Historical VaR Research Articles

RISK EVALUATION OF LIVESTOCK COMMODITIES – VALUE-AT-RISK APPROACH

This paper tries to assess the level of losses that investors in four livestock commodities might have. The analysis comprises live cattle, feeder cattle, lean hogs and milk class III, and for the risk calculation, we use parametric and historical VaR measures. Full sample is divided into pre-crisis and crisis subsamples. According to the results, lean hogs are the riskiest asset in the pre-crisis period, regarding both parametric and historical VaR. In the crisis period, milk is the riskiest asset in terms of parametric VaR in all probability levels. However, in terms of historical VaR, lean hogs have the highest potential of loses between 90-97% VaR, but at 99% VaR, milk takes upper hand. In the crisis period, the level of losses for lean hogs and milk exceeds 4% in one day at 99% probability, which means that these commodities should be hedged if investors want to avoid great losses. The results indicate that parametric VaR significantly deviates from historical VaR in both subsamples, which means that investors in livestock commodities should use historical VaR for downside risk measurement.

Enhancing Sustainable Finance through Green Hydrogen Equity Investments: A Multifaceted Risk-Return Analysis

Amidst the global push for decarbonization, green hydrogen has gained recognition as a versatile and clean energy carrier, prompting the financial sector to introduce specialized investment instruments like Green Hydrogen Exchange-Traded Funds (ETFs). Despite the nascent nature of research on green hydrogen portfolio performance, this study examines two key green hydrogen ETFs (i.e., HJEN and HDRO) from April 2021–May 2023, aiming at conducting a multifaceted exploration of their performance, isolating and measuring their sensitivity to the primary market factor, and assessing the capabilities of systematic trading strategies to preserve capital and minimize losses during market downturns. The results spotlight lower returns and higher risks in green hydrogen investments compared to conventional equity (proxied by ETFs offering exposure to developed markets—EFA and emerging markets—EEM) and green energy portfolios (proxied by the ETF ICLN). To comprehensively evaluate performance, an array of risk-adjusted metrics, including Std Sharpe, ES Sharpe, VaR Sharpe, Information ratio, Sortino ratio, Treynor ratio, and various downside risk metrics (historical VaR, modified VaR, Expected Shortfall, loss deviation, downside deviation, and maximum drawdown) are employed, offering a nuanced understanding of the investment landscape. Moreover, single-factor models highlight significant systematic market risk, reflected in notably high beta coefficients, negative alphas, and active premia, underscoring the sensitivity of green hydrogen investments to market fluctuations. Despite these challenges, a silver lining emerges as the study demonstrates the efficacy of implementing straightforward Dual Moving Average Crossover (DMAC) trading strategies. These strategies significantly enhance the risk-return profile of green hydrogen portfolios, offering investors a pathway to align financial and social objectives within their equity portfolios. This research is motivated by the need to provide market players, policymakers, and stakeholders with valuable insights into the benefits and risks associated with green hydrogen investment, considering its potential to reshape the global energy landscape.

Historical VaR as a stock fund diversification assessment tool

Purpose: The aim of this study is to assess the potential maximum loss in more concentrated investment portfolios and more diversified portfolios using the VaR calculation as a tool for controlling and managing market risk. For this, the study proposes to answer the following research question: "Do more diversified equity funds present less risk?"
 Methodology: The historical simulation model was applied, considering seven portfolios of equity investment funds (FIAs) and 493 daily returns, under the 95% confidence level.
 Results: The results indicated that the maximum expected loss is higher in more concentrated portfolios. Therefore, the diversification strategy helped to reduce risk and is an important instrument to be considered in a stock portfolio.
 Contributions of the Study: The main contribution of the study is to provide subsidies for investors and asset managers, while providing a simulation and practical application of VaR in the analysis of portfolio diversification in equity investment funds.

Word Portfolio Optimization in the Environment of Zero Interest Rate

This paper provides a deep analysis of ten globally diversified portfolios, composed of different financial instruments: bonds, shares, ETF’s, commodities, indexes, currencies, constructed applying various optimization techniques. Statistical moments, such as mean, standard deviation, kurtosis and skewness of portfolios are compared and discussed. Moreover, performance of the portfolios within the time horizon of one year estimating Sharpe ratio, Treynor ratio, Sortino ratio is presented. Furthermore, a risk analysis of created portfolios is evaluated in terms of historical VaR and CVaR applying confidence interval 95%. The main results of this paper reveal that the portfolio, which is optimized to minimize VaR produces high expected shortfall. Secondly, the Risk Parity portfolio, despite reducing volatility, has delivered the highest kurtosis of the return, which may indicate the possible tail loss. Furthermore, the maximum Sharpe ratio portfolio has delivered extremely high kurtosis in comparison with the kurtosis of the other portfolios. Finally, it is observed that for the Naïve diversification portfolio it has been typical to have the highest downside deviation. 

