1 Class Risk and Return Historical returns in the USA. Sigma. CV. Security

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1. 1 Class Risk and Return Historical returns in the USA. Sigma. CV. Security
2. Value of $1 invested in 1926
3. Risk and Return Risk -
4. Total Risk vs. Returns
5. Risk and Return P1 – P0 (+ ∑D)
6. Measuring Returns Historical returns: X1=10%, X2= (-5%), X3 =
7. Общий риск: стандартное отклонение
8. 2. Risk and return relationship Общий риск: стандартное отклонение
9. Return (actual), mean return, %CAPM-return (model return),
10. Measuring Risk: ERR Expected return: The return for
11. Variance: A measure of the dispersion of
12. Standard deviation: Square root of Variance. A
13. Measuring Risk: ERR Example: Calculating ERR, Variance, and Standard deviation
14. Measuring Risk: Historical RR Variance: The variance of
15. Measuring Risk: Historical RR Example: Calculating Mean, Variance, and Standard deviation
16. Risk and Return Relationship Coefficient of Variation (CV)
17. Risk and Return characteristics, World, 2009
18. 1234Return, %Sigma, %• 2 vs. 1; return
19. World Stock Indices, 2009
20. Stock Behavior: Beta and Alpha
21. SCL, Beta and Alpha
22. Beta Beta: A measure of systematic risk, of a
23. Total Risk: Components Systematic Risk - The risk
24. Total Risk: Components
25. Безрисковая доходность
26. Безрисковая доходность
27. Correlations of indices with S&P500 2010 2009North America:
28. Markets: Correlations in 2010
29. Security Market Line (SML) Return,%.rfRisk-free rate
30. rm = 13%, rf = 3%x = 1.20,
31. AlphaAlpha (abnormal return; excess return) = ract
32. SML, 2009, DJIA
33. Beta, 2009, DJIA
34. Markowitz’ Efficient Frontier
35. Coefficient of Determination
36. Stock BEHAVIOUR – from the SCL equationFind and describe:BetaAlpha Correlation coef. Sigma Mean returnCV
37. ClassRisk and ReturnAdditional materials (Advanced level)
38. Capital Allocation Line (CAL) A line created in
39. Portfolio risk and return: Return The rate of
40. Portfolio risk and return: Covariance Covariance is a
41. Portfolio risk and return: Covariance Covariance between Stock
42. Portfolio risk and return: Correlation Correlation is a
43. Portfolio risk and return: Sigma When two risky
44. Portfolio risk and return: Sigma Rule: When a
45. DIVERSIFICATION Coca ColaReebokStandard Deviation35% in Reebok, 65% in
46. Efficient FrontierExample
47. Efficient FrontierExample
48. Efficient FrontierExample
49. Efficient FrontierExample
50. Diversification of Unsystematic Risk
51. Diversification
52. Diversification
53. ОНД, %Стандартное отклонение, %Stock BStock ACorr = +1Corr = -1Corr = 0Portfolio diversification: 2 stocks
54. Efficient Frontier Standard DeviationEach half egg shell represents
55. Efficient Frontier ABNABABNGoal is to move up and leftSigmaReturn, %
56. Efficient Frontier Return, %Low RiskHigh ReturnHigh RiskHigh ReturnLow
57. Efficient (Markowitz) frontier A line created from the risk-reward graph, comprised of optimal portfolios.
58. Political Risks: Mechel Story “В четверг (25 июля)
59. Political Risks
60. Political Risks: MICEX Index, 2008 Inauguration of presidentMedvedevPutin
61. Portfolio risk and return: Beta Systematic Risk -
62. Portfolio risk and return: Beta The Beta of
63. Portfolio diversification
64. Скачать презентанцию

Value of $1 invested in 1926

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1 Class Risk and Return Historical returns in the USA. Sigma. CV. Security

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Слайд 1Class
Risk and Return
Historical returns in the USA.
Sigma. CV. Security Characteristic

Line (SCL). Beta. Security Market Line (SML). CAPM formula.

Study materials:
KR: Ch. 11, 12.
RWJ: Ch. 9, 10
BM: Ch. 7, 8

ClassRisk and ReturnHistorical returns in the USA.Sigma. CV. Security Characteristic Line (SCL). Beta. Security Market Line (SML).

Слайд 2Value of $1 invested in 1926

Слайд 3Risk and Return
Risk - The chance that an investment's actual

return will be different than expected. This includes the possibility of losing some

or all of the original investment. Total risk measured by the standard deviation of the historical returns.

