Statistics 580 Monte Carlo Methods Introduction
... was taken as a sample ... [i.e.,n above is = 4] ... and the mean [and] standard deviation of each sample determined.... This provides us with two sets of ... 750 z’s on which to test the theoretical results arrived at. The height and left middle finger ... table was chosen because the distribution o ...
... was taken as a sample ... [i.e.,n above is = 4] ... and the mean [and] standard deviation of each sample determined.... This provides us with two sets of ... 750 z’s on which to test the theoretical results arrived at. The height and left middle finger ... table was chosen because the distribution o ...
Backtesting Value-at-Risk based on Tail Losses Woon K. Wong
... now widely used by banks and other financial entities such as hedge funds for risk reporting; see, for example, Jorion (2001). One reason for the preference of VaR over other risk measures can be attributed to the fact that the backtest of VaR is easy to implement. VaR can be defined as the maximum ...
... now widely used by banks and other financial entities such as hedge funds for risk reporting; see, for example, Jorion (2001). One reason for the preference of VaR over other risk measures can be attributed to the fact that the backtest of VaR is easy to implement. VaR can be defined as the maximum ...
Risk Management and Financial Institutions
... - It is natural to assume that the volatility of a stock price is caused by new information reaching the market. Fama (1965), French (1980), and French and Roll (1986) show that the variance of stock price returns between Friday and Monday is only 22%, 19% and 10.7% higher than the variance of stock ...
... - It is natural to assume that the volatility of a stock price is caused by new information reaching the market. Fama (1965), French (1980), and French and Roll (1986) show that the variance of stock price returns between Friday and Monday is only 22%, 19% and 10.7% higher than the variance of stock ...
Investments
... standard deviation equals the risky asset’s standard deviation multiplied by the portfolio proportion invested in the risky asset. ...
... standard deviation equals the risky asset’s standard deviation multiplied by the portfolio proportion invested in the risky asset. ...
Banking and FIs 10
... Once in default, banks will often take control of the company as “senior creditors”, sell all remaining company assets and use the proceeds to repay “creditors” in order of seniority If a bank receives less than it is owed following liquidation it has suffered a recovery rate of < 100% ...
... Once in default, banks will often take control of the company as “senior creditors”, sell all remaining company assets and use the proceeds to repay “creditors” in order of seniority If a bank receives less than it is owed following liquidation it has suffered a recovery rate of < 100% ...
risk neutral cash flows
... rates – Expected risk neutral cash flows discounted at risk free rates – Value of replicating portfolio of assets ...
... rates – Expected risk neutral cash flows discounted at risk free rates – Value of replicating portfolio of assets ...
Risk & Rates of Return
... Risk averse investors demand higher returns, or equivalently, a risk premium for undertaking risk. Investors cannot expect the market to compensate them for risk that they can eliminate through diversification. Because stocks can be combined in portfolios to eliminate specific risk, only diver ...
... Risk averse investors demand higher returns, or equivalently, a risk premium for undertaking risk. Investors cannot expect the market to compensate them for risk that they can eliminate through diversification. Because stocks can be combined in portfolios to eliminate specific risk, only diver ...
Lecture 1: Asset pricing and the equity premium puzzle
... Returns appear to be predictable: High current price relative to dividends predicts low future returns. Other variables also have predictive power: CAY, term premium, short-term nominal interest rate (Fed model). Does this violate asset-pricing theory? Econometric issues: overlapping data and standa ...
... Returns appear to be predictable: High current price relative to dividends predicts low future returns. Other variables also have predictive power: CAY, term premium, short-term nominal interest rate (Fed model). Does this violate asset-pricing theory? Econometric issues: overlapping data and standa ...
An Analytic Framework for Computing Value-at
... Sensitivity measures such as delta, gamma and vega1 describes different aspects of a portfolio of financial derivatives. Every night, banks (and other financial institutions) calculate these measures, which results in an enormous amount of data. These data are valuable for each specific trader in managi ...
... Sensitivity measures such as delta, gamma and vega1 describes different aspects of a portfolio of financial derivatives. Every night, banks (and other financial institutions) calculate these measures, which results in an enormous amount of data. These data are valuable for each specific trader in managi ...
What is Financial Mathematics? 1
... • PDE approach to finance • Martingale approach to finance • Numerical methods • Current Research ...
... • PDE approach to finance • Martingale approach to finance • Numerical methods • Current Research ...
robust regression in s-plus - R/Finance 2016
... – Based on linear risk decompositions and reverse optimization – Useful graphical displays for allocation guidance – Well-suited to supporting investment committee decisions ...
... – Based on linear risk decompositions and reverse optimization – Useful graphical displays for allocation guidance – Well-suited to supporting investment committee decisions ...
