Financial Market Risks

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

\(\text{avg. risk premium of a}=\text{real rate of return of a}-\text{real rate of return of risk-free asset}\)

risk-free asset: treasury bill for example

• Skewness: 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)

\(\rho (X,Y)=\frac{Cov[X,Y]}{\sqrt{Var[X]\cdot Var[Y]}}\)

\(\rho>0\): correlated

\(\rho<0\): anti-correlated

\(\rho=0\): uncorrelated

\(\text{portfolio variance}=x_1^2\sigma_1^2+x_2^2\sigma_2^2+2(x_1x_2\rho_{12}\sigma_1\sigma_2)\)

\(x_i\): portion of stock i in portfolio

\(\sigma_i\): standard deviation of stock i return

\(\rho_{12}\): correlation between return of stocks 1 & 2

\(\text{portfolio variance}=N(\frac{1}{N})^2\cdot\text{avg. variance}+(N^2-N)(\frac{1}{N})^2\cdot\text{avg. covariance} \)

\(=\frac{1}{N}\cdot\text{avg. variance}+(1-\frac{1}{N})\cdot\text{avg. covariance}\)

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.

Portfolio whose risk equals the market risk --> \(\beta=1\)