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The equity risk premium is the price of risk in equity markets, and it is a key input in estimating costs of equity and capital in both corporate finance and valuation. Given its importance, it is surprising how haphazard the estimation of equity risk premiums remains in practice. We begin this paper by looking at the economic determinants of equity risk premiums, including investor risk aversion, information uncertainty and perceptions of macroeconomic risk. In the standard approach to estimating the equity risk premium, historical returns are used, with the difference in annual returns on stocks versus bonds, over a long period, comprising the expected risk premium. We note the limitations of this approach, even in markets like the United States, which have long periods of historical data available, and its complete failure in emerging markets, where the historical data tends to be limited and volatile. We look at two other approaches to estimating equity risk premiums – the survey approach, where investors and managers are asked to assess the risk premium and the implied approach, where a forward-looking estimate of the premium is estimated using either current equity prices or risk premiums in non-equity markets. In the next section, we look at the relationship between the equity risk premium and risk premiums in the bond market (default spreads) and in real estate (cap rates) and how that relationship can be mined to generated expected equity risk premiums. We close the paper by examining why different approaches yield different values for the equity risk premium, and how to choose the “right” number to use in analysis.

The rate of failure in quantitative finance is high, and particularly so in financial machine learning. The few managers who succeed amass a large amount of assets, and deliver consistently exceptional performance to their investors. However, that is a rare outcome, for reasons that will become apparent in this presentation. Over the past two decades, I have seen many faces come and go, firms started and shut down. In my experience, there are 7 critical mistakes underlying most of those failures. This paper is partly based on the book Advances in Financial Machine Learning (Wiley, 2018). A full paper can be downloaded at: http://ssrn.com/abstract=3104816.

In the last decade, companies have come under pressure to be socially conscious and environmentally responsible, with the pressure coming sometimes from politicians, regulators and interest groups, and sometimes from investors. The argument that corporate managers should replace their singular focus on shareholders with a broader vision, where they also serve other stakeholders, including customers, employees and society, has found a receptive audience with corporate CEOs and institutional investors. The pitch that companies should focus on “doing good” is sweetened with the promise that it will also be good for their bottom line and for shareholders. In this paper, we build a framework for value that will allow us to examine how being socially responsible can manifest in the tangible ingredients of value and look at the evidence for whether being socially responsible is creating value for companies and for investors.

Our legacy financial infrastructure has both limited growth opportunities and contributed to the inequality of opportunities. Around the world, 1.7 billion are unbanked. Small businesses, even those with a banking relationship, often must rely on high-cost financing, such as credit cards, because traditional banking excludes them from loan financing. High costs also impact retailers who lose 3% on every credit card sales transaction. These total costs for small businesses are enormous by any metric. The result is less investment and decreased economic growth. Decentralized finance, or DeFi, poses a challenge to the current system and offers a number of potential solutions to the problems inherent in the traditional financial infrastructure. While there are many fintech initiatives, we argue that the ones that embrace the current banking infrastructure are likely to be fleeting. We argue those initiatives that use decentralized methods - in particular blockchain technology - have the best chance to define the future of finance. This is an excerpt from a early version of our manuscript, DeFi and the Future of Finance published by John Wiley and Sons. It includes drafts of chapters 1, 2, 7 and 8 plus the DeFi glossary.

As companies and investors globalize, we are increasingly faced with estimation questions about the risk associated with this globalization. When investors invest in China Mobile, Infosys or Vale, they may be rewarded with higher returns but they are also exposed to additional risk. When Siemens and Apple push for growth in Asia and Latin America, they clearly are exposed to the political and economic turmoil that often characterize these markets. In practical terms, how, if at all, should we adjust for this additional risk? We will begin the paper with an overview of overall country risk, its sources and measures. We will continue with a discussion of sovereign default risk and examine sovereign ratings and credit default swaps (CDS) as measures of that risk. We will extend that discussion to look at country risk from the perspective of equity investors, by looking at equity risk premiums for different countries and consequences for valuation. In the final section, we will argue that a company’s exposure to country risk should not be determined by where it is incorporated and traded. By that measure, neither Coca Cola nor Nestle are exposed to country risk. Exposure to country risk should come from a company’s operations, making country risk a critical component of the valuation of almost every large multinational corporation. We will also look at how to move across currencies in valuation and capital budgeting, and how to avoid mismatching errors.

