金融英语课件 Chapter 11Risk_return

Another example (continued)
60% to be Good, return is 0.5
• Return for XYZ,
40% to be bad, return is 0.3
• If E(Rp)= 0.25, then how will this manager allocate the funds?
Table 11.1
• Asset 1 and asset 3, which do you prefer?
Mean-variance analysis
• Standardize the risk per unit of expected return by dividing the standard deviation by the expected return. • Coefficient of variation离散系数 • Lower coefficient of variation is more preferred than higher Coefficient of variation
Two assumptions about investor preference
• Investors prefer more return to less return • They prefer less risk to more risk • Risk averse --- more returns compensate for more risk
• Assume a portfolio consists of asset 1 and asset 2, r1 = 0.12, r 2= 0.15, SD1 = 0.20, SD2 = 0.18, Covariance = 0.01 • W1=0.25, W2 =0.75 • What is E(Rp)? What is the variance of the portfolio?
Chapter 11
• The nature of risk --- mean-variance analysis • Diversification --- portfolio risk • The relationship between risks and return --Capital asset pricing model
Variance
Variance = ∑(R-E(R) )2 ×p Or Variance = E [(R-E(R) ]2 • Measures how much actual returns are likely to diverge from the expected return
Standard deviation SD
The security market line
• E(Ri) =Rf + βi [E(RM) – Rf ] What is a market portfolio?
a market portfolio
• A portfolio consisting of all assets available to investors, with each asset held -in proportion to its market value relative to the total market value of all assets. • biz.yahoo.com/glossary/bfglosm.html
Expected return and mean
• If the probabilities are equally likely • Then the expected return = arithmetic average • If the probability are not equally likely, using the expected return
Expand the portfolio to n assets
n
• E(Rp) =∑xi × E(Ri)
i=1
Expand the portfolio to n assets
• The lower the covariance, the lower the variance of the portfolio • Lower correlation, less risky is the portfolio
Table 11.1
R1 % R2% R3%
1/3 1/3 1/3
32 20 8
2 20 38
38 20 6
• What is the expected return of each asset? • Standard deviation? • Which asset is the riskiest?
Another example
• A portfolio manager has a portfolio with 2 stocks, company ABC and XYZ.
60% to be Good, return is 0.2
• Return for ABC,
40% to be bad, return is 0.1
CAPM-Capital asset pricing model
• Introduced Beta to measure the risk of expected return
CAPM
• A two variable model • Return is dependent upon the riskiness of the asset
An example of covariance
R1 % 1/3 1/3 1/3 32 20 8 R2% 5 20 38 21
E(R ) 20 Covariance -132
A portfolio
• Putting some assets together in the investment • Mix of same or different investment instruments
Score 0 1 2 3 4 5 Total Frequency 6 3 6 2 2 1 20 Relative Frequency 0.3 0.15 0.3 0.1 0.1 0.05 1
Mean
• Arithmetic average •μ • 32, 20, 8 -------mean = 20
Expected return
• Expected return = ∑(p ×R) • p is the probability that the return occurs
Probability distribution
• Using graphs to illustrate the probability of an event occurs
Correlation
Correlation coefficient(相关系数） covariance =
SD 1× SD2Байду номын сангаас
Lower the Correlation coefficient, greater the benefits of diversification
Covariance协方差
A bell curve • 68.24% of all the x-values are within 1 SD of the mean • 95.44% of all the x-values are within 2 SD of the mean • 99.74% of all the x-values are within 3 SD of the mean
• The arithmetic average of the products of deviations around each each variable’s arithmetic average
An example of covariance
R1 % 1/3 1/3 1/3 32 20 8 R2% 5 20 38
A diversified portfolio
• May consist of a variety of assets. • May also consist of stocks if the securities are issued by a variety of firms in different industries. • Reduces unsystematic risk
Variables
• Independent --- tossing dice • Dependent, eg, air pressure and temperature
Correlation相关
• Deal with 2 or more variables and quantify the relationship between them • An example: number of loans and the inflation rate
Some statistics preparation
• • • • • • Return Random variable Expected return Mean Variance Standard deviation
Risk
Definition of risk The probability of actual return differs from expected return
Probability
• The likelihood an event occurs • Tossing dice
Return
profit
• Return =
investment
=
Revenue – investment investment
Random variable
• A variable which can assume any value from a set of possible values. • Return is a random variable
Page 397
• The two assets are negatively correlated • The expected return of the combination is unchanged at 15%, but the SD falls to 0
Example of a portfolio
Characteristics of a portfolio
• Assume the total investment is X, asset 1 is X1, asset 2 is X2, asset 3 is X3……, asset n is Xn; weights are W1… Wn Then • (Rp ) = ∑Wi Ri • E(Rp) = ∑Wi E(Ri) • Variance = E∑(Rp -E(Rp) )2
• For asset 1, CV = 0.49 • For asset 3, CV = 0.614
• Hence, for the risk averse investors, asset 1 is more preferred
Portfolio risk
• Reducing risk by not putting all your eggs in one basket • Portfolio risk can be reduced for a given level of expected returns
• SD 2 = Variance • An estimate of the probable divergence of an actual return from an expected return • The degree of uncertainty
Normal distribution
Frequency
• How many times this number occurred in the sample
Relative Frequency
• The value of the frequency as a percentage of the total
Showing relative frequency