Recovering the probability density function of asset prices using garch as diffusion approximations

This paper uses Garch models to estimate the objective and risk-neutral density functions of financial asset prices and by comparing their shapes, recover detailed information on economic agents' attitudes toward risk. It differs from recent papers investigating analogous issues because it uses Nelson's result that Garch schemes are approximations of the kind of differential equations typically employed in finance to describe the evolution of asset prices. This feature of Garch schemes usually has been overshadowed by their well-known role as simple econometric tools providing reliable estimates of unobserved conditional variances. We show instead that the diffusion approximation property of Garch gives good results and can be extended to situations with (i) non-standard distributions for the innovations of a conditional mean equation of asset price changes and (ii) volatility concepts different from the variance. The objective PDF of the asset price is recovered from the estimation of a nonlinear Garch fitted to the historical path of the asset price. The risk-neutral PDF is extracted from cross-sections of bond option prices, after introducing a volatility risk premium function. The direct comparison of the shapes of the two PDF_s reveals the price attached by economic agents to the different states of nature. Applications are carried out with regard to the futures written on the Italian 10-year bond.     

Disagreement and asset prices

How do differences of opinion affect asset prices? Do investors earn a risk premium when disagreement arises in the market? Despite their fundamental importance, these questions are among the most controversial issues in finance. In this paper, we use a novel data set that allows us to directly measure the level of disagreement among Wall Street mortgage dealers about prepayment speeds. We examine how disagreement evolves over time and study its effects on expected returns, return volatility, and trading volume in the mortgage-backed security market. We find that increased disagreement is associated with higher expected returns, higher return volatility, and larger trading volume. These results imply that there is a positive risk premium for disagreement in asset prices. We also show that volatility in and of itself does not lead to higher trading volume. Instead, only when disagreement arises in the market is higher uncertainty associated with more trading. Finally, we are able to distinguish empirically between two competing hypotheses regarding how information in markets gets incorporated into asset prices. We find that sophisticated investors appear to update their beliefs through a rational expectations mechanism when disagreement arises.     

Transaction Costs and the Pricing of Assets

The existence of transaction costs explains why investors do not fully diversify their portfolios. This paper examines the implications of such limited diversification on equilibrium asset prices in the framework of the capital asset pricing model. In the pricing equation obtained here an asset's risk premium depends on a weighted average of its covariance with the market and its own variance.     

Local risk factors in emerging markets: Are they separately priced?

We provide new evidence on the pricing of local risk factors in emerging stock markets. We investigate whether there is a significant local currency premium together with a domestic market risk premium in equity returns within a partial integration asset pricing model. Given previous evidence on currency risk, we conduct empirical tests in a conditional setting with time-varying prices of risk. Our main results support the hypothesis of a significant exchange risk premium related to the local currency risk. Exchange rate and domestic market risks are priced separately for our sample of seven emerging markets. The empirical evidence also suggests that although statistically significant, local currency risk is on average smaller than domestic market risk but it increases substantially during crises periods, when it can be almost as large as market risk. Disentangling these two factors is thus important in tests of international asset pricing for emerging markets.     

International asset pricing under segmentation and PPP deviations

We analyze the impact of both purchasing power parity (PPP) deviations and market segmentation on asset pricing and investor's portfolio holdings. The freely traded securities command a world market risk premium and an inflation risk premium. The securities that can be held by only a subset of investors command two additional premiums: a conditional market risk premium and a segflation risk premium. Our model is empirically supported with important implications for tests of international asset pricing.     

Operating Hedge and Gross Profitability Premium

We show theoretically that variable production costs reduce systematic risk of firms' cash flows if capital and variable inputs are complementary in firms' production and input prices are procyclical. In our dynamic model, this operating hedge effect is weaker for more profitable firms, giving rise to a gross profitability premium. Moreover, gross profitability and value factors are distinct and negatively correlated, and their premia are not captured by the capital asset pricing model (CAPM). We estimate the model by simulated method of moments, and find that its main implications for stock returns and cash flow dynamics are quantitatively consistent with the data.     

Climate change financial risks: Implications for asset pricing and interest rates

In addition to tail macroeconomic events (e.g. wars, financial crises and pandemics), climate change poses a threat to financial stability — with extreme climatic events increasing in frequency and intensity and policy risks putting pressure on asset valuations. We study the effect of a changing climate on asset prices and interest rates through the lens of a dynamic CAPM with rare disasters, time-varying risk and recursive preferences. In our model, a changing climate makes tail events more frequent and less predictable, increasing the premium of climate risk; interestingly, this change may not be fully reflected in the overall market risk premium that includes both components of risk: macroeconomic and environmental. Our results also support the hypothesis of a declining real rate of interest as the planet warms, while the increasing risk of climate policy reduces the participation of brown assets in the market portfolio.     

