Operational risk

This paper provides an economic and mathematical characterization of operational risk useful for clarifying the issues related to estimation and the determination of economic capital. The insights for this characterization originate in the corporate finance literature. Operational risk is subdivided into two types, either: (i) the risk of a loss due to the firm’s operating technology, or (ii) the risk of a loss due to agency costs. These two types of operational risks generate loss processes with different economic characteristics. We argue that the current methodology for the determination of economic capital for operational risk is overstated. It is biased high because the computation omits the bank’s net present value (NPV) generating process. We also show that although it is conceptually possible to estimate the operational risk processes’ parameters using only market prices, the non-observability of the firm’s value makes this an unlikely possibility, except in rare cases. Instead, we argue that data internal to the firm, in conjunction with standard hazard rate estimation procedures, provides a more fruitful alternative.     

The CAPM and value at risk at different time-scales

By resorting to wavelet analysis, we estimate the capital asset pricing model (CAPM) at different time-scales for the Chilean stock market. Our sample comprises 24 stocks that were actively traded on the Santiago Stock Exchange over 1997-2002. We find evidence in support of the CAPM at a medium-term horizon. We extend the literature in this area to analyze the impact of time scaling on the computation of value at risk. We conclude that risk is concentrated at higher frequencies of the data.     

How to choose the return model for market risk? Getting towards a right magnitude of stressed VaR

Value at Risk (VaR) and stressed value at Risk (SVaR) or expected shortfall are important risk measures widely used in the financial services industry for risk management and market risk capital computation. Fundamental to any (S)VaR model is the choice of the return type model for each risk factor. Because the resulting SVaR numbers are highly sensitive to the chosen return type model it is important to make a prudent choice on the return type modelling. We propose to estimate the return type model from historic data without making an a priori model assumption on the return model. We explain the fundamentals of return type modelling and how it impacts the magnitude of SVaR. We further show how to obtain a global return type model from a set of similar return type models by using geometric calculus. Numerical simulations and illustrations are provided. In this paper, we consider interest rate data, but the proposed methodology is general and can be applied to any other asset class such as inflation, credit spread, equity or fx.     

The Pricing of Risk and Sentiment: A Study of Executive Stock Options

Option pricing models accounting for illiquidity generally imply the options are valued at a discount to the Black‐Scholes value. Our model considers the role of sentiment, which offsets illiquidity. Using executive stock options and compensation data from 1992 to 2004 for S&P 1500 firms, we find that executives value employee stock options (ESOs) at a 48% premium to the Black‐Scholes value. These premia are explained by a sentiment level of 12% in risk‐adjusted, annualized return, suggesting a high level of executive overconfidence. Subjective value relates negatively to illiquidity and idiosyncratic risk, and positively to sentiment in all specifications, consistent with the offsetting roles of sentiment and risk aversion.     

Geopolitical risk,climate risk and energy markets: A dynamic spillover analysis

This paper provides evidence on the dynamic spillover among geopolitical risk, climate risk, and energy markets from an international perspective. Based on data from 13 countries between December 2002 and February 2022, we firstly confirm an overall connectedness among energy future prices, i.e., crude oil, heating oil and natural gas, with geopolitical risk and climate risk. And then, the dynamic analysis indicates that the spillover effect is frequency dependent and more pronounced at a high frequency. Furthermore, the net dynamic spillover results show that the two major shocks of geopolitical risk associated with Russia on energy markets appear in 2014 and 2022. These effects are also more pronounced at a high frequency, indicating that the conflicts can impose an immediate effect on energy markets. The significant connectedness among energy, geopolitical risk and climate risk remains unchanged after accounting for public attention, adding control variables and using the alternative measures of geopolitical risk and climate risk.     

Low-latency liquidity inefficiency strategies

The vast amount of high-frequency data heralds the use of new methods in financial data analysis and quantitative trading. This study delivers a proof-of-concept for a high frequency-based trading system based on an evolutionary computation method. Motivated by a theoretical liquidity asymmetry theorem from the market microstructure literature, grammatical evolution is used to exploit volume inefficiencies at the bid–ask spread. Using NASDAQ Historical TotalView-ITCH level two limit order book data, execution volumes can be tracked. This allows for testing of the strategies with minimal assumptions. The system evolves profitable and robust strategies with high returns and low risk.     

The effects of loan portfolio concentration on Brazilian banks’ return and risk

This paper tests whether diversification of the credit portfolio at the bank level leads to better performance and lower risk. We employ a new high frequency (monthly) panel data for the Brazilian banking system with information at the bank level for loans by economic sector. We find that loan portfolio concentration increases returns and also reduces default risk; the impact of concentration on bank’s return is decreasing on bank’s risk; there are significant size effects; foreign and state-owned banks seem to be less affected by the degree of diversification. An important additional finding is that there is an increasing concentration trend after the breakout of the recent international financial crisis, specially after the failure of Lehman Brothers.     

