Lecture 6 Flashcards
What is the formula for Mean-Variance Utility Function?
U = E(r) - 1/2AVar(r)
What is the formula of the 5% VaR?
5% VaR = Wt (1.645Vol. - Mean)
The 1.645 changes with the percentage of Value at Risk
What happens with the indifference curve when the risk aversion becomes larger?
The indifference curve becomes steeper because the risk averse investor wants more return for the risk he is taking
What is the difference between Value at Risk and Expected Shortfall?
Value at Risk (VaR) estimates the maximum loss over a given time period at a specified confidence level (e.g., 95% or 99%). It answers the question, “What is the worst loss we could expect with a certain level of confidence?”
Expected Shortfall (ES) (also known as Conditional VaR or CVaR) measures the average loss beyond the VaR threshold. It captures the expected average of losses in the worst-case scenarios and gives a fuller picture of tail risk.
In short, VaR gives a loss limit, while ES provides the expected loss when that limit is exceeded. ES is more sensitive to extreme losses than VaR.
Describe the basic formula of first order Taylor approximation in log returns.
r t+1 = ln(Pt+1) - ln(Pt) is approximately (Pt+1 - Pt) / Pt = Rt+1
How can you use log returns when you want to know the annual mean and you have only the quarterly mean?
In case that returns are identical and independent, then we can just do 4*MeanQ = MeanA
How can you use log returns when you want to know the annual volatility and you have only the quarterly volatility?
In case that returns are identical and independent, then we can just do Square Root 4 * Vol.Q = Vol.A.
Why do I have to use a Square Root when multiplying the volatility from monthly to annual and not with mean?
Because the longer the horizon, the more dominant the effect of the expected return will be.
What is the hot hand fallacy or gambler’s fallacy?
People believe that a manager with good results for some years will have greater probability to get good results the year after.
