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Exploring Risk and the Concept of Probability in the Good Old Days

Delve into the historical roots of risk and probability from deterministic beliefs to the emergence of concepts in 17th-century France, including the development of risk measurement tools like standard deviation and diversification strategies. Learn about influential figures like Blaise Pascal and Gottfried von Leibnitz and uncover modern performance measures like the Sharpe ratio and the M-2 measure in the context of managing risk in investments.

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Exploring Risk and the Concept of Probability in the Good Old Days

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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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