# Lernkarten

Karten 31 Karten 1 Lernende English Universität 30.12.2019 / 12.01.2020 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)

• 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 --> $$\beta=1$$