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Academy #4 Risk and the

Academy #4 Risk and the . The good old days. In the old days people believed in deterministic systems: Christianity: “Fortuna’s wheel”: Buddhism: “Karma” Islam: "And in the heaven is your provision and that which ye are promised." There was no concept of randomness.

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Academy #4 Risk and the

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  1. Academy #4 Risk and the

  2. The goodolddays • In the old days people believed in deterministic systems: • Christianity: “Fortuna’s wheel”: • Buddhism: “Karma” • Islam: "And in the heaven is your provision and that which ye are promised." • There was no concept of randomness

  3. The idea of probability • France of the 17th century: • Drinking and gambling • Birthplace of the idea of probability

  4. The idea of probability • Emerged in the France of the 17th century • Blaise Pascal: • “How to split a bet on a game that had been interrupted when one player was winning?”

  5. The idea of probability • Gottfried von Leibnitz: • ”Nature establishes standards that originate the return of events, but only in the majority of cases” • Lloyd's Coffee House • Early insurance market

  6. Risk: • The word “risk” is derived from the latin word “risicare”, which means to dare • Risk is a relatively new concept:

  7. Risk: • How do you measure risk? • Standard deviation: • Most used measure of market risk • Dispersion around the mean

  8. Risk: • Example: • = 2.37%

  9. Risk: • People, usually, do not like risk • They have to be compensated for taking risk • Excess return:

  10. Risk: • Should you take the raw return as a measure of performance? • Why? • Why not?

  11. Risk: • How do stocks move?

  12. Diversification: • Stocks tend to move upwards, but not always in the same direction • It is possible to decrease the risk of your investments through investing in different stocks at the same time • Diversification may reduce risk substantially

  13. Diversification: • Correlation: Measure of linearity between -1 and 1; 0 means no relation

  14. Diversification:

  15. Diversification:

  16. Diversification:

  17. Adjusting returns for risk • The Sharpe ratio: • For =0 -> • Interpretation: how much return do I receive per risk • Problem: • no adjustment for the amount of risk taken

  18. Adjusting returns for risk • Disadvantages: • Sharpe ratio has no measurement unit • How much worse is a portfolio with a shapre ratio of -0.5 compared to a portfolio with a sharpe ratio of 0.5?

  19. Adjusting returns for risk • The M-2 measure: • E[]:Average • : return of the portfolio • : return on the risk free asset • : std. of the benchmark • :std. of the portfolio • : Average risk free rate

  20. Adjusting returns for risk • The M-2 measure: • Outperformance • Measured in percent • Comparable

  21. Adjusting returns for risk • The M-2 measure:

  22. Adjusting returns for risk • Different Scenarios • Change in portfolio return by an additional 1% • Increase the standard deviation by 0.1

  23. Measurement • The M-2 measure: • Weekly observations • : weekly return of the portfolio • : weeks yield of a 9 month German government bond • : std. of the EUROSTOXX index • :std. of the portfolio • : Average of the 9 month German government bond

  24. Why a new performance measure? • More professional • More industry related • Technically feasible

  25. Questions?

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