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THE CAPITAL ASSET PRICING MODEL CAPM

VIEWS: 14 PAGES: 7

									           A. SUMMARY OF PREVIOUS DICSCUSSIONS

           Portfolio choice
           I- Capital Allocation Problem.
           II- Optimal risky portfolio.
                      -without risk-free assets;
                      -with risk free assets.

           End product: Markowitz Portfolio Selection Model

                                              CAL(=CML if rf = T-
                                              bill rate and M is a
                                              broad portfolio of
                                              common stocks, so
Exp. Return                                   that E(rM) is a broad
                                              index of common
                                              stocks)




                                          M


   Risk-free rate



                                                                      risk




           Important conclusions.
           I- Separation property.



                                                                             1
Questions

I- Is the optimal solution easy to implement in practice?
       - How to estimate risk tolerance (or risk aversion?)
       An Answer: Make the best use of the information provided
       by a client to the investment planner.

II- What if the security selection (or the optimal portfolio) problem
is “too hard” to solve?
      -A Passive investment strategy is always available.
      - Make simplification assumptions: for example use an index
      model.

III- Are the individually optimal investment behaviors compatible
with one another? How does the market resolve possible
incompatibilities?

To answer the last question, we need to perform a market
equilibrium analysis. This will result in a comprehensive model.
One such a model is called the Capital Asset Pricing Model.

B. THE CAPITAL ASSET PRICING MODEL (CAPM)

Recall the two themes that we discussed at the beginning of
this course:



  - Risk-Return trade-off: riskier assets tend to offer
    higher return. This can be rationalized by stating that
    investors demand higher risk premiums for holding
    riskier assets. This is also statistically observable.
    Recall the history of interest rates and risk premiums.

                                                                    2
                               1926-2005
   Asset       Small Large Long- Intermediate T-
Characteristic Stocks Stocks Term       (7 years)- Bills
                                (20      Term T-
                               years)     Bonds
                                 T-
                               Bond
  Average      17.95 12.15 5.68            5.35    3.75
   return
  Standard     38.71 20.26 8.09            6.30    3.15
 Deviation
                  See page 146 (Chapter 5)

  - Market efficiency: Financial economists assume that
    all the available information relevant to investment
    profitability is effectively used by investors in their
    investment decisions. This means that most securities
    are priced appropriately given their risk and return
    attributes. This is an assumption. Only its predictions
    can be confronted with observable facts.

  - In the CAPM, these two principles are combined with
    several other assumptions to produce a set of
    predictions concerning equilibrium expected return on
    risky assets. CAPM is the equilibrium model that
    underlies modern financial theory.

  - CAPM is an asset pricing model:



                                                              3
        Recall the definition of the Holding Period
        Return (HPR).
        HPR=dividend yield + Capital gain yield

        Expected HPR is what we called “expected
        return”, (E(r).
        There is a relationship between the expected
        return and the current prices of financial assets.

        The current price of an asset should not be too
        different from the expected cash flows discounted
        to their present value using the expected return.

 - CAPM describes a perfectly competitive financial
   market. On a perfectly competitive market, agents are
   price-takers. Recall the traditional model of
   competitive market.




      COMPETITIVE EQUILIBRIUM MODEL
         Supply Side               Demand Side
  Profit maximizing firms:       Utility maximizing
 each firm has its own cost consumers. Each consumer
function and determines the determines the quantity of
 quantity of the good to be the good to be demanded at
 supplied at the given unit     the given unit price
           price.

                                                             4
This leads to market supply This leads to market demand
(depends on the unit price)   (depends on the unit price)
                 Equilibrium condition:
            Market supply=Market demand



                    Equilibrium price

CAPM is only a demand-side model: its results arise from
the utility maximization problem of investors (investors are
consumers of assets) and a market equilibrium condition.

ASSUMPTIONS OF THE MODEL

  1- Each investor’s endowment is small compared to the
  market’s endowment (total endowment of all investors).
  Investors are price-takers. Investors differ in endowments
  and risk-aversion.

  2- One identical holding period for all investors. This
  implies myopic behavior. Myopic behavior is in general
  sub-optimal (example: Indelible tattoo ink). So, all
  investors have the same time-horizon.


  3- Traded assets (bonds, stock, risk-free, borrowing or
  lending arrangements) are the only assets considered.
  Non-traded assets (ex: human capital) are not considered.
  Borrowing and lending are unrestricted and occur at a


                                                            5
  risk-free rate. So, all investor have the same universe of
  securities.

  4-There are no transaction costs.


  5- All investors are rational mean-variance optimizers.
  So, they all use the same (Markowitz) portfolio
  optimization strategy.

  6- All investor hold the same opinion about the future
     (they have homogenous belief).         All investor
     have the same input list to feed into the Markowitz
     model. Same efficient frontier.

Questions at stake:
 - What portfolio of risky asset is each investor
    demanding?
 - How is each individual asset related to the portfolio of
    risky assets?

PREDICTIONS OF THE MODEL

1-All investors will choose to hold the market portfolio of
risky assets (M), which include all traded assets. Each asset
enters the market portfolio proportionally to its market
value.

2- M will be on the efficient frontier and the Capital
Allocation line (CAL), called here Capital Market Line
(CML). This frontier is the same for all investors. But the

                                                              6
investors differ in the amount they choose to invest in M
and the risk-free asset. WHY?


3- E(rM) – rf = (risk aversion of representative investor).σM2
Note: σM2 is the systematic risk of the universe of traded
assets.
4- E(ri) – rf = [Cov(ri, rM)/ σM2] [E(rM) – rf]
                = βi[E(rM) – rf].

The security market line is the graphic representation of
the expected return-beta relationship. The risk premium
E(rM) – rf becomes the slope.
  Exp. Return




                             M         Security
                                       market line

E(rM)


     r
     f
                                          Beta
                         1




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