Corporate Finance Chap 11

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Môn: Corporate Finance (BA054IU)

Trường: Trường Đại học Quốc tế, Đại học Quốc gia Thành phố Hồ Chí Minh

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Profile Như Hoa
lOMoARcPSD|364906 32
CORPORATE FINANCE
Chapter 11: RETURN AND RISK: THE CAPITAL ASSET PRICING MODEL (CAPM)
I. Individual Securities:
- The characteristics of individual securities that are of interest are the:
● Expected Return
● Variance and Standard Deviation
● Covariance and Correlation (to another security or index)
II. Expected return, variance and covariance:
- Expected return: E(R) = ∑(p
i
x R
i
)
- Variance: V ar(δ )
2
= ∑p
i
(R
i
− E(R
i
))
2
- Standard deviation: SD(δ) = √δ
2
- Covariance: Covar(a, )b = ∑p
i
[R
iA
− E(R
A
)] [R
iB
− E(R
B
)]
- Correlation: p = covδa (x δa,bb) (− 1≤p≤1) III. The Return and Risk for
Portfolios:
E(R
P
) = ∑[W x
i
E(R
i
)] (W
i
: % investment in a certain asset)
- Standard Deviation of a portfolio of 2 assets:
δ = W WA B Aρ ,B
Where: p
i
: probability of state of economy (recession, normal,
boom)
R
i
: rate of return at each stage of economy (recession, normal, boom)
E(R) : expected return of an assets
- W
A
: % investment in asset A
- W
B
: % investment in asset B
-
ρA,B
: return correlation between
A
and B
√
δ
2
=
√
W
σ
W
2
A
2
A
+
2
B
2
B
+2
lOMoARcPSD|364906 32
- By creating a portfolio, risk is much reduced. To minimize risk, should choose
asssets with negative correlation.
IV. The Efficient Set for Two Assets:
- The same return → lower risk.
- The same risk → higher return.
V. The Efficient Set for Many Securities:
- The return on any security consists of two
parts. ● First, the expected returns
● Second, the unexpected or risky returns
- A way to write the return on a stock in the coming month is:
R = R + U
Where
R: the expected part of the return
U : the unexpected part of the return
- Any announcement can be broken down into two parts, the anticipated (or
expected) part and the surprise (or innovation):
Announcement = Expected part + Surprise.
- The expected part of any announcement is the part of the information the market
uses to form the expectation, R, of the return on the stock.
lOMoARcPSD|364906 32
- The surprise is the news that influences the unanticipated return on the stock, U.
VI. Diversification and Portfolio Risk:
- Portfolio Risk and Number of Stocks:
Where: n: number
of shares
- Total risk = systematic risk + unsystematic risk
- A systematic risk is any risk that affects a large number of assets, each to a
greater or
lesser degree.
- An unsystematic risk is a risk that specifically affects a single asset or small
group of assets.
- Unsystematic risk can be diversified away.
- Examples of systematic risk include uncertainty about general economic
conditions, such as GNP, interest rates or inflation.
- On the other hand, announcements specific to a single company are examples of
unsystematic risk.
- The standard deviation of returns is a measure of total risk.
- For well-diversified portfolios, unsystematic risk is very small.
lOMoARcPSD|364906 32
- Consequently, the total risk for a diversified portfolio is essentially equivalent to
the systematic risk.
- Risk free assets (T-bill): Rf; Standard deviation = 0
- Risky assets (Bond Fund /
Stock Fund)
VII. Riskless Borrowing and Lending:
- With a risk-free asset available and the efficient frontier identified, we choose the
capital allocation line with the steepest slope.
VIII. Market equilibrium:
- Beta measures the responsiveness of a security to movements in the market
portfolio (i.e., systematic risk).
βi = covδ ( (2 RRiM,R)M) = p δ(δ(RRMi))
IX. Relationship between Risk and Expected Return (CAPM):
- Expected Return on the Market: R
M
= R
f
+ Market risk premium (MRP)
-
Expected return on an individual security (CAPM):
R
i
= Rf + β
i
x (R
M
– Rf )
lOMoARcPSD|364906 32
R
M
- Rf is market risk premium.
