Financial Market Risks
Fall 2019, ETH D-MTEC, Prof. Didier Sornette
Fall 2019, ETH D-MTEC, Prof. Didier Sornette
Kartei Details
Karten | 31 |
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Sprache | English |
Kategorie | Finanzen |
Stufe | Universität |
Erstellt / Aktualisiert | 30.12.2019 / 12.01.2020 |
Lizenzierung | Kein Urheberrechtsschutz (CC0) |
Weblink |
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Examples for commodities & forms to trade them
Commodities are raw materials categorized as energy (oil, gas, power), metals (industrial, rare earth) or agriculture (grains, veg. oil, meats)
Traded in physical form as:
- Forward: agreement to buy a fixed amount at a fixed price on a set date; contract only between two parties, not traded on the market --> OTC
- Future: same as forward, but traded on the market
How to caluculate average risk premium of different assets
\(\text{avg. risk premium of a}=\text{real rate of return of a}-\text{real rate of return of risk-free asset}\)
risk-free asset: treasury bill for example
Skewness & kurtosis of a distribution curve and what do investors prefer
- Skewness: symmetricity of the curve
skewness = 0 --> symmetric
skewness > 0 --> skewed right
skewness < 0 --> skewed left
Investors prefer right skewed distributions since probability for low return is smaller - Kurtosis: weight of the tails of a curve
kurtosis = 3 --> normally distributed
kurtosis > 3 --> leptokurtic (fat tails)
kurtosis < 3 --> platykurtic (thin tails)
Investors prefer platykurtic distributions since they have fewer risks (outliers)
Correlation formula & range of values
\(\rho (X,Y)=\frac{Cov[X,Y]}{\sqrt{Var[X]\cdot Var[Y]}}\)
\(\rho>0\): correlated
\(\rho<0\): anti-correlated
\(\rho=0\): uncorrelated
Portfolio variance - formula for a 2-stock portfolio
\(\text{portfolio variance}=x_1^2\sigma_1^2+x_2^2\sigma_2^2+2(x_1x_2\rho_{12}\sigma_1\sigma_2)\)
\(x_i\): portion of stock i in portfolio
\(\sigma_i\): standard deviation of stock i return
\(\rho_{12}\): correlation between return of stocks 1 & 2
Portfolio variance - formula for a N-stock portfolio
\(\text{portfolio variance}=N(\frac{1}{N})^2\cdot\text{avg. variance}+(N^2-N)(\frac{1}{N})^2\cdot\text{avg. covariance} \)
\(=\frac{1}{N}\cdot\text{avg. variance}+(1-\frac{1}{N})\cdot\text{avg. covariance}\)
Market risk
Risk that remains in a fully diversified portfolio. Since portfolio variance converges to the market risk (rather than to 0), it is sufficient to buy a representative slice of the market to get a well-diversified portfolio.
Well-diversified portfolio
Portfolio whose risk equals the market risk --> \(\beta=1\)