What's your real cost of capital?

In valuing any investment project or corporate acquisition, executives must decide what discount rate to use in their estimates of future cash flows. The traditional approach is to apply the capital asset pricing model (CAPM), which has remained fundamentally unchanged for 40 years. But the formula--in particular, its beta element--has long been a source of frustration. In fact, corporate executives and investment bankers routinely fudge their CAPM estimates, say the authors, because experience and intuition tell them the model produces inappropriate discount rates. CAPM has three main problems: First, beta is a measure of both a stock's correlation and its volatility; second, beta is based on historical data; and third, CAPM rates don't take into account the term of the investment. These factors together result in discount rates that defy common sense. As an alternative to CAPM and its beta element, the authors developed a forward-looking approach to calculating a company's cost of capital, the market-derived capital pricing model (MCPM). It does not incorporate any measure of historical stock-to-market correlation, relying instead on estimates of future volatility derived from the options market. This is helpful since investor expectations from the options market are built into a company's current stock price. Using GE as an example, the authors give step-by-step instructions for how to calculate discount rates with MCPM. They also offer evidence from a range of industries to show that MCPM's discount rates are more realistic--especially from the corporate investor's perspective--than are CAPM's.     

Understanding Stock Price Volatility: The Role of Earnings

In an efficient capital market, asset prices vary when investors change their expectations about cash flows, discount rates, or both. Using dividends to measure cash flows, previous research shows that the aggregate dividend‐price ratio varies due to changes in expected discount rates (returns) rather than expected cash flows. In contrast, using accounting earnings instead of dividends as a measure of cash flows, this paper shows that as much as 70% of the variation in the dividend‐price ratio can be explained by changes in expected earnings. Moreover, the paper documents a significant negative correlation between expected returns and expected earnings, suggesting that variations in a common factor to both may generate significant price volatility. The results are consistent with the dividend‐policy irrelevance hypothesis.     

Implementing Fischer Black's Simple Discounting Rule

Corporate managers typically estimate the value of capital projects by discounting the project's expected future net cash flows at the cost of capital. The capital asset pricing model (CAPM) is generally used to estimate that cost. But, as anyone who has worked on the finance or business development staff of a public company can attest, there are major challenges in applying the CAPM, including largely unresolved questions about what constitutes the “market portfolio,” how to estimate market risk premiums, and how to estimate the betas of projects. In a short article published in Financial Management in 1988, Fischer Black proposed a valuation “discounting rule” that avoids all these problems—one that involves discounting a relatively certain (as opposed to an expected or average) level of operating cash flows at the risk-free rate. But Black's article does not address the question of how to calculate these “certainty equivalent” or “conditional” cash flows. In this article, the authors propose a way of implementing Black's rule that involves estimating the “conditional” cash flows in a three-step procedure:

• • Find a benchmark security that correlates with the project's cash flows;
• • Estimate the percentiles of the distribution in which the benchmark return equals the risk-free rate over different investment horizons;
• • Use information from corporate managers to assess the cash flows that define the same percentiles in the cash flow distributions.

As the authors point out, the virtue of Black's rule is that it shifts the focus of the analyst away from the assessment of discount factors and puts it squarely on the more challenging, and arguably more relevant, problem of estimating the project's cash flows.     

Discounting Mean Reverting Cash Flows with the Capital Asset Pricing Model

Discounting cash flows requires an equilibrium model to determine the cost of capital. The CAPM of Sharpe and the intertemporal asset pricing model of Merton (1973) offer a theoretical justification for discounting at a constant risk adjusted rate. Two problems arise with this application. First, for mean reverting cash flows the risk adjustment is unknown, and second, if the present value is compounded forward then the distribution of future wealth is likely right skewed. I develop equilibrium discount rates for cash flows whose level or growth rate is mean reverting. Serial correlation also largely eliminates the skewness problem.     

Valuation in Emerging Markets: A Simulation Approach

Most of the foundations of valuation theory have been designed for use in developed markets. Because of the greater, and in some cases different, risks associated with emerging markets (although recent experience might suggest otherwise), investors and corporate managers are often uncomfortable using traditional methods. The typical way of capturing emerging-market risks is to increase the discount rate in the standard valuation model. But, as the authors argue, such adjustments have the effect of undermining some of the basic assumptions of the CAPM-based discounted cash flow model. The standard theory of capital budgeting suggests that estimates of unconditional expected cash flows should be discounted at CAPM discount rates (or betas) that reflect only “systematic,” or “nondiversifiable,” market-wide risks. In practice, however, analysts tend to take what are really estimates of “conditional” expected cash flows—that is, conditional on the firm or its country avoiding a crisis—and discount them at higher rates that reflect not only systematic risks, but diversifiable risks that typically involve a higher probability of crisis-driven costs of default. But there is almost no basis in theory for the size of the increases in discount rates. In this article, the authors propose that analysts in emerging markets avoid this discount rate problem by using simulation techniques to capture emerging-market risks in their estimates of unconditional expected cash flows—in other words, estimates that directly incorporate the possibility of an emerging-market crisis and its consequences. Having produced such estimates, analysts can then discount them using the standard Global CAPM.     

