# Difference between objective and subjective distributions in asset pricing models?

How does one differentiate between "objective" and "subjective" probability distributions in asset pricing models?

In asset pricing, economists often make a distinction between the "subjective" and the "objective" probabilities of future states of the world. What do they mean by this?

• en.wikipedia.org/wiki/Probability_interpretations Nov 20 '15 at 17:22
• I'm voting to close this question as off-topic because it's not about economics. It might have worked on Philosophy or Cross Validated, but I expect a variant answer of it has already been asked and answered on each. May 5 '16 at 9:53
• I disagree with the close votes. I think this is a relevant economic question that is a topic of active research. May 6 '16 at 14:48
• @cc7768 The question was heavily edited yesterday. And not by the OP. And for some reason folks saw it fit to approve the edit rather than encourage a new question. May 6 '16 at 20:25
• @denesp got it. I should read edits beforehand. May 7 '16 at 1:00

Probability judgments are based on an investors' private information sets, i.e. subjective probabilities. In contrast, objective probabilities are the underlying real probabilities that the world will end up in some state. It is necessary to make the distinction because traders do not have perfect information. See Markowitz (1991) for further explanation.

But objective probabilities remain a remarkable concept. If the market reveals objective probabilities, then these are in fact known, and traders can update their subjective probabilities accordingly. But if all traders agree on the probability distributions, they would have very little reason to trade. Hence one implication of portfolio theory is that there is too much trading going on. See Odean (1999) for empirical work on this, or Grossman & Stiglitz (1980) for a theoretical critique.

In asset pricing, the present value of an asset depends on expectations about the future. If you are sure asset A will be worth 100 tomorrow, it is likely to be worth 100/(1+r) today. If you think it might be worth 100 in scenario I or 0 in scenario II with a 1/2 probability each, then its worth [(1/2)*(100) + (1/2)(0)]/(1+r) = 50/(1+r) today.

But, now add the following twist: what if even though the chances of scenarios I and II are 1/2 each, you observe that the asset is worth more than 50/(1+r). Why could this be?

• One reason could be that even though the probabilities are 1/2 and 1/2, investors thing they are 3/4 and 1/4 maybe. These would be the "subjective probabilities" according to most direct sources.Investopedia Subjective Probability

• Another reason could be that investors know that, for some reason, if scenario I comes round they will be desperate for cash, but if scenario II comes round they will be rich from other income sources anyway. If that's the case then they are more interested in the value of the asset in scenario I than in scenario II. Then they value the asset as being worth, maybe,[(3/4)(100) + (1/4)(0)]/(1+r)=75/(1+r), because the Scenario I payoffs are worth more to them than the Scenario II payoffs.

In any case, if you observe the price to be 75/(1+r) then the numbers 3/4 and 1/4, which look like probabilities, are called the "risk-neutral probabilities". They are "weights" that look like probabilities, that describe two things: investor's subjective assessment of the likelihood of the two scenarios, plus the "importance" they put on different future states of nature, beyond the likelihood of their realization.

These risk neutral probabilities are at the core of the paradigm that economists use to model asset prices .

• This seems very inaccurate. It is the utility of the money that changes, not the perceived probability of the outcome. May 5 '16 at 17:20
• OK. I'm positive this is how some people use these terms, but I can't find any references that say exactly that, so I think you are right, that this is not the most appealing interpretation of these terms. ... will rewrite. May 5 '16 at 18:08