Volatility Modelling and VaR: The Case of Bitcoin, Ether and Ripple

Abstract Since Bitcoin introduction in 2008, the cryptocurrency market has grown into hundreds-of-billion-dollar market. The cryptocurrency market is well known as very volatile, mainly for the fact that the cryptocurrencies have not the price to fall back upon and that anybody can join the trading (no license or approval is required). Since empirical literature suggests that GARCH-type models dominate as VaR estimators the overall objective of this paper is to perform comprehensive volatility and VaR estimation for three major digital assets and conclude which method gives the best results in terms of risk management. The methods we used are parametric (GARCH and EWMA model), non-parametric (historical VaR) and Monte Carlo simulation (given by Geometric Brownian Motion). We conclude that the best method for value-at-risk estimation for cryptocurrencies is the Monte Carlo simulation due to the heavy diffusion (stochastic) process and robustness of the results.

COVID-19 Pandemic Versus Global Financial Crisis: Evidence from Currency Market

The COVID-19 pandemic has induced chaos and turbulence in financial markets. The ongoing discussions and expectations for the future are quite bleak. In this study, we analyze the current status of the deterioration in foreign exchange markets by comparing it with the turbulence seen in the Global Financial Crisis in 2008–2009. We employ various tests in this investigation: the Kapetanios m-break unit root test, downside variance, upside risk, volatility skewness, Gaussian VaR, historical VaR, and modified VaR. According to the results of the majority of methods, the turmoil in exchange markets is not as bad yet as the period of the Global Financial Crisis. However, the volatility skewness demonstrates a different picture that is parallel to the pessimism in the media. Additionally, it is seen that of six foreign exchange rates, only the Japanese yen demonstrates a higher risk during the COVID-19 pandemic than that observed in the Global Financial Crisis.

Do Not Torture the Data, Just…Listen to Them: An Alternative Value at Risk Approach

Even though econometric and technological advances have contributed to the vast risk modelling literature, practitioners in most cases use the simplest and most conventional approaches in order to avoid algorithmic complexity and increased costs. In this study we present a new approach which adopts a volatility-based filtering data approach, and uses only the most representative data in order to achieve more accurate VaR estimations than the conventional historical VaR models do. In simple words, the Filtering Historical VaR method, listens to the market’s previously documented behavior and presents more accurate than the conventional approaches VaR estimations.

Forecasting value at risk (VAR) for emerging and developed markets

This paper explores different approaches to modelling and forecasting VaR, using both historical simulation and volatility-weighted bootstrap methods, where volatility is estimated using GARCH (1,1) and EGARCH (1,1). It examines the one day predictive ability of three historical simulation VaR models at the 90%, 95%, and 99% confidence levels for developed and emerging equity markets for the period 2011- 2017 that witnessed difficult and extreme market conditions. 870 scenarios of future returns are generated for each of the 500 days representing the out of sample period extending from March 2015 up to January 2017 in order to estimate the corresponding VaR for both markets. The GARCH (1,1) volatility-weighted model is accepted for both markets and is classified as the best performing model. The EGARCH (1,1) volatility-weighted model’s results were inconclusive; in fact, the back-test was accepted at all confidence levels for the developed markets while rejected at the 99% confidence level for the emerging markets. The basic historical simulation failed in estimating an accurate VaR for the emerging markets.

Deep Option Pricing - Term Structure Models

This paper proposes a data-driven approach, by means of an Artificial Neural Network (ANN), to value financial options within the setting of interest rate term structure models. This aims to accelerate existing numerical methods which is important for applications like historical VaR or exposure calculation being used in financial institutions. With ANNs being a universal function approximation method, this method trains an ANN on synthetically generated data including term structures of yield and volatility. Then, within an VaR or exposure calculation instead of applying costly numerical methods for the financial model, the engine runs the trained ANN. This is faster and more efficient and allows (a) considering term structures of yields, (b) term structures of volatilities and (c) trade interpolation. We outline the generation of the training data, the neural net selection and propose further methods for optimization. In particular we consider a control variate method and the application of no-arbitrage conditions and regularization to the cost function used for learning and calibration. Finally, we test our approach on the Hull-White model with time-dependent term structure for volatility and the the Trolle-Schwartz model. The latter adds an un-spanned stochastic volatility to the rates dynamic. The numerical results show that the ANN solution, especially the one with the control variate, is accurate and reduces the computing time significantly.

