fulga
... solving portfolio optimization problems. In the recent literature, many research papers are devoted to the topic of portfolio optimization using different risk measures, see for example Armeanu and Balu (2009), Fulga (2009a, 2009b), Fulga et al. (2009), Fulga and Dedu (2009), Fulga and Pop (2007, 20 ...
... solving portfolio optimization problems. In the recent literature, many research papers are devoted to the topic of portfolio optimization using different risk measures, see for example Armeanu and Balu (2009), Fulga (2009a, 2009b), Fulga et al. (2009), Fulga and Dedu (2009), Fulga and Pop (2007, 20 ...
View/Open
... “Diversification in Resource Allocation and Minimization of Income Variability” in the Journal of Farm Economics (Heady, 1952). Heady argued that there were two different aspects of diversification. The first involved a farmer planning under certainty and following the simple economic rule of maximi ...
... “Diversification in Resource Allocation and Minimization of Income Variability” in the Journal of Farm Economics (Heady, 1952). Heady argued that there were two different aspects of diversification. The first involved a farmer planning under certainty and following the simple economic rule of maximi ...
No Slide Title
... Statistics and Estimates Mean - Measure of Central Tendency, like Median and Mode. Variance - Measure of dispersion round the mean the squared term ensures that Variance is positive and gives extra weight to observations furthest from the mean. Standard Deviation - Square Root of Variance. It i ...
... Statistics and Estimates Mean - Measure of Central Tendency, like Median and Mode. Variance - Measure of dispersion round the mean the squared term ensures that Variance is positive and gives extra weight to observations furthest from the mean. Standard Deviation - Square Root of Variance. It i ...
The Risk Management process
... Both qualitative and quantitative methods can be evaluating the impact of risk on an organisation. Qualitative evaluation The Risk Manager can use past experience of similar events in measuring uncertainty of risk. Quantitative evaluation Statistical measurement can be applied if adequate and accura ...
... Both qualitative and quantitative methods can be evaluating the impact of risk on an organisation. Qualitative evaluation The Risk Manager can use past experience of similar events in measuring uncertainty of risk. Quantitative evaluation Statistical measurement can be applied if adequate and accura ...
International Portfolio Investment
... “buy and hold” investment strategies, hedge funds may adopt flexible, dynamic trading strategies, often aggressively using leverages, short positions, and derivative contracts, in order to achieve their investment objectives. These funds may invest in a wide spectrum of securities, such as currencie ...
... “buy and hold” investment strategies, hedge funds may adopt flexible, dynamic trading strategies, often aggressively using leverages, short positions, and derivative contracts, in order to achieve their investment objectives. These funds may invest in a wide spectrum of securities, such as currencie ...
Full text - Toulouse School of Economics
... versions of the three-regime model are nested with the linear restrictions µℓ = µu = µm , these constraints can be tested using a standard LR test. The corresponding LR statistics is equal to 16.20 and is χ2 (2) distributed: the constrained three-regime model is strongly rejected. Then, according to ...
... versions of the three-regime model are nested with the linear restrictions µℓ = µu = µm , these constraints can be tested using a standard LR test. The corresponding LR statistics is equal to 16.20 and is χ2 (2) distributed: the constrained three-regime model is strongly rejected. Then, according to ...
Lecture 5 Slides
... • We can derive the continuously compounded mean and variance of a portfolio’s continuously compounded return for a portfolio from the expected return and covariance matrix of continually compounded returns for the assets it contains • Under the assumption that the proportional changes in the portfo ...
... • We can derive the continuously compounded mean and variance of a portfolio’s continuously compounded return for a portfolio from the expected return and covariance matrix of continually compounded returns for the assets it contains • Under the assumption that the proportional changes in the portfo ...
Extreme Value Theory in Finance
... L of a portfolio over a given time period ∆, then VaR is a risk statistic that measures the risk of holding the portfolio for the time period ∆. Assume that L has distribution function FL , then we define VaR at level α ∈ (0, 1) as VaR∆ α (L) = inf{x ∈ R : P (L > x) ≤ 1 − α} = inf{x ∈ R : FL (x) ≥ α ...
... L of a portfolio over a given time period ∆, then VaR is a risk statistic that measures the risk of holding the portfolio for the time period ∆. Assume that L has distribution function FL , then we define VaR at level α ∈ (0, 1) as VaR∆ α (L) = inf{x ∈ R : P (L > x) ≤ 1 − α} = inf{x ∈ R : FL (x) ≥ α ...