A fundamental idea in finance is the relationship between risk and return. The greater the amount of risk that an investor is willing to take on, the greater the potential return. The reason for this is that investors need to be compensated for taking on additional risk. E.g., a U.S. Treasury bonds (bills) is considered
to be the safest investment and, when compared
to a corporate bond, provides a lower return.
The reason is that a corporation is much more
likely to go bankrupt than the U.S. government.

Risk and Return Risk - The chance that an investment's actual return will be different than expected. This

Слайд 4Total Risk vs. Returns

Слайд 5Risk and Return
P1 – P0 (+ ∑D)
HPR, % =

P0

Return, % = P1 / P0 - 1

CV

= sigma / mean return

Risk and Return P1 – P0 (+ ∑D) HPR, % = P0 Return, % = P1 / P0

Слайд 6
Measuring Returns

Historical returns:
X1=10%, X2= (-5%), X3 = 20%

Arithmetic Average:
[0.10

+ (-0.05) + 0.20] / 3 = 8.33% - usual

way

Geometric Average:
[(1.10)*(0.95)*(1.20)]1/3 - 1 = 7.84% - more correct

Measuring Returns Historical returns: X1=10%, X2= (-5%), X3 = 20%Arithmetic Average: [0.10 + (-0.05) + 0.20] / 3 =

Слайд 7Общий риск: стандартное отклонение

Слайд 82. Risk and return relationship
Общий риск: стандартное отклонение

Слайд 9Return (actual), mean return, %
CAPM-return (model return), %
Risk-free return, %
Excess

return, %
Abnormal return, %
Total risk (sigma), %
Systematic risk (beta), t
Unsystematic

risk, %
Coefficient of correlation, t
Coefficient of determination, t
Coefficient of variation (CV), t
Sharpe’s measure (S), t
Treynor’s measure (T), t
Appraisal ratio (AR), t
Z-beta, t
Z-alpha, %
Degree of volatility, t

Risk and Return measures

Return (actual), mean return, %CAPM-return (model return), %Risk-free return, %Excess return, %Abnormal return, % Total risk (sigma), % Systematic

Слайд 10
Measuring Risk: ERR

Expected return:
The return for an asset is

the probability weighted average return in all scenarios.

Measuring Risk: ERR Expected return: The return for an asset is the probability weighted average return in all

Слайд 11 Variance: A measure of the dispersion of a set of

data points around their mean value.
Variance measures the variability

(volatility) from an average. Volatility is a measure of risk, so this statistic can help determine the risk an investor might take on when purchasing a specific security.

The variance of an asset’s expected return is the expected value of the squared deviations from the expected returns.

Measuring Risk: ERR

Variance: A measure of the dispersion of a set of data points around their mean value. Variance

Слайд 12

Standard deviation:
Square root of Variance. A measure of the

dispersion of a set of data from its mean. The

more spread apart the data, the higher the deviation.

In finance, it is a measure of total risk of a financial asset.

Measuring Risk: ERR

Standard deviation: Square root of Variance. A measure of the dispersion of a set of data from

Слайд 13
Measuring Risk: ERR

Example: Calculating ERR, Variance, and Standard deviation

Слайд 14
Measuring Risk: Historical RR

Variance:
The variance of an asset’s historical

returns is the sum of the squared deviations divided by

(n-1).

Standard deviation:
Square root of variance.

Measuring Risk: Historical RR Variance: The variance of an asset’s historical returns is the sum of the squared

Слайд 15
Measuring Risk: Historical RR

Example: Calculating Mean, Variance, and

Standard deviation

Слайд 16
Risk and Return Relationship

Coefficient of Variation (CV) =
Standard deviation

/ Expected (historical) rate of return.
Measures risk-return relationship, i.e.,

sigma per 1 %
of return.
better choice

Risk and Return Relationship Coefficient of Variation (CV) = Standard deviation / Expected (historical) rate of return. Measures

Слайд 17Risk and Return characteristics, World, 2009

Слайд 181
2
3
4
Return, %
Sigma, %
• 2 vs. 1; return is higher

• 2

vs. 3; risk is lower

• 4 vs. 3; return is

higher

Types of investors: Risk-averse, (Risk-neutral), Risk-seeker.

A rational investor would choose the securities that locate in the left upper corner. CV MIN.

R&RR and types of investors

1234Return, %Sigma, %• 2 vs. 1; return is higher• 2 vs. 3; risk is lower• 4 vs.