PERHITUNGAN VALUE AT RISK DENGAN PENDUGA VOLATILITAS STOKASTIK HESTON

Value at risk is a method that measures financial risk of an security or portfolio. The aims of the research is to find out the value at risk of an exchange rate using the Heston stochastic volatility model. Heston model is a strochastic volatility model that assumes that volatility of the security follow stochastic process and consider the mean reversion. Based on simulation results, the value of volatility using Heston volatility estimastor is 0.2887, and the value of Heston VaR with 95 percent confident level is 0.0297. Based on result of backtesting, there are 48 violations obtained VaR using Heston model, while historical VaR there are 2 violations. Thus, VaR using Heston model is more strict in estimating risk.

Initial Margin Optimisation Over Multiple Counterparties

We consider a bank posting Initial Margin (IM) to multiple counterparties under a sensitivity based variance-covariance VaR model. This model is a key component of the ISDA Standardized Initial Margin Model (SIMM) and could also be calibrated to approximate a clearing house IM model, which are usually historical VaR or Expected Shortfall based. Using this variance-covariance model we derive a formula to minimize the aggregate IM across all counterparties assuming that: 1) the bank only hedges with a limited set of trades such as 2Y, 5Y and 10Y swaps, and 2) the hedge trades net across counterparties.

Scaling Historical VAR to Current Market Conditions

Value at Risk is used by many organizations as one of their risk management tools. Very often it is determined using historical simulations. One problem with historical simulations is possibility of different interpretations how shocks observed in the past should be applied to current market conditions. In this article new approach is proposed. This approach provides simple and consistent way of translating shock observed in the past to current conditions.

Comparison of VaR Methods : The Case of Indian Equities

Different approaches to calculate VaR are based on different assumptions. This study dealt with a comparative evaluation of four Value-at-Risk models namely, historical VaR, normal VaR, GARCH (1,1) VaR, and volatility weighted historical simulation (VWHS) VaR in terms of their prediction accuracy for an active portfolio of Indian equities. Daily NAVs of 34 Indian equity growth mutual fund schemes for a period of 10 years were used to calculate 95% VaR and backtest the results using Kupiec's POF test for all four VaR models. To identify the better performing VaR methods accurately, the analysis was performed in two phases : pre-crisis analysis and post crisis analysis. We concluded that there was a significant (insignificant) difference in performance of different VaR models if market conditions during VaR calculation and VaR backtesting periods were in contrast (congruence) to each other. The study found VWHS to be a better methodology for measuring VaR of an active portfolio of Indian equity stocks in both phases of the analysis. The results are relevant for traders & retail and institutional investors who hold stocks of Indian companies in their portfolio and need to calculate VaR as a measure of market risk for their positions.

Speculative investment, heavy-tailed distribution and risk management of Bitcoin exchange rate returns

Since its launch in 2008, Bitcoin becomes one of the most successful and fast-growing alternative currencies. As of 2017, the market capitalization is around $46 billions and arguably expected to continue growing. The Bitcoin to the US dollar exchange rate has been very volatile and fluctuating significantly. Although Bitcoin was designed as a medium of exchange, it is now more as an investment tool and thus the development of effective quantitative risk management tools becomes quite urgent for all the market participants. In this paper, we investigate empirical distribution of the Bitcoin exchange rate returns by using four types of widely-used heavy-tailed distribution and show that the Skewed t distribution has the best empirical performance. We further calculate the VaR based risk measures and found the Skewed t distribution generates the VaR values, which are closest to historical VaR values. Our results could be directly used in the industry’s stress testing practice, and help financial institutions fulfill the regulatory requirements.

Fat Tails, Value at Risk, and the Daily Palladium Returns

The past decade has witnessed the rapid growing of the world palladium market. Thus, it is even more important to develop effective quantitative tools for risk management of palladium assets at this moment. In this paper, we investigate five different types of widely-used statistical distributions and employ the industry standard risk measurement, Value at Risk, for risk management of daily palladium spot returns. We first apply four different criteria to compare the goodness of fit of the five distributions, and then calculate the VaRs based on the parameters estimated from the first step. Our results indicate the Skewed t distribution has the best in-sample fitting and generate VaR values closest to the nonparametric historical VaR values.