Accounting‐based Risk Management and the Capital Asset Pricing Model: An Empirical Comparison

Accounting‐based risk management (ABRM) is a theoretically consistent and practical tool for calculating the cost of capital from underlying financial ratios. In this paper, a sample of ABRM‐generated discount factors is used to generate risk‐adjusted returns, which are compared to CAPM equivalent discount factors. In view of the debates about CAPM's validity, alternative models, the nature and scale of the equity risk premium, and the importance of discount rates in capital budgeting and asset valuation, ABRM's characteristics and resulting discount rates offer a potentially useful alternative. Results suggest that although average discount rates are comparable, their cross‐sectional distributions are dissimilar, so that investors in an average risky firm are overcompensated for systematic risk when using CAPM discount rates, because CAPM discount factors overestimate risk arising from fixed costs in most firms.     

Risk-adjusted discount rates and capital budgeting under uncertainty

This paper is concerned with the valuation of multiperiod cash flows in a world where prices are determined according to the Sharpe-Lintner-Black model of capital market equilibrium. We find that the current market value of any future net cash flow is the current expected value of the flow discounted at risk-adjusted discount rates for each of the periods until the flow is realized. The discount rates are known and non-stochastic, but the rates for the different periods preceding the realization of a cash flow need not to be the same, and the rates relevant for a given period can differ across cash flows. The risk adjustments in the discount rates arise because of uncertainties about reassessments through time of the expected value of a flow and the relationships between these reassessments and the corresponding reassessments of the expected cash flows of all firms.     

Why Is Long‐Horizon Equity Less Risky? A Duration‐Based Explanation of the Value Premium

We propose a dynamic risk‐based model that captures the value premium. Firms are modeled as long‐lived assets distinguished by the timing of cash flows. The stochastic discount factor is specified so that shocks to aggregate dividends are priced, but shocks to the discount rate are not. The model implies that growth firms covary more with the discount rate than do value firms, which covary more with cash flows. When calibrated to explain aggregate stock market behavior, the model accounts for the observed value premium, the high Sharpe ratios on value firms, and the poor performance of the CAPM.     

New estimates of the cost of capital for pharmaceutical firms

Academic researchers, as well as pharmaceutical firms themselves, often use the Capital Asset Pricing Model (CAPM) to estimate a firm's cost of capital. But the CAPM implicitly assumes that cash flows follow a random walk. This assumption is inconsistent with our finding that large U.S.-based pharmaceutical firms' cash flow growth rates display either momentum or mean-reversion. We show that growth rate momentum implies: (1) the systematic risk of a project increases monotonically with time to maturity of the cash flows; and (2) longer duration projects require a higher cost of capital. One of the practical implications of our results is that the traditional CAPM underestimates the cost of capital for some pharmaceutical firms by as much as 2.8%. These findings are quite relevant for the policy debate about the high rates of return earned by pharmaceutical companies, which some claim are pure rents and are not necessary to attract investors. Our theoretical and empirical analysis shows that high returns are often required to compensate for the higher systematic risk of long-duration pharmaceutical cash flows.     

Cost of capital equations under the Australian imputation tax system

Since the introduction of the Australian imputation tax system, there have been problems both in the measurement of the market value of franking (imputation tax) credits and in their application to estimating cash flows and the cost of capital. In the present paper, we provide a convenient and robust resolution to the above problems in the context of an internally consistent set of equations for the cost of capital, asset valuation and the capital asset pricing model (CAPM). The equations apply under both classical and imputation tax systems and under differential taxation of dividends, capital gains and interest. The simple form of the CAPM presented here is shown to encompass more complex versions of the CAPM, which attempt to accommodate the effect of personal taxes. The valuation equations require an estimate of the market value of $1 of the firm's dividends, within which is embedded the market value of the imputation tax credits. Separate estimates of the value of imputation tax credits, or Officer's gamma factor, are not required.     

When are investment projects in the same risk class?

If two investments have the same pay‐off covariance with the market but one has higher expected pay‐off, which asset according to the CAPM has most risk? One answer is that as far as risk goes the two assets are the same, because they have the same covariance with the market. The correct answer, pointed out nearly four decades ago by Eugene Fama, but long overlooked, is that investments have the same risk, the same returns beta and the same CAPM discount rate if and only if they have the same ratio of ex ante pay‐off covariance to pay‐off mean. This insight clarifies much of the conventional wisdom that surrounds capital budgeting and ‘risk‐adjusted’ discount rates, while also displaying the mechanics by which information arrival affects the CAPM cost of capital.     

