return; (2) estimation of the average real equity return, which can then be added to a forecast inflation rate; and (3) estimation of an average equity risk premium, which is then added to a current risk-free rate. Ibbotson and Sinquefeld's data on annual holding period returns are used to test the validity of their assumption that the equity risk premium follows a random walk and that the third of these approaches is thus the best method.
The paper reaches three major conclusions. First, each of these three techniques involves a "bias" of some kind. The use of average equity returns as a forecast is subject to "risk-free rate" and "inflation rate" biases, while the use of an average equity risk premium is subject to a "term premium" bias. As a result, only the data can tell us which approach is best. Second, from analyzing equity and bond return data and the trend in interest rates, the author concludes that the term premium bias when using average historic equity risk premium is by far the largest of the three sources of bias. Indeed, the popular practice of adding an historic average equity risk premium to the 30-year Treasury bond rate significantly overstates equity costs. Third, after examining equity rates of return back to 1871, the author concludes that the real equity return seems to follow a process that is close to a random walk and is thus the "best" of the three techniques to use as a "naive" forecast.     

The paper‐bill spread and real output: what matters more,a change in the paper rate or a change in the bill rate?

This paper adds to the literature on the information content of the paper-bill spread by explicitly taking into account the two sources of wider spreads, rises in the paper rate and declines in the bill rate. Results from impulse response analysis and variance decompositions suggest that decreases in real output are greater and last longer when a widening of the paper-bill spread comes from an increase in the paper rate rather than from an equivalent decrease in the bill rate. This is consistent with the idea that changes in the commercial paper rate have greater information content about future business cycles than do changes in the Treasury bill rate.     

Failed delivery and daily Treasury bill returns

If the seller of a Treasury bill does not provide timely and correct delivery instructions to the clearing bank, the bank does not deliver the security. Furthermore, the seller is not paid until this failed delivery is rectified. Since the purchase price is not changed, these fails generate interest-free loans from the seller to the buyer. This article studies the effect of failed delivery on Treasury bill prices. We find that investors bid prices to a premium to reflect the possibility of obtaining the interest-free loans that fails represent. This premium is a function of the opportunity cost of the fail. We also find that the bid-ask spread varies directly with the length of the fail. We rule out that our results are due to liquidity premiums, or to a general weekly pattern in short-term interest rates or the bid-ask spread.     

ARE TREASURY INFLATION PROTECTED SECURITIES REALLY TAX DISADVANTAGED?

In 1997, the U.S. Treasury introduced Inflation Protected Securities, commonly known as TIPS. Several in the finance field have since described these securities as “tax disadvantaged” relative to conventional securities, leading to serious questions regarding their appropriateness outside of tax‐deferred accounts. In this article, we develop a framework that demonstrates that at least in a real sense the tax treatment of TIPS is trivially different from that of conventional Treasury securities. Moreover, empirically we find evidence that TIPS generally have after‐tax yields comparable to, if not exceeding, conventional fixed‐rate Treasury securities. We also show that TIPS have generally outperformed matched‐maturity conventional Treasury securities in terms of after‐tax rates of return.     

The Fear Premium and Daily Comovements of the S&P 500 E/P ratio and Treasury Yields before and during the 2008 Financial Crisis

I develop a new risk measure called the Total Fear Premium that generalizes Faugere‐Van Erlach (2009) and accounts for both flight‐to‐safety and flight‐to‐liquidity behavior. This new measure helps to explain why the daily S&P 500 forward earnings yield (E/P ratio) is strongly negatively correlated with daily Treasury yields of all maturities during the 2008 financial crisis, which is a reversal from the relation that prevailed before the crisis. The Total Fear Premium “mimics” the VIX during the financial crisis. Once the basic GARCH formulation modeling the interaction between the earnings yield and Treasury yields is augmented with the Total Fear Premium, the relation between the earnings yield and short‐term Treasury yields becomes significantly positive, in line with Fama's (1975) view that short‐term yields are good proxies for expected inflation. Two by‐products of this analysis are: 1) a new risk premium measure associated with flight‐to‐liquidity and 2) a new way to measure the inflation risk premium on a daily basis.     

The Purchasing Power of Money and Nominal Interest Rates: A Re-Examination

While it has been known for some time that, under uncertainty, the original version of the Fisher hypothesis is not precisely correct, empirical researchers have largely ignored this fact. Such an omission has possibly resulted in erroneous conclusions concerning other hypotheses; most notably the impact of prices on the real economy. This paper clarifies some of the previous interpretations of the existing empirical literature and provides a theoretical version of the relation between prices and interest rates. Empirical tests based on both the Livingston survey data and data from time-series forecasting models provide support for the Fisher effect and the hypothesis that only covariance risk is priced in the Treasury bill market.     

Idiosyncratic Variation of Treasury Bill Yields

I document a dramatic increase in the importance of two types of variation in Treasury bill yields beginning in the early 1980s. The first is idiosyncratic variation in individual short-maturity (less than three months) bill yields. The second is a common component in Treasury bill yields that is not shared by yields on other instruments, such as short-maturity privately-issued instruments or longer-maturity Treasury notes and bonds. Some evidence suggests the first type reflects increased market segmentation. These results have important implications for the calibration and testing of no-arbitrage term structure models and interpreting tests of the expectations hypothesis.     

Did the repeated debt ceiling controversies embed default risk in US Treasury securities?

We examine whether the financial market charged a default risk premium to US Treasury securities when the US Federal government repeatedly reached the legally binding debt limits between 2002 and 2006. We show that for the first two of the four recurrences since the first episode in 1996, the financial market charged a small default risk premium to the Treasury securities. However, we find no significant evidence of a pricing effect in the last two recurrences. The results suggest that the financial market gradually perceived the budget standoffs as the boy who cried wolf.     

What went wrong? The Puerto Rican debt crisis,the “Treasury Put,” and the failure of market discipline

What went wrong? Why did seemingly rational, forward-looking bond investors continue to purchase Puerto Rican debt with only a modest risk premium? Why did financial markets fail to exercise market discipline and restrict capital flows to Puerto Rico?This paper examines the hypothesis that investors believed Puerto Rican debt was implicitly insured by the U.S. government by studying a rare situation where this “Treasury Put” was extinguished. The expectation of a federal bailout was perfectly reasonable given past behavior by the federal government. Evaluating the Treasury Put hypothesis with a minimal set of assumptions is possible given three unique features of the economic environment. The key feature is an exogenous “seismic shock” – the non-bailout of the city of Detroit in 2013 that effectively extinguished the Treasury Put, estimated in this paper as 350 basis points. Institutional reforms that would eliminate the Treasury Put are considered, but none are found satisfactory. How to extinguish the Treasury Put on an ongoing basis in a democratic society remains an open question.     

Estimation and Test of a Simple Model of Intertemporal Capital Asset Pricing

A simple valuation model with time‐varying investment opportunities is developed and estimated. The model assumes that the investment opportunity set is completely described by the real interest rate and the maximum Sharpe ratio, which follow correlated Ornstein–Uhlenbeck processes. The model parameters and time series of the state variables are estimated using U.S. Treasury bond yields and expected inflation from January 1952 to December 2000, and as predicted, the estimated maximum Sharpe ratio is related to the equity premium. In cross‐sectional asset‐pricing tests, both state variables have significant risk premia, which is consistent with Merton's ICAPM.