CAPM Flashcards
Vad är nackdelen med CAPM och hur löser man detta?
Nackdelen är att det är en partial-eq modell.
Man löser det i Lucas träd modellen, vilken stoppar in företag i termer av träd.
In a competitive equilibrium, prices are such that all markets clear. Asset prices depend on returns and marginal utilities, which in turn depend on
savings and returns, this creates a potentially complicated interaction.
Vad är slutsattserna som vi kan dra av resultatet i C-CAPM
E_t Ri_t+1 - R’_t = -cov((Buct+1/uct)Ri_t+1)R’_t
Cov < 0, dåligt för då är excess return är positiv. Good hedge.
If the covariance between Ri ,t +1 and Uc ,t +1 is negative, the asset gives higher return when consumption is higher (remember Ucc < 0). In this case, the required excess return is positive. The asset is a bad hedge, i.e. it pays more when marginal utility of an extra resource is lower!
Cov > 0, bra för då är excess return är negative. Bad hedge.
The opposite is true if the covariance between Ri,t+1 and Uc,t+1 is positive.
In other words, in equilibrium consumers are willing to accept a lower return on an asset that provides a hedge against low consumption by paying off more in states where consumption is low.
Households want to smooth consumption across states of the world!
Vad gör Lucas-träd modellen och vilket antagande vilar den på?
▶ Lucas (1978) solves for asset prices in closed form in a general equilibrium setting, by making a crucial simplifying assumption: equilibrium savings in the economy are exogenous.
Vad är själva träd-grejen i Lukas-modellen?
Rather than accumulating capital, people save in ”trees” whose ”fruits” constitute the dividends of the economy.
The number of trees is exogenously given, i.e. a continuum of mass one.
In equilibrium, savings coincides with the number of trees, multiplied by their prices and consumption must equal the exogenous dividend.
The trees are the “production” in this economy, and it is exogenously given. That is, they get one tree each at the beginning. There is no “technology” to production. Just the trees.
Individuals can not “store” the fruit, they need to consume it.
Individuals can however, buy and sell trees with each other.
The task is thus to figure out the market-price of the trees (the asset pricing), relative to consumption (apples = the dividends).
In the Lucas model, what is the crucial thing regarding the representative agent?
This simplifies the model and makes us able to solve it.
Representative agent economy = One person is the whole economy.
Both trees and individuals have the mass of 1 each. So each tree or person are a share of the mass one. We can think of “mass one” as a nation, then each share of that is a individual.
What is our task in the Lucas tree model?
To solve for the price of trees. That is, the asset prices.
Explain the budget-constraint in the Lucas model?
c_t + p_t s_{t+1} = (p_t + d_t)s_t
s = our tree
d = dividence from out trees (the fruit that falls down).
p = price of out tree (market value)
c = consumption of fruits
RHS: Wealth.
Our wealth is given by the fruts that fall down from all our trees and the aggregated market value from our trees. More trees = more fruits and higher aggregated market value.
LHS:
The fruit we consume or the trees we do not sell today. (ptst+1 = alternative cost of not sell ing the trees).
What does the market clearing condition
st = 1
and
dt = ct
say in the Lucas model
st= 1
Since HH is identical, they will choose equally many trees. Since endowment is one, price adjusts so every one does just this. That is, there is no trade.
dt = ct
We eat all fruit that fall to the ground.
What role do the transversality condition play in the Lucas Tree model?
It rules out price bubbles. People will not buy assets just to be able to sell them to higher prices.
What type of economy is the Lucas model?
It is an endowment economy. So, no production size. Individuals are endowed with trees that randomly produce dividends.
What happens in the Lucas setting if the individual is risk-neutral, Beta = 1 and there is no dividence?
The Euler equation reduces to
Et[pt+1] = pt + et+1
That is, prices follow a “martingale”. This means that all the information that is useful to predict next periods expected price is contained in pt. If et+1 is i.i.d, then prices follow a random walk.
