Week One
VaR - “Value at Risk”
- Lets’s say 1%, one-year value at risk of 10 million, it means that there is a 1% chance that the portfolio will lose 10 million in one year.
Cauchy Distribution
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Central Limit Theorem
- Average of a large amount of independent identically distributed stocks are approximately normally distributed
- Can fail if the underlying stocks are fat tailed
- Can fail if the underlying stocks lose their independence
Covariance
- Covariance between two investments or more is the central to Captial Asset Pricing Model, because you always want to ask for a low covariance.
- Risk is determined by the covariance.
Captial Asset Pricing Model (CAPM)
- Based on Rational market and rational investors
- The CAPM implies that the expected return on the i(th) asset is determined from its Beta(𝛽).
- Beta(𝛽) is the regression slope coefficient when the return on the i(th) asset is regressed on the return on the market
Calculating the Optimal Portfolio
Portfolio Expected Return: r=X1r1+(1−X1)r2
Portfolio Variance: X21Var(r1)+(1−X1)2Var(r2)+2X1(1−X1)Cov(r1,r2)
Positive Covariance is bad for you portfolio, it rasie the variance of your portfolio
Negetive Covariance is good, and it reduce the variance of the portfolio
Grodon Growth Model
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