VALUATION AND RISK-ADJUSTED DISCOUNT RATES

There is a continuing controversy as to whether the use of a constant risk adjusted discount rate in capital budgeting decisions implies that the risk of the cash flows increases over time. This paper shows that valuation using these discount rates implies an increasing premium for risk over time but that the increasing premium is due to the net impact of the uncertainty in the cash flow; uncertainty in future market expectations of the cash flow; and changes in the market price of risk. The risk of the cash flow itself need not be increasing over time.     

Presidential Address: Discount Rates

Discount‐rate variation is the central organizing question of current asset‐pricing research. I survey facts, theories, and applications. Previously, we thought returns were unpredictable, with variation in price‐dividend ratios due to variation in expected cashflows. Now it seems all price‐dividend variation corresponds to discount‐rate variation. We also thought that the cross‐section of expected returns came from the CAPM. Now we have a zoo of new factors. I categorize discount‐rate theories based on central ingredients and data sources. Incorporating discount‐rate variation affects finance applications, including portfolio theory, accounting, cost of capital, capital structure, compensation, and macroeconomics.     

The term structures of equity and interest rates

This paper proposes a dynamic risk-based model capable of jointly explaining the term structure of interest rates, returns on the aggregate market, and the risk and return characteristics of value and growth stocks. Both the term structure of interest rates and returns on value and growth stocks convey information about how the representative investor values cash flows of different maturities. We model how the representative investor perceives risks of these cash flows by specifying a parsimonious stochastic discount factor for the economy. Shocks to dividend growth, the real interest rate, and expected inflation are priced, but shocks to the price of risk are not. Given reasonable assumptions for dividends and inflation, we show that the model can simultaneously account for the behavior of aggregate stock returns, an upward-sloping yield curve, the failure of the expectations hypothesis, and the poor performance of the capital asset pricing model.     

Pricing assets with stochastic cash-flow growth

We model the time series behavior of dividend growth rates, as well as the profitability rate, with a variety of autoregressive moving-average processes, and use the capital asset pricing model (CAPM) to derive the appropriate discount rate. One of the most important implications of this research is that the rate of return beta changes with the time to maturity of the expected cash flow, and the degree of mean reversion displayed by the growth rate. We explore the consequences of this observation for three different strands of the literature. The first is for the value premium anomaly, the second for stock valuation and learning about long-run profitability, and the third is for the St. Petersburg paradox. One of the most surprising results is that the CAPM implies a higher rate of return beta for value stocks than growth stocks. Therefore, value stocks must have higher expected returns, and this is what is required theoretically in order to explain the well-known value premium anomaly.     

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.     

Examination of Conditional Asset Pricing in UK Stock Returns

I examine the empirical performance of various specifications of the capital asset pricing model (CAPM) in UK stock returns, using the stochastic discount framework. When the proxy for the market portfolio includes a proxy for labor income growth in addition to the stock market index, the performance of the CAPM improves. The improvement in performance shows in the magnitude and significance of the pricing errors and in the reduced impact of asset characteristics and other factors in the pricing of assets. There is further improvement when I use conditional versions of the models.     

基金业绩归因与投资者行为

本文以2006年1月至2016年12月中国64家股票型主动管理基金为样本,从基金净资金流变化的角度,检验了投资者决策与基金业绩结构的关系,以期更好地理解投资者行为。本文结论有:(1)整体上,投资者在衡量基金经理能力时,更关注原始超额收益率或只基于市场风险调整风险敞口,这可能与中国市场投资工具仍然不够充分、风险难以有效对冲有关;(2)机构投资者相比个人投资者对风险敞口的识别更严格;(3)简单模型的优势集中在市场波动低、投资者情绪高的时期;(4)除基金经理能力外,净资金流变化对市场风险报酬也很敏感;(5)从alpha的角度,我国基金市场仍存在“赎回异象”,可能与“处置效应”有关,仍需提升投资者对风险的认知,引导市场形成更加科学的投资观念。     

Does It Pay to Bet Against Beta? On the Conditional Performance of the Beta Anomaly

Prior studies find that a strategy that buys high‐beta stocks and sells low‐beta stocks has a significantly negative unconditional capital asset pricing model (CAPM) alpha, such that it appears to pay to “bet against beta.” We show, however, that the conditional beta for the high‐minus‐low beta portfolio covaries negatively with the equity premium and positively with market volatility. As a result, the unconditional alpha is a downward‐biased estimate of the true alpha. We model the conditional market risk for beta‐sorted portfolios using instrumental variables methods and find that the conditional CAPM resolves the beta anomaly.