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Probability Concepts

4 important questions on Probability Concepts

How do we define odds for and odds against?

Odds for (1 to 7), implies a a/(a+b) (1/8) probability that the event would take place.
Odds against (15 to 1) implies a b/(a+b) probability that the event would take place. Often used with bets and corresponding profit (wagering).

What is a pairs arbitrage trade?

A trade in two closely related stocks involving the short sale of one and the purchase of the other. Dutch book theorem - - > inconsistent probabilities create profit opportunities.

What does the total probaibility rule state?

That the complement of an unconditional probability and the unconditional probability itself are summed 1 and exhaustive (P(S) + P(Sc) = 1). It puts it into scenarios, S happens or it doesn't. We can have more than two scenarios, for which the rule is still applicable if events are mutually exclusive and exhaustive. It basically states unconditional in multiple conditional events. Via this way we can calculate a weighted average, to come to a expected value.

Use these rule in three, to get from the back to the front.

What is it about un(conditional variances?

Advanced topic, but main points are:
- like expected value, have a conditional counterpart to the unconditional concept.
- we use conditional variances to assess risk, given a particular scenario.

Note that portfolio variances can be derived from summing w*w*Cov for all combinations!

The question on the page originate from the summary of the following study material:

Quantitative Methods - Basic Concepts

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