THE POSSIBILITY OF ESTIMATING RISK PREMIA IN ASSET PRICING MODELS

The authors show that estimates of risk premia on the market based on capital asset pricing models or arbitrage pricing theories can only be estimates of the ex post or sample risk premium on the market and cannot be interpreted as better estimates of the ex ante premium than those provided by sample averages of data. The ex ante premium drops out of the generating function for the returns used in the second-pass regressions. Although previous estimates of nonmarket premia have failed to take appropriate account of the population mean, that mean can in fact be estimated and appropriate adjustments made. Various approaches to estimating the ex ante risk premium and the population mean are discussed.     

Confidence intervals of the premiums of optimal bonus malus systems

In view of the economic importance of motor third-party liability insurance in developed countries the construction of optimal BMS has been given considerable interest. However, a major drawback in the construction of optimal BMS is that they fail to account for the variability on premium calculations which are treated as point estimates. The present study addresses this issue. Specifically, nonparametric mixtures of Poisson laws are used to construct an optimal BMS with a finite number of classes. The mixing distribution is estimated by nonparametric maximum likelihood (NPML). The main contribution of this paper is the use of the NPML estimator for the construction of confidence intervals for the premium rates derived by updating the posterior mean claim frequency. Furthermore, we advance one step further by improving the performance of the confidence intervals based on a bootstrap procedure where the estimated mixture is used for resampling. The construction of confidence intervals for the individual premiums based on the asymptotic maximum likelihood theory is beneficial for the insurance company as it can result in accurate and effective adjustments to the premium rating policies from a practical point of view.     

A time-varying common risk factor affecting corporate yield spreads

A time-varying common risk factor affecting corporate yield spreads is modelled by extending a panel data model. The panel data model accommodates a common factor, which is associated with time-varying individual effects. The factor multiplied by a bond-specific unobservable is identified as a systematic risk premium. In disentangling the systematic risk premium, both credit and liquidity risks are evaluated; the credit risk is assessed by bond rating, and the liquidity risk is indirectly measured by discrepancy in quoted yields by brokerage firms. Parameters are estimated by the generalized method of moments procedure. The model is tested on the corporate bond market in Japan. Empirical results show that the time-varying common risk factor is successfully estimated together with credit and liquidity risks.     

Returns after personal tax on UK equity and gilts, 1919–1998

This paper investigates whether personal tax could help explain the size of the historic equity premium in the UK measured before personal tax. If there has been a higher tax burden on equity, some of the premium could be viewed as compensation for tax. It is estimated here that personal tax reduces the arithmetic mean nominal return on equity from 13.3% to 11.1% pa during the period 1919–1998, and the mean return on gilts from 7.1% to 5.6% pa. Thus, personal tax accounts for a slightly higher proportion of the before-tax return on gilts than on equity, implying that the equity premium is not a compensation for a higher tax burden on equity.     

Equity premium estimates from economic fundamentals under structural breaks

This article compares three estimates of the conditional equity premium using dividend and earnings growth rates to measure the expected rate of capital gain. The premia are estimated using a theory-informed Bayesian model that admits structural breaks. The equity premium fell from 8.16% in 1951 to 1.15% in 1985. Approximately half of this decline was reversion of a high conditional premium to the long run mean and the remainder resulted from a decline in the expected stock return. The decline in the expected stock return was largely driven by the Fed Accord (1951) and the Fed's ‘monetarist policy experiment’ (1979–1982).     

偏度风险溢酬及其预测能力研究——基于人民币对外汇期权的实证分析

基于无模型方法,利用在岸人民币对美元期权的市场价格数据,通过提取风险中性三阶矩和已实现三阶矩估算偏度风险溢酬,并考察其时变特征、与波动率风险溢酬的关系和对汇率尾部风险的预测能力。结果表明,外汇期权市场上存在显著为负的时变偏度风险溢酬;偏度风险溢酬与波动率风险溢酬存在共同的驱动因子。此外,偏度风险溢酬在短期内对汇率暴涨的尾部风险事件具备一定的预测能力。当偏度风险溢酬增加时,投资者对偏度风险的厌恶加剧,预期未来人民币大幅贬值的概率上升。     

