Why Single-Period CAPM Does Not Specify Prices Across Periods
Summary
The note asks how prices connect across periods when returns are defined from consecutive prices in a single-period CAPM setup. It distinguishes the price used to calculate a period’s return from the equilibrium price in a subsequent period, and asks how an investor entering later would be represented if prices moved between those points.
The answer emphasizes that CAPM describes equilibrium in a one-period economy and does not, by itself, define the next period’s prices or dynamics. Extending the analysis requires a multi-period framework with additional assumptions; the response points to an overlapping-generations model with constrained investors as one example. It offers no derivation of that extension, and the conclusion about demand for high-beta stocks is specific to the referenced model rather than a general implication of single-period CAPM.
Key ideas
- Single-period CAPM describes equilibrium over one period and does not specify subsequent price dynamics.
- A multi-period model needs additional assumptions about how periods and investors are linked.
- Returns in a one-period setup use prices at the beginning and end of that period.
- An overlapping-generations extension is cited as one approach to studying multi-period effects and constrained investors.
Tags
Full text
# How do asset prices behave in a single-period and multi-period model?
# How do asset prices behave in a single-period and multi-period model?
When we talk about the single-period CAPM, the return in a particular period t can be defined as $(P_t - P_{t-1})/P_{t-1}$. Investors plan at t-1 and get a payoff at t.
After this period, the same mechanics take place. Does the “new” Pt-1 have to necessarily be equal to Pt? In other words, is the return in each period calculated separately, or is the “opening” price in a period necessarily the “closing” price of the previous period? Or does the “payoff” price potentially differ from the new “equilibrium” price? Can this change given a fixed return distribution? If the return distribution changes, it obviously changes. Does this depend on whether the model is “static” or “dynamic”?
If it is the case that these prices can differ, how does the model incorporate the potential of an investor purchasing the model at time t, and then the price falling (at the new t-1)?
## Answer by quant_son (score 1)
https://quant.stackexchange.com/a/74392
As you write yourself, the CAPM is a one-period model. It states the equilibrium in a single-period economy. It does not in itself say anything about the next period. A suggestion could be to have a look at Pedersen (2013) "Betting against beta" which extends to multi periods (by an over-lapping generations model) and constrained agents. They reach the intuitive conclusion in proposition 1, that "everyone" wants high-beta stocks, so you have to "bet against beta" to increase alpha.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.