A Model of Monetary Policy and Risk Premia

We develop a dynamic asset pricing model in which monetary policy affects the risk premium component of the cost of capital. Risk‐tolerant agents (banks) borrow from risk‐averse agents (i.e., take deposits) to fund levered investments. Leverage exposes banks to funding risk, which they insure by holding liquidity buffers. By changing the nominal rate the central bank influences the liquidity premium, and hence the cost of taking leverage. Lower nominal rates make liquidity cheaper and raise leverage, resulting in lower risk premia and higher asset prices, volatility, investment, and growth. We analyze forward guidance, a “Greenspan put,” and the yield curve.     

The price of power: The valuation of power and weather derivatives

Pricing contingent claims on power presents numerous challenges due to (1) the unique behavior of power prices, and (2) time-dependent variations in prices. We propose and implement a model in which the spot price of power is a function of two state variables: demand (load) and fuel price. In this model, any power derivative price must satisfy a PDE with boundary conditions that reflect capacity limits and the non-linear relation between load and the spot price of power. Moreover, since power is non-storable and demand is not a traded asset, the power derivative price embeds a market price of risk. Using inverse problem techniques and power forward prices from the PJM market, we solve for this market price of risk function. During 1999–2001, the upward bias in the forward price was as large as $50/MWh for some days in July. By 2005, the largest estimated upward bias had fallen to $19/MWh. These large biases are plausibly due to the extreme right skewness of power prices; this induces left skewness in the payoff to short forward positions, and a large risk premium is required to induce traders to sell power forwards. This risk premium suggests that the power market is not fully integrated with the broader financial markets.     

The ex ante real rate and inflation premium under a habit consumption model

This paper analyzes and quantifies ex ante components of bond yields – real rate of returns and risk premiums – from observed prices of nominal and indexed bonds in the United Kingdom from 1983 to 2000. The estimation uses an asset pricing framework based on a habit consumption model together with a joint formulation of consumption growth and inflation. Nominal yields carry a time-varying inflation premium that is significant throughout the period, increasing in the bond's maturity and contributing up to 25 basis points to yearly nominal yields. The analysis allows the extraction of the ex ante real rate from indexed bonds by properly taking into account both the incomplete indexation on these instruments and the inflation premium embedded in the nominal bonds.     

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.     

Risk,uncertainty, and asset prices

We identify the relative importance of changes in the conditional variance of fundamentals (which we call “uncertainty”) and changes in risk aversion in the determination of the term structure, equity prices, and risk premiums. Theoretically, we introduce persistent time-varying uncertainty about the fundamentals in an external habit model. The model matches the dynamics of dividend and consumption growth, including their volatility dynamics and many salient asset market phenomena. While the variation in price–dividend ratios and the equity risk premium is primarily driven by risk aversion, uncertainty plays a large role in the term structure and is the driver of countercyclical volatility of asset returns.     

Risks for the Long Run: A Potential Resolution of Asset Pricing Puzzles

We model consumption and dividend growth rates as containing (1) a small long‐run predictable component, and (2) fluctuating economic uncertainty (consumption volatility). These dynamics, for which we provide empirical support, in conjunction with Epstein and Zin's (1989) preferences, can explain key asset markets phenomena. In our economy, financial markets dislike economic uncertainty and better long‐run growth prospects raise equity prices. The model can justify the equity premium, the risk‐free rate, and the volatility of the market return, risk‐free rate, and the price–dividend ratio. As in the data, dividend yields predict returns and the volatility of returns is time‐varying.     

Conditional Equity Premium and Aggregate Corporate Investment

We document a strong negative relation between aggregate corporate investment and conditional equity premium estimated from direct stock market risk measures. Consistent with the investment-based asset pricing model, the comovement with conditional equity premium fully accounts for aggregate investment's market return predictive power. Similarly, conditional equity premium is a significant determinant of classic Tobin's q measure, although q has much weaker explanatory power for aggregate investment possibly because of its measurement errors. Moreover, the positive relation between aggregate investment and investor sentiment documented in previous studies reflects the fact that both variables correlate closely with conditional equity premium.     