Equity portfolio diversification with high frequency data

Investors wishing to achieve a particular level of diversification may be misled on how many stocks to hold in a portfolio by assessing the portfolio risk at different data frequencies. High frequency intradaily data provide better estimates of volatility, which translate to more accurate assessment of portfolio risk. Using 5-min, daily and weekly data on S&P500 constituents for the period from 2003 to 2011, we find that for an average investor wishing to diversify away 85% (90%) of the risk, equally weighted portfolios of 7 (10) stocks will suffice, irrespective of the data frequency used or the time period considered. However, to assure investors of a desired level of diversification 90% of the time (in contrast to on average), using low frequency data results in an exaggerated number of stocks in a portfolio when compared with the recommendation based on 5-min data. This difference is magnified during periods when financial markets are in distress, as much as doubling during the 2007–2009 financial crisis.     

Risk management under extreme events

This article presents two applications of extreme value theory (EVT) to financial markets: computation of value at risk (VaR) and cross-section dependence of extreme returns (i.e., tail dependence). We use a sample comprised of the United States, Europe, Asia, and Latin America. Our main findings are the following. First, on average, EVT gives the most accurate estimate of VaR. Second, tail dependence of paired returns decreases substantially when both heteroscedasticity and serial correlation are filtered out by a multivariate GARCH model. Both findings are in agreement with previous research in this area for other financial markets.     

The asset pricing effects of UK market liquidity shocks: Evidence from tick data

Using tick data covering a 12 year period including much of the recent financial crisis we provide an unprecedented examination of the relationship between liquidity and stock returns in the UK market. Previous research on liquidity using high frequency data omits the recent financial crisis and is focused on the US, which has a different market structure to the UK. We first construct several microstructure liquidity measures for FTSE All Share stocks, demonstrating that tick data reveal patterns in intra-day liquidity not observable with lower frequency daily data. Our asymptotic principal component analysis captures commonality in liquidity across stocks to construct systematic market liquidity factors. We find that cross-sectional differences in returns exist across portfolios sorted by liquidity risk. These are strongly robust to market, size and value risk. The inclusion of a momentum factor partially explains some of the liquidity premia but they remain statistically significant. However, during the crisis period a long liquidity risk strategy experiences significantly negative alphas.     

Convertible Bond Arbitrage: Risk and Return

Abstract:  This paper specifies a simulated convertible bond arbitrage portfolio to characterise the risks in convertible bond arbitrage. For comparison the risk profile of convertible bond arbitrage hedge fund indices at both monthly and daily frequencies is also examined. Results indicate that convertible bond arbitrage is positively related to default and term structure risk factors. These risk factors are augmented with the simulated convertible bond arbitrage portfolio, mimicking a passive investment in convertible bond arbitrage, to assess the risk and return of individual hedge funds. We provide estimates of the performance of two hedge fund indices (an equally weighted and value weighted index) and a sample of convertible bond arbitrage hedge funds using a factor model methodology. Lagged and contemporaneous observations of the risk factors are specified, controlling for illiquidity in the securities held by funds. Our results cover two time periods. Initially we find evidence of abnormal risk adjusted returns in the individual hedge fund data and the equally weighted hedge fund index and no evidence of abnormal risk adjusted returns in the value weighted hedge fund index. When we examine performance during the credit crisis of 2007 and 2008 we find evidence of negative abnormal returns amongst individual hedge funds and the hedge fund indices.     

Value creation around merger waves: The role of managerial compensation

This paper examines the relation between executive compensation and value creation in merger waves. The sensitivity of CEO wealth to firm risk increases the likelihood of out-of-wave merger transactions but has no influence on in-wave merger frequency. CEOs with compensation linked to firm risk have better out-of-wave merger performance in comparison to in-wave mergers. We also present evidence that cross-sectional acquirer return dispersion is greater for in-wave acquisitions. Our results suggest that the underperformance of acquiring firms during merger waves can be attributed in part to ineffective compensation incentives, and appropriate managerial incentives can create value, particularly in non-wave periods.     

Arithmetic variance swaps

Biases in standard variance swap rates (VSRs) can induce substantial deviations below market rates. Defining realized variance as the sum of squared price (not log-price) changes yields an ‘arithmetic’ variance swap with no such biases. Its fair value has advantages over the standard VSR: no discrete monitoring or jump biases; and the same value applies for any monitoring frequency, even irregular monitoring and to any underlying, including those taking zero or negative values. We derive the fair value for the arithmetic variance swap and compare it with the standard VSR by: analysing errors introduced by interpolation and integration techniques; numerical experiments for approximation accuracy; and using 23 years of FTSE 100 options data to explore the empirical properties of arithmetic variance (and higher moment) swaps. The FTSE 100 variance risk has a strong negative correlation with the implied third moment, which can be captured using a higher moment arithmetic swap.     