DEFAULT RISK PREMIA IN THE NEAR-CASH INVESTMENT MARKET: THE CASE OF AUCTION RATE PREFERRED STOCK VERSUS COMMERCIAL PAPER

Auction rate preferred stock (ARPS) is often regarded as an alternative to other near-cash instruments such as commercial paper while the dividend exclusion for ARPS offers tax advantages to corporate purchasers. The mean default risk premium for ARPS, relative to commercial paper, is estimated at 83 basis points during stable financial markets. This default premium appears to surge during unstable equity markets, having jumped by 192 basis points in November 1987. Lower-rated ARPS shows even larger changes, with yields 40–50 basis points above yields on high-rated ARPS, adjusted for the normal risk premium differential. The perceived risk change of ARPS underscores how quickly market participants re-evaluate default risk, and even the importance of the priority order among debt and equity claimants. Findings suggest ARPS and commercial paper are not an acceptable substitute for commercial paper during times of unsettled equity markets.     

The relation between stock returns and short-term interest rates

This study examines the relation between the expected returns on common stocks and short-term interest rates. Using a two-factor model of stock returns, we show that the expected returns on common stocks are systematically related to the market risk and the interest-rate risk, which are estimated as the sensitivity of common-stock excess returns to the excess return on the equally weighted market index and to the federal fund premium, respectively. We find that the interest-rate risk for small firms is a significant source of investors' portfolio risk, but is not properly reflected in the single-factor market risk. We also find that the interest-rate risk for large firms is “negative” in the sense that the market risk estimated from the single-factor model overstates the true risk of large firms. An application of the Fama-MacBeth methodology indicates that the interest-rate risk premium as well as the market's risk premium are significant, implying that both the market risk and the interest-rate risk are priced. We show that the interest-rate risk premium explains a significant portion of the difference in expected returns between the top quintile and the bottom quintile of the NYSE and AMEX firms. We also show that the turn-of-the-year seasonal is observed for the interest-rate risk premium; however, the risk premium for the rest of the year is still significant, although small in mangitude.     

Volatility Risk Premium,Risk Aversion,and the Cross‐Section of Stock Returns

We test if innovations in investor risk aversion are a priced factor in the stock market. Using 25 portfolios sorted on book‐to‐market and size as test assets, our new factor together with the market factor explains 64% of the variation in average returns compared to 60% for the Fama‐French model. The new factor is generally significant with an estimated risk premium close to its time series mean also when industry portfolios and portfolios sorted on previous returns are augmented to the test assets.     

The Equity Premium and Structural Breaks

A long return history is useful in estimating the current equity premium even if the historical distribution has experienced structural breaks. The long series helps not only if the timing of breaks is uncertain but also if one believes that large shifts in the premium are unlikely or that the premium is associated, in part, with volatility. Our framework incorporates these features along with a belief that prices are likely to move opposite to contemporaneous shifts in the premium. The estimated premium since 1834 fluctuates between 4 and 6 percent and exhibits its sharpest drop in the last decade.     

Isolating the disaster risk premium with equity options

The US equity risk premium is approximated with a mean unhedged equity return. I utilize out-of-the-money put options to obtain a hedged equity return, which allows me to quantify the disaster risk premium as the difference between the means of unhedged and hedged equity returns. I demonstrate that a substantial fraction of the U.S. equity risk premium over the period from 1996 to 2016 is attributed to disasters defined as stock price depreciations below a pre-specified strike price. Employing alternative hedging schemes increases the contribution of disasters to the equity risk premium.     

A macroeconomic hedge portfolio and the cross section of stock returns

We use a stock's returns on days when important macroeconomic news is released to form a hedge portfolio, which is long (short) in stocks which have a sensitive (insensitive) reaction to the surprise component of the macroeconomic news. This macroeconomic hedge portfolio (MHP) earns a risk premium of about 5% p.a. over time and a similar premium when used as a risk factor in an asset pricing model. This premium can be interpreted as a cost of an insurance against unexpected changes in an investor's marginal utility. We show that risk premiums associated with the MHP are estimated with a higher precision than traditional macroeconomic tracking portfolios. Furthermore, when the MHP is present in a common factor model, risk factors like high minus low lose much of their ability to explain the cross section of stock returns.     

Is Default Event Risk Priced in Corporate Bonds?

This article provides an empirical decomposition of the default,liquidity, and tax factors that determine expected corporatebond returns. In particular, the risk premium associated witha default event is estimated. The intensity-based model is estimatedusing bond price data for 104 US firms and historical defaultrates. Significant risk premia on common intensity factors andimportant tax and liquidity effects are found. These componentsgo a long way towards explaining the level of expected corporatebond returns. Adding a positive default event risk premium helpsto explain the remaining error, although this premium cannotbe estimated with high statistical precision.     