Value-at-Risk (VaR)
... We consider the VaR of a portfolio manager who has invested in only two assets: A domestic stock index and a foreign bond. For simplicity we assume that the value of this portfolio is wholly determined by only several parameters: Í The current price of the stock index Í The foreign market interest r ...
... We consider the VaR of a portfolio manager who has invested in only two assets: A domestic stock index and a foreign bond. For simplicity we assume that the value of this portfolio is wholly determined by only several parameters: Í The current price of the stock index Í The foreign market interest r ...
PDF
... can be estimated. The returns generated through the joint distribution function will be used to calculate the CVaR. CVaR builds upon the original theory of VaR. The foundations of VaR can be traced back to 1952 (Roy, 1952). Roy defined in his seminal article the safety first theory. The safety theor ...
... can be estimated. The returns generated through the joint distribution function will be used to calculate the CVaR. CVaR builds upon the original theory of VaR. The foundations of VaR can be traced back to 1952 (Roy, 1952). Roy defined in his seminal article the safety first theory. The safety theor ...
Actuarial Science Meets Financial Economics
... Incorporate risk into calculations Use specialized languages ...
... Incorporate risk into calculations Use specialized languages ...
Value at Risk - dedeklegacy.cz
... repayment of a bond or coupons of the bond, repayment of loan or charged interest); ii) debtors are downgraded by credit agencies iii) credit spreads are widened due to external events beyond debtor’s control (i.e. increased political uncertainty, a higher macroeconomic instability) rating agencies ...
... repayment of a bond or coupons of the bond, repayment of loan or charged interest); ii) debtors are downgraded by credit agencies iii) credit spreads are widened due to external events beyond debtor’s control (i.e. increased political uncertainty, a higher macroeconomic instability) rating agencies ...
1Q13 Basel 2.5 - Final
... constructs a distribution of hypothetical daily changes in the value of trading portfolios based on the following: historical observation of daily changes in key market indices or other market risk factors; and information on the sensitivity of the portfolio values to these market risk factor change ...
... constructs a distribution of hypothetical daily changes in the value of trading portfolios based on the following: historical observation of daily changes in key market indices or other market risk factors; and information on the sensitivity of the portfolio values to these market risk factor change ...
Institute of Actuaries of India November 2011 Examinations
... the underlying portfolio assumptions and characteristics, in order to gain insight into portfolio sensitivities to pre defined risk factors. This pertains in particular to asset correlations and volatilities In other words, stress testing can be considered as a way of taking into account extreme eve ...
... the underlying portfolio assumptions and characteristics, in order to gain insight into portfolio sensitivities to pre defined risk factors. This pertains in particular to asset correlations and volatilities In other words, stress testing can be considered as a way of taking into account extreme eve ...
Solution
... Unlike the Monte Carlo approach, it uses the actual historical distribution of returns to simulate the VAR of a portfolio. Real data plus ease of implementation, have made historical simulation a very popular approach to estimating VAR. Historical simulation avoids the assumption that returns on ...
... Unlike the Monte Carlo approach, it uses the actual historical distribution of returns to simulate the VAR of a portfolio. Real data plus ease of implementation, have made historical simulation a very popular approach to estimating VAR. Historical simulation avoids the assumption that returns on ...
MTH 202 : Probability and Statistics
... Statistics deals with studying samples collected from various experiments or observations. For obvious reasons it would best if we can get a large number of such data which would ensure to detect statistically the best expectation. However, often this is practically impossible to obtain. We would th ...
... Statistics deals with studying samples collected from various experiments or observations. For obvious reasons it would best if we can get a large number of such data which would ensure to detect statistically the best expectation. However, often this is practically impossible to obtain. We would th ...
L4_stochastics
... A man starts from a point O and walks l yards in a straight line; he then turns through any angle whatever and walks another l yards in a second straight line. He repeats this process n times. I require the probability that after these n stretches he is at a distance between r and r + dr from his st ...
... A man starts from a point O and walks l yards in a straight line; he then turns through any angle whatever and walks another l yards in a second straight line. He repeats this process n times. I require the probability that after these n stretches he is at a distance between r and r + dr from his st ...
Document
... An expanding economy brings profits to entrepreneurs who are the beneficiaries of either their skills or luck. Greater profit in the real sector spurs greater demand for assets. Rising asset prices elicit greater demand for assets. Greed is infused with optimism, confidence, animal spirits, etc The ...