Remarks on a copula-based conditional value at risk for the portfolio problem

We deal with a multivariate conditional value at risk. Compared with the usual notion for the single random variable, a multivariate value at risk is concerned with several variables, and thus, the relation between each risk factor should be considered. We here introduce a new definition of copula-based conditional value at risk, which is real valued and ready to be computed. Copulas are known to provide a flexible method for handling a possible nonlinear structure; therefore, copulas may be naturally involved in the theory of value at risk. We derive a formula of our copula-based conditional value at risk in the case of Archimedean copulas, whose effectiveness is shown by examples. Numerical studies are also carried out with real data, which can be verified with analytical results.     

Habit formation,the cross section of stock returns and the cash-flow risk puzzle

Non-linear external habit persistence models, which feature prominently in the recent “equity premium” asset pricing and macroeconomics literature, generate counterfactual predictions in the cross-section of stock returns. In particular, we show that in the absence of cross-sectional heterogeneity in firms’ cash-flow risk, these models produce a “growth premium,” that is, stocks with high price-to-fundamental ratios command a higher premium than stocks with low price-to-fundamental ratios. This implication is at odds with the well-established empirical observation of a “value premium” in the cross-section of stock returns. Substantial heterogeneity in firms’ cash-flow risk yields both a value premium as well as most of the stylized facts about the cross-section of stock returns, but it generates a “cash-flow risk puzzle”: Quantitatively, value stocks have to have “too much” cash-flow risk compared to the data to generate empirically plausible value premiums.     

Risk,uncertainty and monetary policy

The VIX, the stock market option-based implied volatility, strongly co-moves with measures of the monetary policy stance. When decomposing the VIX into two components, a proxy for risk aversion and expected stock market volatility (“uncertainty”), we find that a lax monetary policy decreases both risk aversion and uncertainty, with the former effect being stronger. The result holds in a structural vector autoregressive framework, controlling for business cycle movements and using a variety of identification schemes for the vector autoregression in general and monetary policy shocks in particular. The effect of monetary policy on risk aversion is also apparent in regressions using high frequency data.     

Equity Risk Premium

Abstract

The equity risk premium (ERP) is an essential building block of the market value of risk. In theory, the collective action of all investors results in an equilibrium expectation for the return on the market portfolio excess of the risk-free return, the ERP. The ability of the valuation actuary to choose a sensible value for the ERP, whether as a required input to capital asset pricing model valuation, or any of its descendants, is as important as choosing risk-free rates and risk relatives (betas) to the ERP for the asset at hand.

The historical realized ERP for the stock market appears to be at odds with pricing theory parameters for risk aversion. Since 1985, there has been a constant stream of research, each of which reviews theories of estimating market returns, examines historical data periods, or both. Those ERP value estimates vary widely from about ?1% to about 9%, based on a geometric or arithmetic averaging, short or long horizons, short- or long-run expectations, unconditional or conditional distributions, domestic or international data, data periods, and real or nominal returns.

This paper examines the principal strains of the recent research on the ERP and catalogues the empirical values of the ERP implied by that research. In addition, the paper supplies several time series analyses of the standard Ibbotson Associates 1926–2002 ERP data using short Treasuries for the risk-free rate. Recommendations for ERP values to use in common actuarial valuation problems also are offered.     

Tails,Fears, and Risk Premia

We show that the compensation for rare events accounts for a large fraction of the average equity and variance risk premia. Exploiting the special structure of the jump tails and the pricing thereof, we identify and estimate a new Investor Fears index. The index reveals large time‐varying compensation for fears of disasters. Our empirical investigations involve new extreme value theory approximations and high‐frequency intraday data for estimating the expected jump tails under the statistical probability measure, and short maturity out‐of‐the‐money options and new model‐free implied variation measures for estimating the corresponding risk‐neutral expectations.     

The value, size, and momentum spread during distressed economic periods

We study the behavior of market risk, value, small cap, and momentum premia under different macro economic scenarios. If these factors are risk factors, then these factors offer high returns to investors at times when the gain (marginal utility) of additional consumption is low (good economic times) and low returns at times when the gain (marginal utility) of additional consumption is high (bad economics times). Our results show that market risk and small cap premia behave more like risk factors while value premium does not. In fact, our results show that a portfolio with a long position in value and a short position in growth is a hedge in the down market and recessionary periods. Our results also show that a momentum premium exists under different economically distressed scenarios we studied.