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Summary (hoorcolleges en literatuur) Corporate Finance And Behaviour (ECB2FIN)
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This document contains a summary of all lectures and literature for the course Corporate Finance and Behaviour.
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Corporate Finance and Behaviour - Week 1: CAPM, Risk and theCost of Capital (Chapter 8.2 – 8.3, 9)
Chapter 8: Portfolio Theory and Capital Asset Pricing Model (CAPM)
Portfolio selection
Investors try to increase the expected return on their portfolios and try to reduce the
variability of that return. → A portfolio that gives the highest expected return for a given
standard deviation, or the lowest standard deviation for a given expected return, is known as
an efficient portfolio.
→ The intention is to make an efficient portfolio where expected return is balanced against
the risk appreciation. Harry Markowitz created the Portfolio Theory to find the optimal
portfolio on the efficient frontier.
What is needed to work out which portfolios are efficient? → Expected return, standard
deviation, degree of correlation between each pair of stocks.
Investors, who:
… are restricted to holding common stocks → should choose efficient portfolios that
suit their attitudes to risk
… can borrow and lend at risk-free rate of interest → should choose the best
common stock portfolio regardless of their attitudes to risk → they can set the risk of
their overall portfolio by deciding what proportion of their money they are willing to
invest in stocks
→ the best efficient portfolio offers the highest ratio of forecasted risk premium to
portfolio standard deviation
Beta
The risk of a well-diversified portfolio depends on the market risk of the securities included
in the portfolio. If you want to know the contribution of an individual security to the risk of a
well-diversified portfolio, you need to measure its market risk. Beta ( β ): a measurement of
how sensitive a security is to market movements; A measure of market risk.
β=1: beta of the market portfolio → The market is the portfolio of all stocks, so the
‘average’ stock has a beta of 1.
β >1: amplify overall movements of the markets → A company having a higher beta than
+1.0 means higher risk compared to the market, which will be compensated by
higher returns. → higher discount rate
0< β <1: move in the same direction as the market, but not as far → less risk
The beta of stock iis: βi =σ ℑ/ σ 2m
1
,σ ℑ : the covariance between the stock returns and the market returns
2
σ m : variance of the returns on the market
CAPM
A stock’s marginal contribution to portfolio risk is measured by its sensitivity to changes in
the value of the portfolio. The marginal contribution of a stock to the risk of the market
portfolio is measured by beta.
→ That is the fundamental idea behind the capital asset pricing model (CAPM), which
concludes that each security’s expected risk premium should increase in proportion to its
beta:
Expected risk premium=beta× market risk premium
r −r f =β (r m −r f )
The CAPM model is the best-known model of risk and return. It is plausible and widely used
but far from perfect.
Drawbacks of the CAPM model → Actual returns are related to beta over the long run, but
the relationship is not as strong as the CAPM predicts, and other factors seem to explain
returns better. Stocks of small companies, and stocks with high book values relative to
market prices, appear to have risks not captured by the CAPM.
Alternative theory → The arbitrage pricing theory states that the expected risk premium on
a stock should depend on the stock’s exposure to several pervasive macroeconomic factors
that affect stock returns (see page 213):
Expected risk premium=b1 ( r factor 1−r f ) +b 2 ( r factor 2−r f ) +⋯
Here b’s represent the individuals security’s sensitivities to the factors, and ( r factor−r f ) is the
risk premium demanded by investors who are exposed to this factor.
Arbitrage pricing theory does not say what these factors are. It asks for economists to hunt
for unknown game with their statistical toolkits.
→ Fama and French have suggested three factors:
1. The return on the market portfolio less the risk-free rate of interest
2. The difference between the return on small- and large-firm stocks
3. The difference between the return on stocks with high book-to-market ratios and
stocks with low book-to-market ratios
In the Fama-French three-factor model, the expected return on each stock depends on its
exposure to these three factors.
Common ideas within risk and return models:
Investors require extra expected return for taking on risk
Investors appear to be concerned predominantly with the risk that they cannot
eliminate by diversification
Systematic an Unsystematic Risk
Systematic risk: Risk that influences a large number of assets also known as ‘market
risk’. It comes from other economywide perils that threaten all businesses. → cannot
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, be eliminated by diversification
An investor can expect a higher return from holding shares with more systematic risk.
