CF

• Risk refers to the uncertainty of the future outcomes of an investment
• Probability


  The likelihood of an outcome
• The sum of the probabilities of all the possible outcomes is equal to 1.0
• Risk of expected return


  The degree of uncertainty that actual return will be different from the expected return
• Expected Return


  1. ∑(Pt*Rt)

  2. Where Pt = probability for possible return i at time t

  3. Rt = possible return i at time t
• Excess Return


  Rt - rf
• Risk Premium


  E[Rt] - rf
• Mean


  μt ≡ E[Rt]
• Variance


  σt^2 ≡ E[(Rt - μt)^2]
• Median


  50th percentile (probability of 1/2 that Rt< median)
• Skewness


  Measure of the asymmetry of the distribution
• Correlation


  How closely two variables move together
• Normal distribution is a bell-shaped, symmetric distribution

  
• Central Limit Theorem states that the sum of independent random variables will be normally distributed

  
• If R is normally distributed, then 68% of observations fall within +/- 1.00 std. deviations from mean, 90% within +/- 1.65 std. deviations, 95% within +/- 1.96 std. deviations, and 99% within +/- 2.58 std. deviations

  
• Real interest rate has been slightly positive on average
• Return on more risky assets has been higher on average than return on less risky assets
• Returns on risk assets can be highly correlated to each other
• Returns on risky assets are (usually) serially uncorrelated
• Basic statistics, U.S, 1946-2001 (monthly, in percent)


  • Inflation
  • Tbill (1 yr)
  • Tnote (10 yr)
  • VW stock index
  • EW stock index
  • Motorola

  
• The stock market was not bad because there was no FEAR!
• The risk/reward relationship seems to apply over long periods
• Anomalies exist in the stock market, such as the size effect, January effect, value premium, and momentum

  
• Financial assets


  • Sovereign bonds
  • Corporate bonds
  • Structured financial instruments
  • Derivatives
  • Alternative investments
• Hedge funds


  Private investment vehicles that manage portfolios of securities and derivative positions using a variety of strategies, often with long and short positions and high leverage
• Venture capital and private equity


  Investing in private companies, either startups or established, that are not listed on a public exchange
• Real estate investment


  May be in building and/or land, either directly or indirectly through securitizations and investment funds
• Commodities investment


  May be in physical commodity products or through derivative products and commodity indexes
• Infrastructure investment


  Capital-intensive, long-lived, real assets that provide essential public services, often through public-private partnerships
• Passion investments


  Non-traditional assets that allow enjoyment of ownership, such as fine wine, art, antiques, and collectibles
• The standard deviation of returns for the overall stock market is 4.5% monthly (16.4% annually)

  
• The average monthly standard deviation of an individual stock is around 17% (50% annually)
• Stocks tend to move together over time, but the correlation is far from perfect

  
• Stock returns are nearly unpredictable
• Market volatility changes over time, with the standard deviation of monthly returns varying from roughly 2% to 20%
• Financial ratios like P/E ratios vary widely over time
• Different financial assets have different risk levels