- Assume β
i
= 0, then the expected return is
R F.
- Assume β
i
= 1, then R
i = R
M
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lOMoARcPSD|364 906 32 CORPORATE FINANCE
Chapter 11: RETURN AND RISK: THE CAPITAL ASSET PRICING MODEL (CAPM) I.
Individual Securities: -
The characteristics of individual securities that are of interest are the: ● Expected Return
● Variance and Standard Deviation
● Covariance and Correlation (to another security or index)
II. Expected return, variance and covariance: -
Expected return: E(R) = ∑(pi x Ri) -
Variance: V ar(δ )2 = ∑pi(Ri − E(Ri))2 -
Standard deviation: SD(δ) = √δ2 -
Covariance: Covar(a, )b = ∑pi[RiA − E(RA)] [RiB − E(RB)] -
Correlation: p = covδa (x δa,bb) (− 1≤p≤1) III. The Return and Risk for Portfolios:
E(RP ) = ∑[W xi E(Ri)] (W i : % investment in a certain asset) -
Standard Deviation of a portfolio of 2 assets: √ 2 2 2
δ 2 = √W σ W σ A A + 2 B B +2 δ = W WA B Aρ ,B
Where: pi : probability of state of economy (recession, normal, boom)
Ri : rate of return at each stage of economy (recession, normal, boom)
E(R) : expected return of an assets -
W A : % investment in asset A -
W B : % investment in asset B - ρA,B
: return correlation between A and B lOMoARcPSD|364 906 32 -
By creating a portfolio, risk is much reduced. To minimize risk, should choose
asssets with negative correlation. IV.
The Efficient Set for Two Assets:
- The same return → lower risk. - The same risk → higher return. V.
The Efficient Set for Many Securities: -
The return on any security consists of two
parts. ● First, the expected returns
● Second, the unexpected or risky returns -
A way to write the return on a stock in the coming month is:
R = R + U Where
R: the expected part of the return
U : the unexpected part of the return
- Any announcement can be broken down into two parts, the anticipated (or
expected) part and the surprise (or innovation):
Announcement = Expected part + Surprise.
- The expected part of any announcement is the part of the information the market
uses to form the expectation, R, of the return on the stock. lOMoARcPSD|364 906 32
- The surprise is the news that influences the unanticipated return on the stock, U. VI.
Diversification and Portfolio Risk:
- Portfolio Risk and Number of Stocks: Where: n: number of shares
- Total risk = systematic risk + unsystematic risk - A systematic risk
is any risk that affects a large number of assets, each to a greater or lesser degree.
- An unsystematic risk is a risk that specifically affects a single asset or small group of assets.
- Unsystematic risk can be diversified away.
- Examples of systematic risk include uncertainty about general economic
conditions, such as GNP, interest rates or inflation.
- On the other hand, announcements specific to a single company are examples of unsystematic risk.
- The standard deviation of returns is a measure of total risk.
- For well-diversified portfolios, unsystematic risk is very small. lOMoARcPSD|364 906 32
- Consequently, the total risk for a diversified portfolio is essentially equivalent to the systematic risk.
- Risk free assets (T-bill): Rf; Standard deviation = 0 - Risky assets (Bond Fund / Stock Fund) VII.
Riskless Borrowing and Lending:
- With a risk-free asset available and the efficient frontier identified, we choose the
capital allocation line with the steepest slope.
VIII. Market equilibrium:
- Beta measures the responsiveness of a security to movements in the market
portfolio (i.e., systematic risk).
βi = covδ ( (2 RRiM,R)M) = p δ(δ(RRMi)) IX.
Relationship between Risk and Expected Return (CAPM):
- Expected Return on the Market: RM = Rf + Market risk premium (MRP) -
Expected return on an individual security (CAPM):
Ri = Rf + βi x (RM – Rf ) lOMoARcPSD|364 906 32
RM - Rf is market risk premium.
- Assume β i = 0, then the expected return is R F. - Assume β i = 1, then R i = R M
Document Outline

  • CORPORATE FINANCE