AN ECONOMETRIC ANALYSIS OF EQUITY COSTS AND RISK PREMIUMS IN THE ELECTRIC UTILITY INDUSTRY: 1971–1985

This paper develops a varying parameter econometric model that estimates the cost of equity of individual utility firms from 1971 to 1985. The equity costs estimated in this framework can be analyzed in terms of their statistical precision. The paper also examines, theoretically and empirically, the relationship between the econometric estimates of the equity risk premiums and the risk-free interest rates. The data do not support the hypothesis that risk premiums are independent of interest rates. Also, the relationship appears to vary over time. These results invalidate the risk premium approach in which equity costs are estimated by adding a constant, historical average risk premium to the prevailing interest rates.     

An introduction to security returns

The equity premium - the difference between the return achievable from investment in the equity market (R_M ) and the risk-free rate of return (R_F )- plays an important part in corporate finance. The expression equity premium (sometimes referred to as the equity risk premium) is used to denote the ex ante expectation of investors. The term excess return refers to the ex post achievement of stock returns over and above the risk-free return. If we compare US and UK returns, we find that total returns, real returns and the value of (R_M - R_F ) are all marginally higher for the UK. Summarized evidence appears in Table 1 and Table 6. Such greater returns may be due to an increased risk premium related to increasing unexpected inflation. Particularly important in estimating the equity risk premium is whether excess returns are measured using a geometric or an arithmetic mean return. To a significant extent, this question revolves around mean reversion in stock returns. Evidence of mean reversion is substantial, although it cannot be proved unequivocally. Given the weight of evidence of mean reversion, there may be a strong case for the use of a geometric mean with an equity premium of between 3% and 5% - or even less.     

Forward Foreign Exchange Rates,Expected Spot Rates,and Premia: A Signal-Extraction Approach

In this paper, we implement a methodology to identify and measure premia in the pricing of forward foreign exchange that involves application of signal-extraction techniques from the engineering literature. Diagnostic tests indicate that these methods are quite successful in capturing the essence of the time-series properties of premium terms. The estimated premium models indicate that premia show a certain degree of persistance over time and that more than half the variance in the forecast error that results from the use of current forward rates as predictors of future spot rates is accounted for by variation in premium terms. The methodology can be applied straightforwardly to the measurement of unobservables in other financial markets.     

Mean reversion and consumption smoothing

Most models of the evolution of wealth and consumption assumethat wealth volatility and risk premium are constant. But infact, volatility decliners, and risk premium seems to decline,as wealth rises. A model that allows mean reversion in the sensethat the risk premium declines as wealth rises can help explainboth the 'consumption smoothing puzzle' and the 'equity premiumpuzzle'. In an example of such a model that gives us an analyticsolution, direct and derived risk aversion are both constant,but differ.     

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.     

The components of the illiquidity premium: An empirical analysis of US stocks 1927–2010

This paper implements a conditional version of the liquidity adjusted CAPM (LCAPM). The conditional LCAPM allows for a time-varying decomposition of the total illiquidity premium into a level component and three risk components. The estimated average annual total illiquidity premium for US stocks 1927–2010 is 1.74–2.08%, which is substantially lower than in most previous studies. The contributions from illiquidity level and illiquidity risk are 1.25–1.28% and 0.46–0.83%, respectively. Of the three illiquidity risk components, risk related to the hedging of wealth shocks is the most important, while commonality risk is the least important. The illiquidity premia are clearly time-varying, with peaks in downturns and crises, but with no general tendency to decrease over time. The level premium and the risk premium are significantly positively correlated, at around 0.35; indicating that in periods of turbulence both illiquidity cost and illiquidity risk premia tend to be high.     

The joint cross-sectional variation of equity returns and volatilities

This paper analyzes the determinants of the simultaneous cross-sectional variation of return and volatility risk premia. Independently of the model specification employed, the estimated risk premium associated with the default premium beta is always positive and statistically different from zero. Moreover, the risk premium of the market volatility risk premium beta is negative and statistically significant. However, both risk factors are priced economically and statistically differently in the volatility and return segments of the market. On average, common factors in both segments explain 90% of the variability of volatility risk premium portfolios, but only 65% of the variability of equity return portfolios.