Prior research has documented a carbon premium in realized returns, which have been assumed to proxy for expected returns and thus the cost of capital. We find that the carbon premium partially represents unexpected returns and thus outperformance. Companies with higher scope 1, scope 2, or scope 3 emissions enjoy superior earnings surprises and earnings announcement returns; quarterly earnings announcements account for 30-50% of the premium. When adding in announcement returns to events related to earnings calls, earnings guidance, dividends, and buybacks, this proportion rises to 40-65%. We find similar results for changes in emissions but not scaled emissions, consistent with earlier findings on realized returns. Our results suggest that the carbon premium, where it exists, partially results from an unpriced externality, highlighting the need for government action.

After the credit and liquidity crisis started in summer 2007 the market has recognized that multiple yield curves are required for estimation of both discount and FRA rates with dfferent tenors (e.g. Overnight, Libor 3 months, etc.), consistently with the large basis spreads and the wide diffusion of bilateral collateral agreements and central counterparties for derivatives transactions observed on the market. This paper recovers and extends our previous work to the modern multiple-curve bootstrapping of both discounting and FRA yield curves, consistently with the funding of market instruments. The theoretical pricing framework is introduced and modern pricing formulas for plain vanilla interest rate derivatives, such as Deposits, Forward Rate Agreements (FRA), Futures, Swaps, OIS, and Basis Swaps, are derived from scratch. The concrete EUR market case is worked out, and many details are discussed regarding the selection of market instruments, synthetic market quotes, smooth interpolation, effect of OIS discounting, possible negative rates, turn of year effect, local vs non local delta sensitivities, performance and yield curve sanity checks. The implementation of the proposed algorithms is available open source within the QuantLib framework.

It is often said by proponents of the Efficient Market Hypothesis that no strategy can consistently outperform a simple buy and hold investment in broad stock averages over time. However, using a strategy based on the principles of intermarket analysis, we find that this assertion is not entirely accurate. The Utilities sector has many unique characteristics relative to other sectors of the broader stock market, including its higher yield, lower beta, and relative insensitivity to cyclical behavior. Our analysis suggests that rolling outperformance in the sector is not only exploitable, but also provides important signals about market volatility, seasonality, and extreme market movement. We explore historical price behavior and create a simple buy and rotate strategy that is continuously exposed to equities, positioning into either the broad market or the Utilities sector based on lead-lag dynamics. Absolute performance and risk-adjusted returns for this beta rotation approach significantly outperform a buy and hold strategy of the market and of the Utilities sector throughout multiple market cycles.

Noted economist, Harry Markowitz (“Markowitz) received a Nobel Prize for his pioneering theoretical contributions to financial economics and corporate finance. His innovative work established the underpinnings for Modern Portfolio Theory — an investment framework for the selection and construction of investment portfolios based on the maximization of expected portfolio returns and simultaneous minimization of investment risk. This paper presents a simplified perspective of Markowitz’ contributions to Modern Portfolio Theory, foregoing in-depth presentation of the complex mathematical/statistical models typically associated with discussions of this theory, and suggesting efficient computer-based ‘short-cuts’ to these performing these intricate calculations.

Recent scholarship shows that informed traders increasingly disguise trades in economically linked securities such as exchange-traded funds (ETFs). Linking that work to longstanding literature on financial markets’ reactions to military conflict, we document a significant spike in short selling in the principal Israeli-company ETF days before the October 7 Hamas attack. The short selling that day far exceeded the short selling that occurred during numerous other periods of crisis, including the recession following the financial crisis, the 2014 Israel-Gaza war, and the COVID-19 pandemic. Similarly, we identify increases in short selling before the attack in dozens of Israeli companies traded in Tel Aviv. For one Israeli company alone, 4.43 million new shares sold short over the September 14 to October 5 period yielded profits (or approximates avoided losses) of millions on that additional short selling for one out of hundreds of securities traded on the TASE. Although we see no aggregate increase in shorting of Israeli companies on U.S. exchanges, we do identify a sharp and unusual increase, just before the attacks, in trading in risky short-dated options on these companies expiring just after the attacks. We identify similar patterns in the Israeli ETF at times when it was reported that Hamas was planning to execute a similar attack as in October. Our findings suggest that traders informed about the coming attacks profited from these tragic events, and consistent with prior literature we show that trading of this kind occurs in gaps in U.S. and international enforcement of legal prohibitions on informed trading. We contribute to the growing literature on trading related to geopolitical events and offer suggestions for policymakers concerned about profitable trading on the basis of information about coming military conflict.

