Linear beta pricing with inefficient benchmarks in a given factor structure*

ABSTRACT

We show the equivalence between the zero-beta version of a multi-factor arbitrage pricing model and a linear pricing model utilizing undiversified inefficient benchmarks in a given factor structure. The resulting linear model is a two-beta model, with one beta related to the inefficient benchmark and another adjusting for its inefficiency. This linear model shows that there are only two distinctive and computable sources of risk, affecting security expected returns, despite the existence of several risk factors. In a short empirical example we demonstrate that the model can be employed to provide guidance and allow researchers to test for the validity of their selection of the underlying risk factors driving variations in security returns.     

Stochastic duration and fast coupon bond option pricing in multi-factor models

Generalizing Cox, Ingersoll, and Ross (1979), this paper defines the stochastic duration of a bond in a general multi-factor diffusion model as the time to maturity of the zero-coupon bond with the same relative volatility as the bond. Important general properties of the stochastic duration measure are derived analytically, and the stochastic duration is studied in detail in various well-known models. It is also demonstrated by analytical arguments and numerical examples that the price of a European option on a coupon bond (and, hence, of a European swaption) can be approximated very accurately by a multiple of the price of a European option on a zero-coupon bond with a time to maturity equal to the stochastic duration of the coupon bond. This revised version was published online in June 2006 with corrections to the Cover Date.     

基于套利理论与ICIR模型的债券市场发行定价偏离研究

基于套利定价理论与利率期限结构理论,运用Tobit多元线性回归模型,得出债券发行定价的主要影响因素为债券无风险利率、债券期限溢价、债项信用评级、债券主体信用评级和债券赎回风险溢价,在此基础上再通过改进的CIR定价模型(ICIR)对2006～2010年各债券定价偏离现象进行研究的结果表明,在1%的显著性水平上,ICIR模型测算的债券理论价格通过了二级市场的定价检验,ICIR模型对债券发行定价偏离进行检验具有较强的合理性;同时,从发行年份来看,近五年来,债券定价偏离总体呈逐年下降趋势,债券发行定价与ICIR定价与二级市场定价逐步接轨,市场化程度越来越高。     

Production and the Real Rate of Interest: A Sample Path Equilibrium

This paper examines a multiperiod production economy where investorsdo not observe the realizations of productivity factors or securityexpected returns. Unlike previous work, which expresses theequilibrium conditions as functions of unobservable (to bothreal-world investorsand empiricists) moments of the distributionsof returns, we express the equilibrium real rate asa functionof the observable sample paths of realizations of returns. Weprovide a framework for empirically testing this and other assetpricing models without outside-the-model econometric assumptionsneeded for producing the unobservable moments of returns. Weconstruct versions of the restrictions for any time intervalbetween observations. JEL codes: E43, G12, D92, D80, D51     

Production and the Real Rate of Interest: A Sample Path Equilibrium

This paper examines a multiperiod production economy where investors do not observe the realizations of productivity factors or security expected returns. Unlike previous work, which expresses the equilibrium conditions as functions of unobservable (to both real-world investors and empiricists) moments of the distributions of returns, we express the equilibrium real rate as a function of the observable sample paths of realizations of returns. We provide a framework for empirically testing this and other asset pricing models without outside-the-model econometric assumptions needed for producing the unobservable moments of returns. We construct versions of the restrictions for any time interval between observations.     

The impact of exchange rates on stock market returns: new evidence from seven free-floating currencies

This paper provides evidence of a significant exchange rate effect on stock index returns using data from seven selected countries practicing free-floating exchange rate regimes. This research uses parity and asset pricing theories, thus placing it within the monetary-cum-economics framework for international asset pricing. In this study, we apply a system of seemingly unrelated regression to control for unobserved heterogeneity and cross-sectional dependence. The findings constitute evidence of a statistically significant exchange rate impact on stock index returns across selected countries. These findings can be considered as falling under the arbitrage pricing approach of the international capital asset pricing model of Solnik who also used the parity-theoretical framework on exchange rate determination.     

Relationship between franking credits and the market risk premium: a comment

This paper examines two arguments presented in Gray and Hall (2006). First, that the generally used estimate of 0.06 for the market risk premium within the Officer version of the capital asset pricing model (CAPM) and the generally used estimate of 0.50 for the parameter ‘gamma’ within the Officer framework are jointly inconsistent with evidence concerning the market risk premium in the standard version of the CAPM. Second, that the first two of these parameter estimates are also jointly inconsistent with the observed cash dividend yield on the Australian market. To resolve these problems, Gray and Hall recommend setting gamma to zero. The present paper shows that the first argument does not account for the fact that imputation induces a reduction in the market risk premium as defined in the standard version of the CAPM. The present paper also shows that both arguments identify a problem that characterizes only parts of the Officer framework, and these parts are not generally used in Australia. Therefore, rather than suggesting that gamma should be zero, Gray and Hall's analysis identifies parts of the Officer framework that should be avoided.     

