A Few Words on Risk
1) Definition
- “Uncertainty” surrounding an event
* It does not necessarily mean a loss or a danger.
2) Determinants of its effect
- Expected value of the relevant variable
- Its variance → σ (standard deviation) as the common metric for risk
- Exposure: The value of the underlying asset, size of the contract for instance
3) Nature
- Human beings are in general risk-averse.
- Normally, a high return is expected from a high risk.
Þ The principle of “high risk, high return”
4) Now you can check your own risk-return profile
and at the same time you can prove the high risk-high return principle.
The game: Which bet would you like to take?
- A fair coin: 50% head, 50% tail
- The basic bet:
. Tail---You lose $1 million
. Head ---You win the prize in million dollars:
Table of Your Payoff
(In million dollars)
(In million dollars)
*Expected value (EP, 期待値): Weighted average of all possibilities, which you calculate from the probability distribution.
** Variations:
- (1/10) x 10 →You take ten bets with the stake of each bet being one tenth of the basic bet.
- (1/100) x 100 →You take 100 bets with a 1/100 stake.
- (1/10000) x 10000 →10000 bets with a 1/10000 stake.
→ Real payoff from a “Variation” is a probability distribution whose standard deviation (σ) decreases as you increase the number of trials. You can have 95% confidence in having a payoff within (EP±3σ).
5) Conclusion
I would take the any bet in the shaded area.
Your preference would be somewhat similar.
→ See, I told you so: High risk high return or more precisely low risk low return.
For your reference, this conclusion is due to the law of large numbers (大數의 법칙).
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