Two New Risk Metrics: Liquidity Asian Put VaR(TM) and Shortfall(TM) to LIQUIDATION Based on Tail Volatilities & Correlations 'The Need for New Valuation, Risk and Policy Making Models'

This paper derives two new improved risk metrics LAPVaR and LAPSF. Traditional VaRDeltaNormal valuation exaggerates market and liquidity risks to the point it could be larger than the actual portfolio value. Put VaR – PVaR – as well as Put Shortfall – PSF – uses option theory to solve the problem that, under any circumstance, the risk amount is never greater than the portfolio value. Risk to LIQUIDATION means every day-t, a portion of portfolio assets-i, for integer i ϵ (1, N) is unwound without disturbing the market; thus the final unwind price equals the sum-product of asset-i and price-return-(i,t), where for each asset-i ϵ (1, N), there is t ϵ (1, Hi,t), such that day-Hi, t is the last unwind day of asset-i. This method calculates Asian PVaR – APVaR – and Asian PSF – APSF – because it’s marked at the asset-i average unwind price from day-1 to day Hi,t. A formula is derived to estimate a horizon-Ĥ necessary to measure analytic VaRs. Liquidity haircut-Li are incorporated endogenously modifying forward-i value in the analytic formulas – LAPVaR and LAPSF – representing a great advantage over calculating exogenously Liquidity Haircuts in traditional VaRHistorical and analytic VaRDeltaNormal. The new formula is compared to the traditional risk measure, the Bullet Historical VaR to LIQUIDATION – i.e. VaR Historical.

Risk Measure Estimates in Quiet and Turbulent Times: An Empirical Study

In this study we empirically explore the capacity of historical VaR to correctly predict the future risk of a financial institution. We observe that rolling samples are better able to capture the dynamics of future risks. We thus introduce another risk measure, the Sample Quantile Process, which is a generalization of the VaR calculated on a rolling sample, and study its behavior as a predictor by varying its parameters. Moreover, we study the behavior of the future risk as a function of past volatility. We show that if the past volatility is low, the historical computation of the risk measure underestimates the future risk, while in period of high volatility, the risk measure overestimates the risk, confirming that the current way financial institutions measure their risk is highly procyclical.

Speculative Investment and Risk Management of Bitcoin Exchange Rate Returns

Since its launch in 2008, Bitcoin becomes one of the most successful and fast-growing alternative currencies. As of 2017, the market capitalization is around $46 billions and arguably expected to continue growing. The Bitcoin to the US dollar exchange rate has been very volatile and fluctuating significantly. Although Bitcoin was designed as a medium of exchange, it is now more as an investment tool and thus the development of effective quantitative risk management tools becomes quite urgent for all the market participants. In this paper, we investigate empirical distribution of the Bitcoin exchange rate returns by using four types of widely-used heavy-tailed distribution and show that the Skewed t distribution has the best empirical performance. We further calculate the VaR based risk measures and found the Skewed t distribution generates the VaR values, which are closest to historical VaR values. Our results could be directly used in the industry’s stress testing practice, and help financial institutions fulfill the regulatory requirements.

Heavy-Tailed Distributions and Risk Management of Equity Market Tail Events

Traditional econometric modelling typically follows the idea that market returns follow a normal distribution. However, the concept of tail risk indicates that the distribution of returns is not normal, but skewed and has heavy tails. Thus, a heavy-tailed distribution, which accurately estimates the tail risk, would significantly improve quantitative risk management practice. In this paper, we compare four widely used heavy-tailed distributions using the S&P 500 daily returns. Our results indicate that the Skewed t distribution in Hansen (1994) has the superior empirical performance compared with the Student’s t distribution, the normal reciprocal inverse Gaussian distribution and the generalized hyperbolic distribution. We further showed the Skewed t distribution could generate the VaR estimates closest to the nonparametric historical VaR estimates compared with other heavy-tailed distributions.

Correlation Stress in a Historical VAR Setting

This paper describes a reasonably straightforward methodology for assessing the impact of different correlation stress assumptions in a historical VaR setting. This is accomplished by first introducing continuous empirical distribution functions for the marginal risk factor distributions, and using this to define standardized normal drivers for each. Then assuming a normal copula structure, a mixing of these standardized drivers is introduced in order to arrive at the target correlation structure. Finally the mixed drivers are re-converted into values for the risk factors using the inverse marginal distribution functions, from which a stressed correlation VaR calculation can be performed.