Dynamic Spanning in the Consumption-Based Capital Asset Pricing Model

Under the assumptions of the Consumption-based Capital Asset Pricing Model (CCAPM), Pareto optimal consumption allocations are characterized by each agent's consumption process being adapted to the filtration generated by the aggregate consumption process of the economy. The wealth processes of the agents, however, are adapted to the finer filtration generated by aggregate consumption and the conditional distribution of future aggregate consumption. Therefore, in order to achieve Pareto optimal consumption allocations, a sufficiently varied set of assets must exist such that any wealth process adapted to this finer filtration can be implemented by dynamically trading in that set of assets. We provide sufficient conditions for the existence of such a set of assets based on dynamically trading contingent claims on aggregate consumption. In addition, we give sufficient conditions for the existence of equilibria in a dynamically effectively complete market in which agents are only able to trade in contingent claims on aggregate consumption, the market portfolio of firms, and a (numeraire) zero-coupon bond. We demonstrate the role of short- and long-term contingent claims on aggregate consumption for the implementation of Pareto optimal allocations in the presence of short- andlong-term risks. In addition, in the presence of personal risks, we demonstrate the role of insurance contracts.     

Dynamic Spanning in the Consumption-Based Capital Asset Pricing Model

Under the assumptions of the Consumption-based Capital AssetPricing Model (CCAPM), Pareto optimal consumption allocationsare characterized by each agent's consumption process beingadapted to the filtration generated by the aggregate consumptionprocess of the economy. The wealth processes of the agents,however, are adapted to the finer filtration generated by aggregateconsumption and the conditional distribution of future aggregateconsumption. Therefore, in order to achieve pareto optimal consumptionallocations, a sufficiently varied set of assets must existsuch that any wealth process adapted to this finer filtrationcan be implemented by dynamically trading in that set of assets.We provide sufficient conditions for the existence of such aset of assets based on dynamically trading contingent claimson aggregate consumption. In addition, we give sufficient conditionsfor the existence of equilibria in a dynamically effectivelycomplete market in which agents are only able to trade in contingentclaims on aggregate consumption, the market portfolio of firms,and a (numeraire) zero-coupon bond. We demonstrate the roleof short- and long-term contingent claims on aggregate consumptionfor the implementation of Pareto optimal allocations inthe presenceof short- and long-term risks. In addition, in the presenceof personal risks, we demonstrate the role of insurance contracts.JEL Classification: G13.     

An implementation of the HJM model with application to Japanese interest futures

In this paper, we propose a new specification of the forward rate model of Heath, Jarrow and Morton [5] and apply it to the Japanese 3 month interest rate futures. Our empirical result shows that the model we propose can capture the forward interest rate movement.     

REIT Risk Premium Sensitivity and Interest Rates

This analysis investigates several aspects of the relationship between daily REIT stock risk premiums and various interest rates. Consistent with prior research, the general findings indicate that interest rates do impact REIT returns. This study specifically finds that stock returns are more sensitive to maturity rate spread between short- and long-term treasuries than the credit rate spread between commercial bonds and treasuries. In addition, the analyses document a structural model shift during the nineties that has made REITs more sensitive to credit risk. In additional to change in investor clientele, an analysis of declining REIT credit-worthiness points to a root cause for this shift.     

Modeling the behavior of real asset prices

Recently there has been much research treating housing and other real assets as financial claims, primarily in order to value their derivative assets, such as mortgages and mortgage-backed securities. Real asset prices are then typically modeled as a lognormal process, in the same manner that has traditionally been applied to firm value. The service flow or implicit value of a house is thus considered, in analogy with stock dividends, to be a fixed proportion of the fluctuating house price. We consider the appropriateness of this formulation and draw some distinctions between real assets, such as a house, and investment enterprises, such as a firm. We then propose an alternative method of formulating the service flow and the price of real assets which seems more appropriate to the economic characteristic of such assets.     

A Model of the Convenience Yields in On-the-Run Treasuries

The convenience yield differential between on- and off-the-run Treasury securities with identical maturities has two components. A non-cyclical component may arise due to the higher illiquidity of off-the-run bonds. Also, trading in the market for the next issue often causes cyclical shortages of the on-the-runs. When this occurs, owners of the on-the-run bond can earn riskless profits by borrowing at a special repo rate while lending at the prevailing risk free market rate. This second component of the convenience yield, induced by the auction, is cyclical. We first show that special repo rates and the convenience yield are jointly cyclical over the auction cycle. The patterns are statistically significant and pervasive. Repo specials are highest around the announcement day and disappear by the issue day. The off- minus on-the-run yield spread is highest at the beginning of the cycle and collapses near its end, consistent with a decreasing present value of profits over a decreasing horizon. Second, we develop a first no-arbitrage continuous-time model, with both interest and special repo rates stochastic, that prices the on-the-run bonds that command this convenience yield. A simple implementation of the model can generate yields consistent with the evidence.     

