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Financial Market Risks

Fall 2019, ETH D-MTEC, Prof. Didier Sornette

Fall 2019, ETH D-MTEC, Prof. Didier Sornette

Kartei Details

Karten 31
Sprache English
Kategorie Finanzen
Stufe Universität
Erstellt / Aktualisiert 30.12.2019 / 12.01.2020
Lizenzierung Kein Urheberrechtsschutz (CC0)
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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 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 --> \(\beta=1\)