Слайд 19World Stock Indices, 2009

Слайд 20Stock Behavior: Beta and Alpha

Слайд 21SCL, Beta and Alpha

Слайд 22
Beta
Beta: A measure of systematic risk, of a security (or a

portfolio) in comparison to the market (market index, proxy). Measure

of elasticity.

Equals the variable coefficient “b” in the linear regression equation:
Y = a + b*X + ε
Graphically, Beta = Y / X

A beta of greater than 1 indicates that the security's price is more volatile than the market, more risky. “Aggressive” security.
The Security characteristic line is more steep.
A beta of less than 1 indicates that the security's price is less volatile than the market, less risky. “Defensive” security.

Beta Beta: A measure of systematic risk, of a security (or a portfolio) in comparison to the market (market

Слайд 23
Total Risk: Components

Systematic Risk - The risk inherent to the

entire market, or market
segment. Also known as “non-diversifiable risk"

or "market risk."
E.g., interest rates, recession and wars represent sources of systematic risk because they affect the entire market and cannot be avoided through diversification. Affects a broad range of securities. Even a portfolio of well-diversified assets cannot escape all risk.
Measured with BETA.

Unsystematic Risk – Company-specific risk that is inherent in each
investment. Can be reduced through appropriate diversification (=strategy
designed to reduce risk by spreading the portfolio across many
investments.
Also known as "specific risk", "diversifiable risk“, or "residual risk".
E.g., a sudden strike by the employees of a company is considered
to be unsystematic risk.

Total Risk: Components Systematic Risk - The risk inherent to the entire market, or market segment. Also known

Слайд 24Total Risk: Components

Слайд 25Безрисковая доходность

Слайд 26Безрисковая доходность

Слайд 27Correlations of indices with S&P500

2010 2009
North America: 0,80 – 0,95 0,88

– 0,99
South America: 0,70 – 0,76 0,83 – 0,88
Western Europe: 0,80 –

0,87 0,79 – 0,92
Australia and NZ: 0,76 – 0,80 0,47 – 0,65
Russia: 0,71 – 0,76 0,53 – 0,59
Asia: 0,45 – 0,77 0,27 – 0,76
Ukraine: 0,46 – 0,51 0,44 – 0,48

Correlations of indices with S&P500 2010 2009North America: 0,80 – 0,95 0,88 – 0,99South America: 0,70 – 0,76 0,83 – 0,88Western

Слайд 28
Markets: Correlations in 2010

Слайд 29
Security Market Line (SML)

Return,%
.
rf
Risk-free rate
Market Portfolio
Beta
1.0
SML
SML equation

= rf +  ( rm - rf ) =

CAPM

Security Market Line (SML) Return,%.rfRisk-free rate Market PortfolioBeta1.0SMLSML equation = rf +  ( rm -

Слайд 30rm = 13%, rf = 3%

x = 1.20, then:
E(rx) = 3%

+ 1.2*(13%-3%) = 15%

y = 0.80, then:
E(ry) = 3% +

0.8*(13%-3%) = 11%

Sample Calculations for SML

rm = 13%, rf = 3%x = 1.20, then: E(rx) = 3% + 1.2*(13%-3%) = 15%y = 0.80, then: E(ry)

Слайд 31Alpha
Alpha (abnormal return; excess return) = ract - rf
rp =

rf + p ( rm - rf ) (+/- alpha)

AlphaAlpha (abnormal return; excess return) = ract - rfrp = rf + p ( rm - rf

Слайд 32SML, 2009, DJIA

Слайд 33Beta, 2009, DJIA

Слайд 34Markowitz’ Efficient Frontier

Слайд 35Coefficient of Determination

Слайд 36Stock BEHAVIOUR – from the SCL equation
Find and describe:

Beta

Alpha

Correlation

coef.

Sigma

Mean return

CV

Слайд 37Class
Risk and Return
Additional materials (Advanced level)

Слайд 38Capital Allocation Line (CAL)

A line created in a graph of

all possible combinations of risky and risk-free assets.
The graph displays

to investors the return they can make by taking on a certain
level of risk. Also known as the "reward-to-variability ratio".