The Influence of Monetary Conditions on the Response of Interest Rate Futures to M1 Releases: 1976–1998

Abstract:   This study examines the response of T‐bill and T‐bond futures prices to weekly M1 announcements over the period March 1976 to November 1998 conditioned upon monetary operating procedures and the stance in monetary policy. In concurrence with previous studies, this study finds that unanticipated increases in M1 are negatively related to changes in T‐bill and T‐bond futures prices. However, when the data is sorted by monetary regime, the stance in monetary policy, and direction of money surprise, we find evidence to support the several competing theories historically suggested by Cornell (1983b) to explain the impact of money supply announcements.     

The Term Structure of Interest Rates: Bounded or Falling?

This short paper resolves an apparent contradiction between Feldman's (1989) and Riedel's (2000) equilibrium models of the term structure of interest rates under incomplete information. Feldman (1989) showed that in an incomplete information version of Cox, Ingersoll, and Ross (1985), where the stochastic productivity factors are unobservable, equilibrium term structures are ``interior' and bounded. Interestingly, Riedel (2000) showed that an incomplete information version of Lucas (1978), with an unobservable constant growth rate, induces a ``corner' unbounded equilibrium term structure: it decreases to negative infinity. This paper defines constant and stochastic asymptotic moments, clarifies the apparent conflict between Feldman's and Riedel's equilibria, and discusses implications. Because productivity and growth rates are not directly observable in the real world, the question we answer is of particular relevance.     

The relationship between implied and realized volatility: evidence from the Australian stock index option market

This paper examines the relationship between the volatility implied in option prices and the subsequently realized volatility by using the S&P/ASX 200 index options (XJO) traded on the Australian Stock Exchange (ASX) during a period of 5 years. Unlike stock index options such as the S&P 100 index options in the US market, the S&P/ASX 200 index options are traded infrequently and in low volumes, and have a long maturity cycle. Thus an errors-in-variables problem for measurement of implied volatility is more likely to exist. After accounting for this problem by instrumental variable method, it is found that both call and put implied volatilities are superior to historical volatility in forecasting future realized volatility. Moreover, implied call volatility is nearly an unbiased forecast of future volatility.

Valuation of a spark spread: an LM6000 power plant

This paper analyzes a power plant powered by two General Electric LM6000 gas turbines combined with a steam generator that allows combined cycle operations. We consider four distinct operating modes for the plant. Such a plant can be characterized as a real option on a spark spread: optimally converting natural gas to electricity. We use a Margrabe approach by using the market heat rate (the ratio of the electricity price to the natural gas price) as our underlying stochastic variable. We estimate a stochastic model for market heat rates that incorporates time of day, day of week, month, and the incidence or otherwise of a spike in heat rates. We use the model and its residuals in a bootstrap process simulating future market heat rates, and use a least-squares Monte Carlo approach to determine the optimal operating policy. We find that the annual average market heat rate is a good explanatory variable for the time integral of the plant operating margin, denominated in the natural gas numeraire. This allows us to express plant values in terms of the numeraire and convert to dollars by multiplying this by the natural gas forward curve and a forward curve of riskless discount rates. We also provide information about the optimal operating modes selected, the number of transitions between modes and how they relate to transition costs and the average heat rate for the year.     

International interest rates and US monetary policy announcements: Evidence from Hong Kong and Singapore

This paper investigates the responses of market interest rates to US monetary policy announcements for the US and two emerging economies, Hong Kong and Singapore which are similar on many respects but have experienced opposite exchange rate regimes in the last twenty years. Our results, based on market expectations extracted from federal fund futures rates, document that FOMC announcements significantly affect the term structure of interest rate in the US and both Asian countries. Further, international interest rate differentials around FOMC meeting dates tend to be negative for short maturities with the impact gradually dissipating as bond maturity increases. Finally, for the case of Singapore, we find that domestic interest rates react to both external and domestic monetary policy announcements with a magnitude that is larger over the full bond maturity spectrum for domestic announcements. These results are robust to time-varying futures risk premia and alternative measures of interest rates expectations.     

Modeling time series information into option prices: An empirical evaluation of statistical projection and GARCH option pricing model

This paper compares the empirical performances of statistical projection models with those of the Black–Scholes (adapted to account for skew) and the GARCH option pricing models. Empirical analysis on S&P500 index options shows that the out-of-sample pricing and projected trading performances of the semi-parametric and nonparametric projection models are substantially better than more traditional models. Results further indicate that econometric models based on nonlinear projections of observable inputs perform better than models based on OLS projections, consistent with the notion that the true unobservable option pricing model is inherently a nonlinear function of its inputs. The econometric option models presented in this paper should prove useful and complement mainstream mathematical modeling methods in both research and practice.