Week 3 - Asset Valuation Theories

7/31/2019 Week 3 - Asset Valuation Theories

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Contents

Elementary asset pricing theory

History and theoretic development of

the portfolio theory Separation theorem

Capital Asset Pricing Model

Arbitrage pricing theory


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Elementary Pricing Theory

Based on fundamental valuation ofsecurities, the theory asserts that thevalue of an asset is determined as the

present value of the cash flowsexpected from it; ascertained using aspecific discount rate.

The discount rate is expected to reflectthe risk inherent in the generation of

cash flows by the asset.


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Portfolio Analysis andSelection

The best combination of expectedvalue of return and standard deviationdepends on the investors utility

function.

Risk averse investors associate riskwith divergence from the expectedvalue of return in an indifference curvesituation (upward).


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Portfolio choice

Investors want to hold the portfolio ofsecurities that place them on thehighest indifference curve, and will

therefore choose it from theopportunity set of available portfolios.

Markowitz mean-variance rule:Investors should choose a portfolio ofsecurities that lie on the efficient

frontier.


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Investment Opportunity Set


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Risk taking

Risk can be quantified as the sum ofthe variance of the returns over time.

It is possible to assign a utility score(utility value, utility function) to

any portfolio by subtracting itsvariance from its expected return toyield a number that would becommensurate with an investors

tolerance for risk, or a measure of their


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Utility Score and risk taking

Utility Score = Expected Return 0.005 2 x Risk AversionCoefficient

Risk aversion coefficient - a number

proportionate to the amount of riskaversion of the investor and is usuallyset to integer values less than 6,


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Illustration

The t-bill rate is 8%, expected returnon a portfolio is 16%, volatility is 25%.Determine if its viable for the investor

to invest in the portfolio. Assume riskaversion coefficient of 2.

Note: U = E(r) 0.05A 2


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Risk Aversion


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Presence of a Risk FreeAsset


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Separation Theorem

Individuals utility preferences areindependent or separate from theoptimal portfolio of risky assets.

The determination of an optimal

portfolio of risky assets is independentof the individuals risk preferences.Two phases of investment;


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Optimal Combination withthe Risk Free Asset


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Capital Asset Pricing Model

- Implies an equilibrium relationshipbetween risks and returns for eachsecurity.

- In a market equilibrium, a securitywill be expected to provide a returncommensurate with the unavoidablerisk (cannot be avoided withdiversification)


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CAPM Assumptions

1. Capital markets are efficient

2. Absence of transaction costs

3. Absence of taxes4. No investor is large enough to affect

prices in the market

5. Information symmetry


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The Characteristic Line Security Market Line


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SML

Compares the expected return for anindividual stock with the marketportfolio.

The greater the expected return for themarket, the greater the expectedexcess return for the stock. Threemeasures;


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Alpha

The intercept of the characteristic lineon the vertical axis. If the excessreturn of the market portfolio was zero,

the alpha would be the expectedexcess return for the stock.

The alpha for the individual stock = 0;in theory


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Beta

A measure of the systematic risk

The slope of the SML

Depicts the sensitivity of thesecuritys excess return to that of themarket portfolio

Historical betas should be adjustedmost popular method of adjustmentbeing the bayesian approach

The adjustment considers the debt


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CAPM

R = Rf + (Rm Rf)B

B = (rjm j m)/ 2m

(rjm j m) = The covariance of the

security with the market


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Distortions of the CAPM

1. Heterogeneous expectations of theinvestors

2. Transaction and information costs

3. Faulty use of the market index

4. Allowance for a tax effect

5. The presence of inflation

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Week 3 - Asset Valuation Theories