E(r)

E(rp) = 15%

rf = 7%

p = 22%

E(rp) -

rf = 8%



CAL

Capital Allocation Line (CAL) A line created in a graph of all possible combinations of risky and risk-free

Слайд 39
Portfolio risk and return: Return

The rate of return on a

portfolio is a weighted average of the rates of return

of each asset comprising the portfolio, with the portfolio proportions ($) as weights.

rp = w1r1 + w2r2

w1 = Proportion of funds in Security 1, %
w2 = Proportion of funds in Security 2, %
r1 = Expected return on Security 1, %
r2 = Expected return on Security 2, %

Portfolio risk and return: Return The rate of return on a portfolio is a weighted average of the

Слайд 40
Portfolio risk and return: Covariance

Covariance is a measure of the

linear association between the 2 variables. A measure of the

degree to which returns on two risky assets move
in tandem. A positive covariance means that asset returns
move together. A negative covariance means that returns move inversely.

Covariance between Stock 1 and Stock 2 =

OR:

Portfolio risk and return: Covariance Covariance is a measure of the linear association between the 2 variables. A

Слайд 41
Portfolio risk and return: Covariance

Covariance between Stock 1 and Stock

2 =
= Cov 1,2 = ρ1,2 σ 1 σ

Portfolio risk and return: Covariance Covariance between Stock 1 and Stock 2 = = Cov 1,2 = ρ1,2

Слайд 42
Portfolio risk and return: Correlation

Correlation is a measure of the

linear association between
the 2 variables. In the world of

finance, a statistical measure of
how two securities move in relation to each other.

ρ 1,2 = Cov 1,2 / σ 1 σ 2

Correlation coefficient is ALWAYS [-1; 1].

Perfect positive correlation (a correlation coefficient of +1) implies that as one security moves, either up or down, the other security will move in lockstep, in the same direction. Alternatively, perfect negative correlation means that if one security moves in either direction the security that is perfectly negatively correlated will move by an equal amount in the opposite direction. If the correlation is 0, the movements of the securities are said to have no correlation; they are completely random.

Portfolio risk and return: Correlation Correlation is a measure of the linear association between the 2 variables. In

Слайд 43
Portfolio risk and return: Sigma

When two risky assets with variances

 12 and  22, respectively, are combined into a

portfolio with portfolio weights w1 and w2, respectively, the portfolio variance is given by:

p2 = w1212 + w2222 + 2w1w2 Cov(r1r2) =
= w1212 + w2222 + 2w1w2 ρ 1 2

Hence, the portfolio’s standard deviation - p - is the square root of the above formula.

Portfolio risk and return: Sigma When two risky assets with variances  12 and  22, respectively, are

Слайд 44
Portfolio risk and return: Sigma

Rule: When a risky asset is

combined with a risk-free asset, the portfolio standard deviation equals

the risky asset’s standard deviation multiplied by the portfolio proportion invested in the risky asset.

Portfolio risk and return: Sigma Rule: When a risky asset is combined with a risk-free asset, the portfolio

Слайд 45
DIVERSIFICATION

Coca Cola
Reebok
Standard Deviation
35% in Reebok, 65% in Coca-Cola

Expected Returns and Standard Deviations vary given different weighted combinations

of the stocks

Expected Return, %

See: file “port.xls”

Слайд 46Efficient Frontier
Example

Correlation Coefficient = 0.4
Stocks s % of Portfolio Avg

Return
ABC Corp 28 60% 15%
Big Corp 42 40% 21%

Standard Deviation = weighted avg = 33.6
Standard Deviation = Portfolio = 28.1
Return = weighted avg = Portfolio = 17.4%

Efficient FrontierExample Correlation Coefficient =

Слайд 47Efficient Frontier
Example

Correlation Coefficient = 0.4
Stocks s % of Portfolio Avg

Return
ABC Corp 28 60% 15%
Big Corp 42 40% 21%

Standard Deviation = weighted avg = 33.6
Standard Deviation = Portfolio = 28.1
Return = weighted avg = Portfolio = 17.4%

Let’s Add stock New Corp to the portfolio

Слайд 48Efficient Frontier
Example

Correlation Coefficient = 0.3
Stocks s % of Portfolio Avg

Return
Portfolio 28.1 50% 17.4%
New Corp 30 50% 19%

NEW Standard Deviation = weighted avg = 31.80
NEW Standard Deviation = Portfolio = 23.43
NEW Return = weighted avg = Portfolio = 18.20%

Слайд 49Efficient Frontier
Example

Correlation Coefficient = 0.3
Stocks s % of Portfolio Avg

Return
Portfolio 28.1 50% 17.4%
New Corp 30 50% 19%

NEW Standard Deviation = weighted avg = 31.80
NEW Standard Deviation = Portfolio = 23.43
NEW Return = weighted avg = Portfolio = 18.20%

