風險與報酬

RETURNS AND RISK

• Return is the change in value of a financial asset or investment over a given period of time.– Expected/required return: ex ante

– Actual return: ex post

• Risk is the chance of loss;the variability of returns; the uncertainty associated with given asset.

• Dollar return

Total dollar return = dividend income + capital gain (loss)

ex. = 1.85 + (40-20)• Percentage return

dividend yield = D1/P0

capital gain yield = (P1-P0)/P0

ex. Percentage return = 1.85/20 + (40-20)/20 = 9.25% +

100% = 109.25%

The historical record

Investment average returncommon stock 12.30%long-term corporate bonds 5.90%long-term government bonds 5.40%U.S. Treasury bills 3.70%Inflation 3.20%

Normal return and abnormal returnIn an efficient capital market, current market price fully reflect available information, investors can only earn normal return.

Rate of Return

r= real interest rate (riskless rate)

p= purchase-power-risk premium

b= business-risk premium

f = financial-risk premium

m = market-risk premium

= errors • Risk premium: The excess return required from an inve

stment in a risky asset over a risk free investment.

mfbpri

• Systematic risk: m, r, and p. Systematic risk is a risk that influences a large number of assets.

• Unsystematic risk: b and f. Unsystematic risk is a risk that affects a unique asset.

Risk preference

Risk-lover (taking) is an attitude that a decrease return is acceptable for increases in risk.Risk-indifferent is an attitude that no change in expected return is necessary due to change in risk.Risk-averse is an attitude that increased return is required for increases in risk. Most investors are risk averse and require higher returns for increasing risks.

East West Mean Std. Dev.

0 1 0.103 0.088606

0.1 0.9 0.10414 0.069759

0.2 0.8 0.10528 0.06614

0.3 0.7 0.10642 0.079847

0.4 0.6 0.10756 0.104256

0.5 0.5 0.1087 0.133626

0.6 0.4 0.10984 0.165334

0.7 0.3 0.11098 0.198261

0.8 0.2 0.11212 0.231889

0.9 0.1 0.11326 0.265952

1 0 0.1144 0.300302

Portfolio Frontier

0.1

0.105

0.11

0.115

0 0.1 0.2 0.3 0.4

Standard Deviation

Expe

cted

Ret

urn

The effect of diversification

Numbers of assets in portfolio Average deviation of portfolio returns (in %)

1 49.24

2 37.36

4 29.69

6 26.64

8 24.98

10 23.93

20 21.68

30 20.87

40 20.46

50 20.2

100 19.69

200 19.42

300 19.34

400 19.29

500 19.27

1000 19.21

Average Portfolio Standard Deviation

diversifiable risk

19.2

nondiversifiable risk

Number of assets

Diversification

• Diversification is a method of reducing the risk of a portfolio by combining assets that have negative (or low positive) correlation.

• Combinations of assets that are:

– Negative correlated can reduce portfolio risk below the risk of any of the portfolio’s assets held in isolation.

– Uncorrelated can reduce portfolio risk, but not as effectively as with negative correlated assets.

– Positively correlated can not reduce portfolio risk below the risk of the least risky asset when held in isolation.

資本資產定價模式 Capital Asset Pricing Model

• The CAPM is a centerpiece of modern finance that gives predictions about the relationship between risk & expected return

• Based on original work on portfolio theory of Harry Markowitz by William Sharpe & John Lintner in 1965-66.

• Begins with simplistic assumptions for hypothetical world of investors and builds into reasonable & comprehensive model

Investors hold Market Portfolio

0.00

0.10

0.20

0.30

0.40

0.50

Standard Deviation

Exp

ecte

d R

etu

rn

M=“Market”

Equilibrium Expected Returns• In equilibrium, all assets (and all portfolios) should have the same reward to risk tradeoff.

• However, this implies that this should hold for the market portfolio as well.

• We have a simple expression for expected returns on any asset or portfolio.

m

fm

i

fi rRErRE

)()(

])([)( fmifi rrErrE

j

fj

i

fi rRErRE

)()(

The Efficient Market Hypothesis• The weak form of efficiency suggests that the current p

rice of a stock reflects its own past prices. In other words, studying past prices in an attempt to identify mispriced securities is futile if the market is weak form efficient.

• If the market is semistrong form efficient, then all public information is reflected in the stock price.

• If the market is strong form efficient, then all information of every kind is reflected in stock prices. In such a market, there is no such thing as inside information.

Inside Trading: 內線交易•內線交易是指那些擁有未公開資訊的內線人士，如公司的經理人 , 董監事 , 大股東 , 以及參與股票發行或承銷業務的人員 , 利用內線資訊來賺取不正當的利益。