Unsystematic risk: Risk that affects at most a small number of assets. Also referred to
as ‘unique’ or ‘asset/firm-specific’ or ‘idiosyncratic’ risk. As unsystematic risk is
unique to the asset, it is also unrelated to other asset’s unique risk. → can be
eliminated by diversification
A reduction of risk (lower SD) can be achieved whilst obtaining a higher return or obtaining a
higher return with the same original risk (=standard deviation).
Expected return is the weighted average of the returns of A and B:
R portfolio =ωa Ra +(1−ω a) Rb
The variance of the portfolio returns:
2 2 2 2
σ portfolio =ω a σ a +2 ωa ( 1−ω a ) ρ ab σ a σ b + ( 1−ω a ) 2σ b
The portfolio variance can also be described as:
σ 2portfolio =ω2a σ 2a +2 ωa ( 1−ω a ) Cov ( Ra , Rb ) + ( 1−ω a ) 2 σ 2b
Covariance between 2 shares is defined as:
Cov ( Ra , R b)=σ ab =ρab σ a σ b
Risk premium r −r f
Sharpe ratio = =
Standard deviation σ
The risk-free rate represents the interest an investor would expect from an absolutely risk-
free investment over a specified period of time. The so-called "real" risk-free rate can be
calculated by subtracting the current inflation rate from the yield of the Treasury bond
matching your investment duration
Introducing borrowing and Lending:
Investors can borrow or lend against the risk free rate r f belonging to the riskfree assets
allowing a higher return. As of S superior returns can be realized. Therefore there is no point
in investing BELOW S (e.g. T) => not smart...!
Chapter 9: Risk and cost of capital
→ How to apply the principles from chapter 8 when valuing capital investment projects
Cost of capital
(a) Suppose the project to be valued has the same market risk as the company’s existing
assets. → In this case, the project cash flows can be discounted at the company cost of
capital.
3
, The company cost of capital is the expected rate of return that investors require on a
portfolio of all of the company’s outstanding debt and equity securities. It is the
opportunity cost of capital for an investment in all of the firm’s assets, and therefore
the appropriate discount rate for the firm’s average-risk projects. It is usually
calculated as an after-tax weighted-average cost of capital (after-tax WACC).
Expected return :r =r f + β(r m−r f )
The pure time value of money: As measured by the risk-free rate, Rf, this is the
reward for merely waiting for your money, without taking any risk.
The reward for bearing systematic risk: As measured by the market risk premium,
E(RM) Rf, this component is the reward the market offers for bearing an average
amount of systematic risk in addition to waiting.
The amount of systematic risk: As measured by i, this is the amount of
systematic risk present in a particular asset or portfolio, relative to that in an
average asset.
E ( R A ) −Rf E ( R B )−R f
=
βA βB
In equilibrium, the reward-to-risk ratio must be the same for all the assets in the
market.
(b) The company cost of capital is not the correct discount rate if the new projects are more
or less risky than the firm’s existing business. → Each project should be evaluated at its own
opportunity cost of capital.
Firm value=PV ( AB )=PV ( A )+ PV ( B )=∑ of separate asset values
The market-value balance sheet is different from the book balance sheet. The cost of debt is
always less than the cost of equity.
On the market-value balance sheet:
overall firm value ( V )=debt ( D ) +equity ( E ) , so V =D+ E
Weighted-average cost of capital (WACC)
The after-tax weighted-average cost of capital (after-tax WACC) is the weighted average of
the after-tax cost of debt and the cost of equity. The weights are the relative market values
of debt and equity. The cost of debt is calculated after tax because interest is a tax-
deductible expense.
D E
Company cost of capital :r D × +r E × =r assets
V V
D/V = debt ratio
E/V = equity ratio
rD = cost of debt
rE = cost of equity
D E
After−tax WACC=(1−T c ) ×r D × + r E ×
V V
(1 - Tc) x rD = after-tax cost of debt
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