The present manuscript provides a basis in non-life insurance mathematics and statistics which form a core subject of actuarial science. It discusses collective risk modeling, individual claim size modeling, approximations for compound distributions, ruin theory, premium calculation principles, tariffication with generalized linear and neural network models, credibility theory, claims reserving and solvency.

The Kalman Filter is a time series estimation algorithm that is applied extensively in the field of engineering and recently (relative to engineering) in the field of finance and economics. However, presentations of the technique are somewhat intimidating despite the relative ease of generating the algorithm. This paper presents the Kalman Filter in a simplified manner and produces an example of an application of the algorithm in Excel. This scaled down version of the Kalman filter can be introduced in the (advanced) undergraduate classroom as well as the graduate classroom.

Spanish Abstract: La valoración por descuento de flujos se basa en la valoración de los bonos del Estado: consiste en aplicar el procedimiento con el que se valoran los bonos del Estado a la deuda y las acciones de la empresa. Es una aplicación fácil de entender (apartados 1, 2 y 3). Pero se complica con añadidos que no aportan más que aderezos (ver apartados 4 a 15) para que la valoración parezca más “científica”, “seria”, “intrigante”, “impenetrable.”English Abstract: This paper shows several valuation methods based on equity cash flow; free cash flow; capital cash flow; APV (Adjusted Present Value), economic profit and EVA. Valuing companies by Cash Flow Discounting is just to apply the method for valuing Government Bonds to the valuation of the debt and to the valuation of the shares. From that point of view, Betas, FCF, WACC, CCC are unnecessary complications that only complicate the understanding of the non-finance professionals.

Factor investing asks: how well can a particular investor weather hard times relative to the average investor? Answering helps her reap long-run factor premiums by embracing risks that lose money during bad times, but make up for it the rest of the time with attractive rewards. When factor investing can be done cheaply, it raises the bar for active management.

We study intraday market intermediation in an electronic market before and during a period of large and temporary selling pressure. On May 6, 2010, U.S. financial markets experienced a systemic intraday event - the Flash Crash - where a large automated selling program was rapidly executed in the E-mini S&P 500 stock index futures market. Using audit trail transaction-level data for the E-mini on May 6 and the previous three days, we find that the trading pattern of the most active nondesignated intraday intermediaries (classified as High Frequency Traders) did not change when prices fell during the Flash Crash.

This paper contains the statistics of a survey about the Risk-Free Rate (RF) and the Market Risk Premium (MRP) used in 2021 for 88 countries. We got answers for 92 countries, but we only report the results for 88 countries with more than 6 answers. Many respondents use for European countries a RF higher than the yield of the 10-year Government bonds. The coefficient of variation (standard deviation / average) of RF is higher than the coefficient of variation of MRP for the Euro countries. The paper also contains the links to previous years surveys, from 2008 to 2020.

We challenge two central tenets of lifecycle investing: (i) investors should diversify across stocks and bonds and (ii) the young should hold more stocks than the old. An even mix of 50% domestic stocks and 50% international stocks held throughout one’s lifetime vastly outperforms age-based, stock-bond strategies in building wealth, supporting retirement consumption, preserving capital, and generating bequests. These findings are based on a lifecycle model that features dynamic processes for labor earnings, Social Security benefits, and mortality and captures the salient time-series and cross-sectional properties of long-horizon asset class returns. Given the sheer magnitude of US retirement savings, we estimate that Americans could realize trillions of dollars in welfare gains by adopting the all-equity strategy.

We perform a comparative analysis of machine learning methods for the canonical problem of empirical asset pricing: measuring asset risk premia. We demonstrate large economic gains to investors using machine learning forecasts, in some cases doubling the performance of leading regression-based strategies from the literature. We identify the best performing methods (trees and neural networks) and trace their predictive gains to allowance of nonlinear predictor interactions that are missed by other methods. All methods agree on the same set of dominant predictive signals which includes variations on momentum, liquidity, and volatility. Improved risk premium measurement through machine learning simplifies the investigation into economic mechanisms of asset pricing and highlights the value of machine learning in financial innovation.