Consumption Volatility Risk

We show that time variation in macroeconomic uncertainty affects asset prices. Consumption volatility is a negatively priced source of risk for a wide variety of test portfolios. At the firm level, exposure to consumption volatility risk predicts future returns, generating a spread across quintile portfolios in excess of 7% annually. This premium is explained by cross‐sectional differences in the sensitivity of dividend volatility to consumption volatility. Stocks with volatile cash flows in uncertain aggregate times require higher expected returns.     

Volatility,the Macroeconomy,and Asset Prices

How important are volatility fluctuations for asset prices and the macroeconomy? We find that an increase in macroeconomic volatility is associated with an increase in discount rates and a decline in consumption. We develop a framework in which cash flow, discount rate, and volatility risks determine risk premia and show that volatility plays a significant role in explaining the joint dynamics of returns to human capital and equity. Volatility risk carries a sizable positive risk premium and helps account for the cross section of expected returns. Our evidence demonstrates that volatility is important for understanding expected returns and macroeconomic fluctuations.     

Secured Loans and Risky Assets in a Monetary Economy

We study the implication of secured credit with a default option for monetary equilibrium. The intermediary structure has the feature of costly state verification, with the monitoring cost interpreted as the cost of foreclosing assets once a default occurs. Without monitoring costs, uncertainty in asset payoffs does not matter for allocation. The asset price can exhibit a liquidity premium because more assets as collateral raises the borrower's credit limit. When there are monitoring costs, the asset's liquidity premium is strictly positive because pledging more assets reduces the default probability and thus the chance to incur monitoring costs. Under some circumstances, increased risk to dividends of the pledged asset may decrease the marginal borrowing cost to such an extent that bank lending rises, and higher default rates are accompanied by larger aggregate liquidity.     

Time-varying risk aversion and asset prices

This paper uses a variant of the consumption-based representative agent model in Campbell and Cochrane [Campbell, J.Y., Cochrane, J.H., 1999. By force of habit: Consumption-based explanation of aggregate stock market behavior. Journal of Political Economy 107, 205–251] to study how investors’ time-varying risk aversion affects asset prices. First, we show that a countercyclical variation of risk aversion drives a procyclical conditional risk premium. Second, we show that with a small value for the volatility of the log surplus consumption ratio, a large value of risk aversion may not determine whether the equity premium and the risk-free rate puzzles can be resolved or not. Third, we show that countercyclical risk aversion may not help explain the predictability of long-horizon stock returns, the univariate mean-reversion of stock prices and the “leverage effect” in return volatility.     

Pricing options in incomplete equity markets via the instantaneous Sharpe ratio

We use a continuous version of the standard deviation premium principle for pricing in incomplete equity markets by assuming that the investor issuing an unhedgeable derivative security requires compensation for this risk in the form of a pre-specified instantaneous Sharpe ratio. First, we apply our method to price options on non-traded assets for which there is a traded asset that is correlated to the non-traded asset. Our main contribution to this particular problem is to show that our seller/buyer prices are the upper/lower good deal bounds of Cochrane and Saá-Requejo (J Polit Econ 108:79–119, 2000) and of Björk and Slinko (Rev Finance 10:221–260, 2006) and to determine the analytical properties of these prices. Second, we apply our method to price options in the presence of stochastic volatility. Our main contribution to this problem is to show that the instantaneous Sharpe ratio, an integral ingredient in our methodology, is the negative of the market price of volatility risk, as defined in Fouque et al. (Derivatives in financial markets with stochastic volatility. Cambridge University Press, 2000).     

Asset pricing in China's domestic stock markets: Is there a logic?

China's stock markets have grown rapidly since their inception and have become an increasingly important emerging market for international investors. However, there are few systematic studies on how asset prices are formed in Chinese domestic equity markets; popular financial media even depict the market as irrational. In this paper, we study the asset pricing mechanism in the nascent Chinese stock markets, with the objective of identifying variables that capture the cross-sectional variation in average stock returns. We focus on the effects of various market imperfections in China. We find that while the market risk (beta) is not priced, there is a significantly negative relationship between firm-specific risk and expected returns. Chinese investors are willing to pay a significant premium for more liquid stocks or for dividend-paying stocks. Furthermore, investors value local A-shares more if there are offshore counterparts (e.g., B- and H-shares) for foreigners, implying that a Chinese firm with a foreign shareholder base has a lower cost of capital, ceteris paribus. Lastly, as with U.S. and other mature markets, firm size and the book-to-market ratio are systematically related to stock returns. Given market imperfections, stocks are priced rather rationally in China, despite the widespread perception to the contrary.