# What are the essential characteristics of asset prices?

I think the question has already been asked about stylized facts of asset returns; this question regards the essential characteristics and normative assumptions used to evaluate asset prices. I.e., given that the economic value of a generic asset is its discounted expected utility, what are some assumptions by which an economic stakeholder may assess a claim's worth?

To start, here are a few:

1. Price is an expressed belief of value.
2. The efficient market hypothesis (EMH): the market acts as a price discovery mechanism in which market prices reflect participants' capital-weighted expectation. It should be difficult to prove that the market price is not "correct". "Price is what you pay -- value is what you get" applies only in cases where the market is not efficient.
3. The fundamental theorem of asset pricing (FTAP) which posits (i) a risk-neutral measure equal to a probabilistic measure which can only be rigorously demonstrated given (ii) complete markets.
4. FTAP's correlary to EMH: in an efficient market place, any price which reflects a $\mathbb P$ (i.e., "acturial" and/or "real-world") expectation that does not have a different $\mathbb Q$ ("risk-neutral") measure can be considered an efficient price. I.e., any "no-arbitrage" price is permitted under EMH.
5. Asset prices cannot be negative (or can they???). Since maximum loss is (typically) constrained to principal invested, asset prices cannot theoretically be negative -- but, in practice, investors may assign them negative values (vis-a-vis, the "drag" on value whereby the inclusion of an asset causes a portfolio to be valued less than it if were dis-included).
6. Corollary of requirement that prices be supported over the domain $\left[0, \infty \right]$: price paid determines both expected return as well as maximum loss (à la Seth Klarman's synthesis regarding Warren Buffet-esque "Margin of Safety").
7. The fair price of any generic asset is equal to the expected net present value of the discounted cash flows that it is expected to generate.
8. Time value of money (TVM): Time is money. Time has monetary value which can be expressed as a utility function. Utility is usually interchangeably expressed as a discount factor or an interest rate which represents an expected and/or required rate of return based on an investor's intertemporal preferences regarding consumption and risk. Rational utility should always be a monotonically decreasing utility function with respect to time -- i.e.,"a dollar today is always worth more than a dollar at any time in the future". Therefore, discount rates cannot be negative (or can they???). Also, a discounting function need not be an exponential/geometric (i.e., normative) function, continuous, symmetrical, or time-invariant.
9. Modigliani-Miller's postulates on (i) the value of a firm and (ii) the irrelevance of capital structure inform the intuition that -- under a broad range of regulatory frameworks -- capital structuring decisions are not a major factor in determining an asset's enterprise value.
10. Corollary to MM II: it is simpler to price the firm's underlying assets in totality (and then allocate value to claims in order of seniority) vice value each class of claim individually, vis-a-vis "in order to value a company's stock, one must first value the company itself" (attribution needed).
11. Arbitrage Theory of Pricing's (APT) statement that asset prices are reflexively a transformed function of returns.
12. The Capital Asset Pricing Model's (CAPM) application of APT which states that asset prices are a function of diversifiable and non-systemic risk under a mean-variance framework.
13. Equity is analogous to a long call option on a firm's value; debt is analogous to short put option on a firm's value. A position which is long equity and long debt is a synthetic long position on the firm's underlying assets.

Good responses should add depth to and/or expand upon those characteristics already identified. I also would appreciate any relevant references including compendia and/or primers.

I appreciate your thoughts and references.

• Asset returns are just a simple function of asset prices, stylized facts about asset returns are just stylized facts about changes in prices. See the book Asset Pricing by John Cochrane for a start. – jd8 Jul 14 '17 at 11:23
• @jd8 I agree that prices should be reflexively defined by returns. However, when I ask about the axioms of asset returns, I get responses regarding the prior and/or posterior distributions and not regarding their pricing. Also, I checked out John Cochrane's site... appears to be on point as per the question. Thank you. – David Addison Jul 17 '17 at 16:35
• I thought stylized fact refers to empirical findings that are so consistent that they are accepted as truth. These to me are more like common assumptions that make your life easier, no? – Will Gu Aug 8 '17 at 21:13
• @WillGu. I agree. I was actually thinking earlier that "facts" may be an inappropriate term. Yet, some of the above "characteristics" may be stylized as facts such as the observation that securities prices are lower bounded at zero, even if expected values (i.e., returns) are negative. But in general I agree, I will rephrase to use "stylized characteristics". – David Addison Aug 8 '17 at 21:16
• This question has the potential to be a good source of information but currently has no focus. 9 is a point about discount rates. 11,12 are theories about expected returns, i.e. discount rates that are used to discount cash flows to arrive at prices. 10 is a straw man and does not relate to asset prices empirically - although it is a great framework that helps us think about capital structure and firm value. – jd8 Aug 10 '17 at 1:11