The validity of day trading as a long-term consistent and uncorrelated source of income is a matter of debate. In this paper, we investigate the profitability of the well-known Opening Range Breakout (ORB) strategy during the period of 2016 to 2023. This period encompasses two bear markets and a few events with abnormal volatility. Our results suggest that with the proper use of leverage or leveraged products (such as 3x leveraged ETFs), day trading can empirically produce significant returns when compared to a standard buy and hold strategy on benchmark indexes in the US public equity markets (Nasdaq or NYSE). Without any loss of generality, we studied the results of an ORB strategy implemented in QQQ. By comparing the results of the active day trading approach with a passive exposure in QQQ, we prove that it is possible for the ORB portfolio to significantly outperform the passive investment. In fact, the day trading portfolio produced an annualized alpha of 33% (net of commissions). Nevertheless, due to leverage constraints enforced by brokers, an active trader would have capped the full upside potential given by the ORB strategy. To overcome this issue, we introduced the use of TQQQ, a leveraged ETF of QQQ, which allows day traders to fully exploit the benefit of the active strategy while adhering to leverage constraints. The resulting portfolio would have earned an outstanding return of 1,484% during the same period of 2016 to 2023, while an investment in the QQQ ETF would have earned only 169%.

To the best of our knowledge, the application of machine learning and in particular graphical models in the field of quantitative risk management is still a relatively recent and new phenomenon. This paper presents a new and effective methodology for decoding strategies. Given an investment universe, we calculate dynamic weights for a sparse portfolio whose aim is to replicate the strategy with the most stable allocation rules. Naturally, this can be formulated as a reinforcement learning problem whose reward is a weighted sum of tracking error and turnover. We show on stylized examples that we can accurately decode strategies or funds with meaningful factors and allocations.

We estimate the equity premium using dividend and earnings growth rates to measure the expected rate of capital gain. Our estimates for 1951-2000, 2.55% and 4.32%, are much lower than the equity premium produced by the average stock return, 7.43%. Our evidence suggests that the high average return for 1951-2000 is due to a decline in discount rates that produces large unexpected capital gains. Our main conclusion is that the stock return of the last half-century is a lot higher than expected.

We define a quality security as one that has characteristics that, all-else-equal, an investor should be willing to pay a higher price for: stocks that are safe, profitable, growing, and well managed. High-quality stocks do have higher prices on average, but not by a very large margin. Perhaps because of this puzzlingly modest impact of quality on price, high-quality stocks have high risk-adjusted returns. Indeed, a quality-minus-junk (QMJ) factor that goes long high-quality stocks and shorts low-quality stocks earns significant risk-adjusted returns in the U.S. and globally across 24 countries. The price of quality varies over time, reaching a low during the internet bubble, and a low price of quality predicts a high future return of QMJ. Analysts’ price targets suggest that the required return of quality stock is low despite the high realized return.

We introduce the multivariate Ornstein-Uhlenbeck and discuss how it generalizes a vast class of continuous-time and discrete-time multivariate processes. Relying on the simple geometrical interpretation of the dynamics of the Ornstein-Uhlenbeck process we introduce cointegration and its relationship to statistical arbitrage. We illustrate an application to swap contract strategies. Fully documented code illustrating the theory and the applications is available at MATLAB Central.

We use a new database of long-run stock, bond, bill, inflation, and currency returns to estimate the equity risk premium for 17 countries and a world index over a 106-year interval. Taking U.S. Treasury bills (government bonds) as the risk-free asset, the annualised equity premium for the world index was 4.7% (4.0%). We report the historical equity premium for each market in local currency and US dollars, and decompose the premium into dividend growth, multiple expansion, the dividend yield, and changes in the real exchange rate. We infer that investors expect a premium on the world index of around 3-3 1/2% on a geometric mean basis, or approximately 4 1/2-5% on an arithmetic basis.

I show that the three residual Income models for equity valuation always yield the same value as the Discounted Cash Flow Valuation models.I use three residual income measures: Economic Profit (EP), Economic Value Added (EVA) and Cash Value Added (CVA). I first show that the present value of the EP discounted at the required return to equity plus the equity book value equals the value of equity (the present value of the Equity cash flow discounted at the required return to equity).Then, I show that the present value of the EVA discounted at the WACC plus the enterprise book value (equity plus debt) equals is the enterprise market value ( the present value of the Free cash flow discounted at the WACC).Then, I show that the present value of the CVA discounted at the WACC plus the enterprise book value (equity plus debt) is also equal to the enterprise market value.