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![]() ![]() This result suggests that the VaR violations are not independent, and there are probably periods with multiple failures in a short span. Both confidence levels got rejected in the conditional coverage independence, and time between failures independence ( cci and tbfi columns). The 99% VaR does not pass these same tests, as indicated by the yellow and reject results. The 95% VaR passes the frequency tests, such as traffic light, binomial and proportion of failures tests ( tl, bin, and pof columns). "S&P" "Normal99" 0.99 yellow reject reject accept reject accept reject reject "S&P" "Normal95" 0.95 green accept accept accept accept reject reject reject The article was written in December 2021 by Jayati WALIA (ESSEC Business School, Grande Ecole – Master in Management, 2019-2022).PortfolioID VaRID VaRLevel TL Bin POF TUFF CC CCI TBF TBFI (2007) Value at Risk, Third Edition, Chapter 10 – VaR Methods, 274-276. ▶Jayati WALIA The Monte Carlo simulation method for VaR calculation Useful resources ▶ Jayati WALIA The historical method for VaR calculation ▶ Jayati WALIA Quantitative Risk Management However, the assumptions of return normality and constant covariances and correlations between assets in the portfolio may not hold true in real life. The variance–covariance approach helps us measure portfolio risk if returns are assumed to be distributed normally. Investors can estimate the probable loss value of their portfolios for different holding time periods and confidence levels. Advantages and limitations of the variance-covariance method Where the parameter ɑ links the quantile of the normal distribution and the standard deviation: ɑ = 2.33 for p = 99% and ɑ = 1.65 for p = 95%. Now we can estimate the VaR of our portfolio as: Where w i corresponds to portfolio weights of asset i. We calculation the standard deviation of portfolio P with the following formula: Next, we compute the correlation coefficients as: Where X t and Y t are returns for asset X and Y on period. The covariance between returns of two assets X and Y can be expressed as: To measure how assets vary with each other, we calculate the covariance. The variance of returns for asset X can be expressed as: The first step is to compute the variance-covariance matrix. The two parameters of the normal distribution (the mean and standard deviation) are estimated with historical data from the CAC 40 index.Ĭonsider a portfolio P with N assets. You can download below the Excel file for the VaR calculation with the variance-covariance method. Source: computation by the author (data source: Bloomberg). Normal distribution for VaR for the CAC40 index Where R t is the return on period and R the average return.įigure 1. In practice, the variance (and then the standard deviation) is estimated from historical data. Where the parameter ɑ links the quantile of the normal distribution and the standard deviation: ɑ = 2.33 for p = 99% and ɑ = 1.645 for p = 90%. The daily VaR is simply a function of the standard deviation and the desired confidence level and can be expressed as: From the distribution of returns calculated from daily price series, the standard deviation (σ) under a certain time horizon is estimated. VaR calculation for a single asset is straightforward. This method assumes that the standard deviation of asset returns and the correlations between asset returns are constant over time. Assets may have tendency to move up and down together or against each other. The variance-covariance method assumes that asset returns are normally distributed around the mean of the bell-shaped probability distribution. The variance-covariance method uses the variances and covariances of assets for VaR calculation and is hence a parametric method as it depends on the parameters of the probability distribution of price changes or returns. In this post, we discuss in detail the variance-covariance method for computing value at risk which is a parametric method of VaR calculation. There are various methods used to compute the VaR. The two key elements of VaR are a fixed period of time (say one or ten days) over which risk is assessed and a confidence level which is essentially the probability of the occurrence of loss-causing event (say 95% or 99%). Thus, VaR attempts to measure the risk of unexpected changes in prices (or return rates) within a given period. VaR is used extensively to determine the level of risk exposure of an investment, portfolio or firm and calculate the extent of potential losses. VaR is typically defined as the maximum loss which should not be exceeded during a specific time period with a given probability level (or ‘confidence level’). In this article, Jayati WALIA (ESSEC Business School, Grande Ecole – Master in Management, 2019-2022) presents the variance-covariance method for VaR calculation. ![]()
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