FIN 685: Risk Management
... – Banks encouraged to use internal models to measure VaR – Use to ensure capital adequacy (liquidity) – Compute daily at 99th percentile – Minimum price shock equivalent to 10 trading days (holding period) – Historical observation period ≥1 year ...
... – Banks encouraged to use internal models to measure VaR – Use to ensure capital adequacy (liquidity) – Compute daily at 99th percentile – Minimum price shock equivalent to 10 trading days (holding period) – Historical observation period ≥1 year ...
Risk
... variance. Standard deviation is also known as historical volatility and is used by investors as a gauge for the amount of expected volatility. ...
... variance. Standard deviation is also known as historical volatility and is used by investors as a gauge for the amount of expected volatility. ...
Law for Business - Matawan-Aberdeen Regional School District
... variance. Standard deviation is also known as historical volatility and is used by investors as a gauge for the amount of expected volatility. ...
... variance. Standard deviation is also known as historical volatility and is used by investors as a gauge for the amount of expected volatility. ...
Chapter 26
... focus on the worst that might happen – Insurance companies, for example, assess the likelihood of insured events, and the resulting possible losses for the insurer – Financial institutions must understand their portfolio risks in order to determine the capital buffer needed to support their business ...
... focus on the worst that might happen – Insurance companies, for example, assess the likelihood of insured events, and the resulting possible losses for the insurer – Financial institutions must understand their portfolio risks in order to determine the capital buffer needed to support their business ...
bYTEBoss Chapter_11
... -- risk seeker or lover -- will pay to take the riskier project -- casinos and lottery tickets Constant -- risk neutral -- is indifferent to risk -- will accept the same expected return for risky as well as safe projects Decreasing -- risk averse -- prefer safety to risk and must be compensated ...
... -- risk seeker or lover -- will pay to take the riskier project -- casinos and lottery tickets Constant -- risk neutral -- is indifferent to risk -- will accept the same expected return for risky as well as safe projects Decreasing -- risk averse -- prefer safety to risk and must be compensated ...
Performance Measurement
... You note the returns 3, 8, 3, 5, 11. Mean is 6. Thus 3 returns are less than the mean. The semi variance is [(6-3)^2 + (6-3)^2 + (6-5)^2]/3 = 6.33 and the semi-standard deviation is 6.33^.5 = 2.51. Compare this to the population standard deviation which is [(6-3)^2 + (6-8)^2 + (6-3)^2 + (6-5)^2+(6-1 ...
... You note the returns 3, 8, 3, 5, 11. Mean is 6. Thus 3 returns are less than the mean. The semi variance is [(6-3)^2 + (6-3)^2 + (6-5)^2]/3 = 6.33 and the semi-standard deviation is 6.33^.5 = 2.51. Compare this to the population standard deviation which is [(6-3)^2 + (6-8)^2 + (6-3)^2 + (6-5)^2+(6-1 ...
Presentation (PowerPoint File)
... “Best” feasible random variable? Barycenter of feasible region? If u is quadratic, this maximizes investor’s expected utility; if “locally nearly quadratic” it nearly does so The value maximizing expected value for some probability? Perhaps investor trusts seller to have a better estimate of ...
... “Best” feasible random variable? Barycenter of feasible region? If u is quadratic, this maximizes investor’s expected utility; if “locally nearly quadratic” it nearly does so The value maximizing expected value for some probability? Perhaps investor trusts seller to have a better estimate of ...
6
... loss on an investment over a specified horizon given some confidence level2. It therefore reflects the potential downside risk faced on investments in terms of nominal losses. We therefore show how VaR can be implemented into the asset allocation framework using shortfall constraints. The advantage ...
... loss on an investment over a specified horizon given some confidence level2. It therefore reflects the potential downside risk faced on investments in terms of nominal losses. We therefore show how VaR can be implemented into the asset allocation framework using shortfall constraints. The advantage ...
File - Glorybeth Becker
... number of red marbles in a jar number of heads when flipping three coins ...
... number of red marbles in a jar number of heads when flipping three coins ...
ASTIN`s Next Greatest Contributions
... Need for Different Risk Metrics – Corporation • For a corporation as a whole and rating agencies – Maximum loss would be the stockholders’ equity – Size of any loss larger than that is irrelevant – Portfolio effect is important ...
... Need for Different Risk Metrics – Corporation • For a corporation as a whole and rating agencies – Maximum loss would be the stockholders’ equity – Size of any loss larger than that is irrelevant – Portfolio effect is important ...
Mathematical Finance/Financial Engineering
... Operational risk(Basel II Accord): Risk of losses resulting from inadequate or failed internal processes, people and systems, or external events ...
... Operational risk(Basel II Accord): Risk of losses resulting from inadequate or failed internal processes, people and systems, or external events ...
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.