Week 6 Flashcards
what does VAR: 10 day 5% VAR of a 1000 mean?
over next 10 days, you have a 5% to lose at least 1000 euros
Value at risk (var) formula (delta normal method)
- As its measured in euros and you need value of portfolio –> pt
- Its a risk measure so sdev; Sdev doesn’t make assets move
- you need sth else to make sigma move, Z
- its scaled with square root T, as u need horizon, (10 day value at risk, 100 day)
portfolio variance in excel formula
Steps in doing historical simulation to calculate Var and expected shortfall
4 steps
How do you calculate the 5th percentile returns in excel
=percentile.inc( all returns, 1- 95% confidence interval/100)
What are the steps of monti carlo VAR and expected shortfall simulation?
5 steps
How do you calculate the Z’s and asset returns for monti carlo simulation
Z3 its not just your normal.s. inverse
Z3 is a combo of z1 and z2. z1 force that drives asset 1. and z2 is the internal force of asset2 except asset 2 is not just driven by its own randomness but also of asset 2.
The stronger the correlation, the more closly the movements of the second asset will follow the first asset. And this is + second assets will be scaled by the square root of 1 - correlation^2
What is the formula of exponentially weighted moving average (EWNA)
variance not volatility
What is the formula of Generalized Autoregressive Conditional Heteroskedasticity (GARCH)
Multiply gamma with long term variance + alpha * previous return^2 + beta * Previous variance
portfolio volatility not with matrix algebra
Suppose you use both the historical simulation approach and the delta-normal method to estimate the 10-day 99% VaR for a stock, using the same historical sample of 100 daily returns on the stock. Assume that the distribution of the daily stock return is normal. Which of the two VaR estimates you computed is more precise? Why?
Delta-normal method yields more precise VaR estimate because the sample SD used to compute the delta-normal VaR is based on all 100 observations in the sample, whereas the sample quantile used to compute VaR in the historical simulation method uses only observations in left tail. In this question, the 99% historical VaR would be the second-largest simulated daily portfolio loss (which is then scaled by the square root of 10 to get 10-day 99% VaR), so it depends on only 2 observations.
Why can you expect higher VAR’s at low percentile’s for historic simulation compared to delta normal?
At low percentiles, delta-normal simulation might produce lower VaR estimates compared to historic simulation because it assumes a normal distribution and might not adequately capture extreme events or tail risks. This method is less influenced by extreme observations in the historical data and might not fully account for the potential severity of tail events.
What are the 4 types of risk
Expected shortfall returns
=AVERAGEIF(returns,”<=”&percentile returns)
What are the steps of computing exponentially weighted moving average volatility (EWMNA)