... An expanding economy brings profits to entrepreneurs who are the beneficiaries of either their skills or luck. Greater profit in the real sector spurs greater demand for assets. Rising asset prices elicit greater demand for assets. Greed is infused with optimism, confidence, animal spirits, etc The ...
Midterm1Winter07.doc
... and print a message based on the average. The values must be read using prompt and the result must be printed using document.writeln. The following data represents the cutoffs to be used for the generation of the output message: Average >= 90.0 “You did very well” Average >= 80.0 “You did good” ...
... and print a message based on the average. The values must be read using prompt and the result must be printed using document.writeln. The following data represents the cutoffs to be used for the generation of the output message: Average >= 90.0 “You did very well” Average >= 80.0 “You did good” ...
Chapter 2 Value at Risk and other risk measures 1 Motivation and
... To illustrate this calculation, let us take α = 2% and the window size n = 250 business days. Then the observed empirical quantiles correspond to the level of probability of 0.002, 0.006, 0.010, 0.014, 0.018, 0.022 . . . ..., 0.998. Hence the α-quantile is determined as the value in the middle betwe ...
... To illustrate this calculation, let us take α = 2% and the window size n = 250 business days. Then the observed empirical quantiles correspond to the level of probability of 0.002, 0.006, 0.010, 0.014, 0.018, 0.022 . . . ..., 0.998. Hence the α-quantile is determined as the value in the middle betwe ...
Value at Risk (VaR)
... using the parametric method. This is generally an acceptable assumption for daily VaR calculations because daily returns usually are very small; it is less acceptable for VaR calculations with longer time horizons because returns tend to deviate substantially from zero as the time horizon increases. ...
... using the parametric method. This is generally an acceptable assumption for daily VaR calculations because daily returns usually are very small; it is less acceptable for VaR calculations with longer time horizons because returns tend to deviate substantially from zero as the time horizon increases. ...
VaR Exceedances at Large Financial Institutions
... One possibility is that there is no problem. Maybe the models are useful in their current form and would not be more useful if they were more accurate. It’s possible that the models are biased in a predictable fashion, and that risk managers simply correct for these biases when using the numbers pr ...
... One possibility is that there is no problem. Maybe the models are useful in their current form and would not be more useful if they were more accurate. It’s possible that the models are biased in a predictable fashion, and that risk managers simply correct for these biases when using the numbers pr ...
CONDITIONAL TAIL VARIANCE AND
... In application, X is often interpreted as the stock price or insurance loss. We see that CTVα is the conditional variance of X when X exceeds VaRα . (i.e. The distribution of X lefttruncated by VaRα .) It tells us on average how far away the extreme events deviate from CVaRα. If CTVα is fairly ...
... In application, X is often interpreted as the stock price or insurance loss. We see that CTVα is the conditional variance of X when X exceeds VaRα . (i.e. The distribution of X lefttruncated by VaRα .) It tells us on average how far away the extreme events deviate from CVaRα. If CTVα is fairly ...
Sums of independent variables approximating a boolean function
... In our proofs we did not attempt to make the constants sharp. In view of PCP theorem applications this is no problem — the constants involved in the PCP theory tend to be uncontrollable anyway. If one would wish to obtain better results, a Chernoff type argument (for instance as given in [4]) has to ...
... In our proofs we did not attempt to make the constants sharp. In view of PCP theorem applications this is no problem — the constants involved in the PCP theory tend to be uncontrollable anyway. If one would wish to obtain better results, a Chernoff type argument (for instance as given in [4]) has to ...
Value at risk
VaR redirects here. For the statistical technique VAR, see Vector autoregression. For the statistic denoted Var or var, see Variance.In financial mathematics and financial risk management, value at risk (VaR) is a widely used risk measure of the risk of loss on a specific portfolio of financial exposures. For a given portfolio, time horizon, and probability p, the p VaR is defined as a threshold loss value, such that the probability that the loss on the portfolio over the given time horizon exceeds this value is p. This assumes mark-to-market pricing, and no trading in the portfolio.For example, if a portfolio of stocks has a one-day 5% VaR of $1 million, there is a 0.05 probability that the portfolio will fall in value by more than $1 million over a one day period if there is no trading. Informally, a loss of $1 million or more on this portfolio is expected on 1 day out of 20 days (because of 5% probability). A loss which exceeds the VaR threshold is termed a ""VaR break.""VaR has four main uses in finance: risk management, financial control, financial reporting and computing regulatory capital. VaR is sometimes used in non-financial applications as well.Important related ideas are economic capital, backtesting, stress testing, expected shortfall, and tail conditional expectation.