Intermediate Investments F303 1

The General Use of Predictive Models

• Weather

• Sports

• Accuracy?

Intermediate Investments F303 2

Efficient Portfolios

• To find the Optimal risky Portfolio we have used:– Mean return

– Variance

– Standard Deviation

– Covariance

– Correlation

– The benefits of diversification

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Pricing Models for Individual Securities

• Defining terms– CAPM: a model that provides a precise prediction of

the relationship we should observe between the risk of an asset and its expected return

– Arbitrage: The exploitation of security mis-pricing to earn risk free economic profits

– Equilibrium Pricing: pricing situation under which there are no opportunities for Arbitrage

– Beta: The sensitivity of a security’s return to systematic risk

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CAPM and CAL, CML & SML

• Capital Allocation Line (CAL)

• Capital Market Line (CML)

• Security Market Line (SML)– CAPM expected return-beta relationship =

E(ra) = rf + Betaa [ E(rm) – rf]

– Purpose of CAPM

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Underlying Assumptions for CAPM (p. 233)

1. Investors cannot affect prices by their own individual trades

2. All investors have the same holding periods

3. All investments are publicly traded and investors can borrow or lend at the risk free rate

4. There are no taxes or transaction costs

5. All investors will select the optima portfolio (market portfolio)

6. All investors have the same expectations about the variables affecting securities

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What does this imply for a market in equilibrium?

1. All investors will choose to hold the market portfolio

2. The market portfolio will fall on the efficient frontier and be the optimal risky portfolio

3. The risk premium on M will be proportional to the variance of the market portfolio and the investors’ typical degree of risk aversion

E(rm) – rf = A*Varm

Note: The greater the value of A* the more risk averse the investor

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What does this imply for a market in equilibrium?

4. The risk premium on individual assets will be proportional to the risk premium on the market portfolio, M, and to the beta coefficient of the security on the market portfolio. So, the rate rate of return on a single asset is determined by the rate of return on the Market and the security’s beta.

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Beta

• Beta is the regression coefficient obtained from regressing a security’s return against the returns of the market portfolio

Beta = Cov (Ri , Rm) / Varm