Capital Asset Pricing Model - Finance - Lecture Slides, Slides of Finance

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Capital Asset Pricing Model

Lecture Agenda

1. Attainable Portfolio Combinations

2. New Efficient Frontier

3. Capital Asset Pricing Model

4. Market Risk

5. Alternative Pricing Models

Attainable Portfolios Efficient Frontier CAPM^ Market Risk Alternatives

Achievable Portfolio

Combinations

The Capital Asset Pricing Model

(CAPM)

Achievable Portfolios

The Two-Asset Case

• It is possible to construct a series of portfolios with different risk/return

characteristics just by varying the weights of the two assets in the portfolio.

• Assets A and B are assumed to have a correlation coefficient of -0.379 and

the following individual return/risk characteristics

Expected Return Standard Deviation

Asset A 8% 8.72%

Asset B 10% 22.69%

The following table shows the portfolio characteristics for 100 different weighting schemes for just these two securities:

Portfolio Combinations

Attainable Portfolio Combinations for a Two Asset Portfolio

0.00%

2.00%

4.00%

6.00%

8.00%

10.00%

12.00%

0.0% 5.0% 10.0% 15.0% 20.0% 25.0% Standard Deviation of Returns

Expected Return of the

Portfolio

Two Asset Efficient Frontier

• Figure 8 – 10 describes five different

portfolios (A,B,C,D and E in reference to

the attainable set of portfolio

combinations of this two asset portfolio.

(See Figure 8 -10 on the following slide)

Achievable Set of Portfolios

Getting to the ‘n’ Asset Case

• In a real world investment universe with all of the investment

alternatives (stocks, bonds, money market securities, hybrid

instruments, gold real estate, etc.) it is possible to construct many

different alternative portfolios out of risky securities.

• Each portfolio will have its own unique expected return and risk.

• Whenever you construct a portfolio, you can measure two

fundamental characteristics of the portfolio:

• Portfolio expected return ( ER (^) p )
• Portfolio risk ( σp )

The Achievable Set of Portfolios

• You could start by randomly assembling

ten risky portfolios.

• The results (in terms of ER p and σp

)might look like the graph on the

following page:

The Achievable Set of Portfolios

• You could continue randomly

assembling more portfolios.

• Thirty risky portfolios might look like the

graph on the following slide:

Achievable Portfolios

Thirty Combinations Naively Created

Portfolio Risk (σp)

30 Risky Portfolio Combinations

ERp

Achievable Portfolios

More Possible Combinations Created

Portfolio Risk (σp)

ERp

E

E is the minimum variance portfolio Achievable Set of Risky Portfolio Combinations

The highlighted portfolios are ‘efficient’ in that they offer the highest rate of return for a given level of risk. Rationale investors will choose only from this efficient set.

The Efficient Frontier

The Capital Asset Pricing Model

(CAPM)

The New Efficient Frontier

Efficient Portfolios

Figure 9 – 1 illustrates three achievable portfolio combinations that are ‘efficient’ (no other achievable portfolio that offers the same risk, offers a higher return.)

Risk

9 - 1 FIGURE

Efficient Frontier

ER

MVP

A

B

Underlying Assumption

Investors are Rational and Risk-Averse

• We assume investors are risk-averse wealth maximizers.
• This means they will not willingly undertake fair gamble.
  • A risk-averse investor prefers the risk-free situation.
  • The corollary of this is that the investor needs a risk premium to be induced into a risky situation.
  • Evidence of this is the willingness of investors to pay insurance premiums to get out of risky situations.
• The implication of this, is that investors will only choose portfolios that are

members of the efficient set (frontier).