NOTE: Higher return & Lower risk
How did we do that? DIVERSIFICATION

Слайд 50
Diversification of Unsystematic Risk

Слайд 51Diversification

Слайд 52Diversification

Слайд 53ОНД, %
Стандартное отклонение, %
Stock B
Stock A
Corr = +1
Corr = -1
Corr

= 0
Portfolio diversification: 2 stocks

Слайд 54
Efficient Frontier

Standard Deviation
Each half egg shell represents the possible weighted

combinations for two stocks.
The composite of all stock sets constitutes

the efficient frontier

Expected Return, %

Efficient Frontier Standard DeviationEach half egg shell represents the possible weighted combinations for two stocks.The composite of all

Слайд 55
Efficient Frontier

A
B
N
AB
ABN
Goal is to move up and left
Sigma
Return, %

Слайд 56
Efficient Frontier

Return, %
Low Risk
High Return
High Risk
High Return
Low Risk
Low Return
High Risk
Low

Return
Sigma
Goal is to move up and left

Слайд 57
Efficient (Markowitz) frontier

A line created from the risk-reward graph, comprised

of optimal portfolios.

Слайд 58
Political Risks: Mechel Story

“В четверг (25 июля) премьер-министр Владимир Путин

встретился в Нижнем Новгороде с представителями крупнейших российских металлургических

и угольных компаний и высказался о ситуации на российском рынке стали.
Премьер-министр неожиданно сделал ряд жестких заявлений в отношении Мечела (ОАО «ЧМЗ»). По сути, он обвинил компанию в нерыночном поведении и предположил, что прокуратуре следуетобратить внимание на торговую деятельность компании.
Этих заявлений оказалось достаточно, чтобы обрушить котировки Мечела – с четверга они упали на 37,6%, заставив инвесторов гадать о будущем компании – ведущего производителя коксующегося угля в России.”
«Тройка-Диалог», 25 июля 2008 г. (www.troika.ru)

Political Risks: Mechel Story “В четверг (25 июля) премьер-министр Владимир Путин встретился в Нижнем Новгороде с представителями

Слайд 59
Political Risks

Слайд 60
Political Risks: MICEX Index, 2008

Inauguration of president
Medvedev
Putin accuses
“Mechel” of

fishy business

Russian
intrusion into
Georgia
Putin’s speech in Sochi,
VII Economics Forum
Medvedev:

to establish a missile complex in Kaliningrad

Political Risks: MICEX Index, 2008 Inauguration of presidentMedvedevPutin accuses “Mechel” of fishy businessRussianintrusion intoGeorgiaPutin’s speech in Sochi, VII

Слайд 61
Portfolio risk and return: Beta

Systematic Risk - The risk inherent

to the entire market, or market
segment. Also known as

"un-diversifiable risk" or "market risk."

E.g., interest rates, recession and wars represent sources of systematic
risk because they affect the entire market and cannot be avoided through
diversification. Affects a broad range of securities. Even a portfolio of well-
diversified assets cannot escape all risk.

Measured with BETA.

Still, one can diversify the systematic risk – in the sense that
one can choose securities with different betas (defensive vs. aggressive stocks) and combine them.

Portfolio risk and return: Beta Systematic Risk - The risk inherent to the entire market, or market segment.

Слайд 62
Portfolio risk and return: Beta

The Beta of a portfolio is

the weighted average of the rates of return of each

asset comprising the portfolio, with the portfolio proportions ($) as weights.

bp = w1 b1 + w2 b2

w1 = Proportion of funds in Security 1, %
w2 = Proportion of funds in Security 2, %
b1 = Beta of Security 1
b2 = Beta of Security 2

Portfolio risk and return: Beta The Beta of a portfolio is the weighted average of the rates of

Слайд 63Portfolio diversification

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1 Class Risk and Return Historical returns in the USA. Sigma. CV. Security

Содержание

Слайды и текст этой презентации

Слайд 1ClassRisk and ReturnHistorical returns in the USA.Sigma. CV. Security Characteristic

Line (SCL). Beta. Security Market Line (SML). CAPM formula.

Слайд 2Value of $1 invested in 1926

Слайд 3Risk and Return Risk - The chance that an investment's actual

return will be different than expected. This includes the possibility of losing some

Слайд 4Total Risk vs. Returns

Слайд 5Risk and Return P1 – P0 (+ ∑D) HPR, % =

P0 Return, % = P1 / P0 - 1 CV

Слайд 6Measuring Returns Historical returns: X1=10%, X2= (-5%), X3 = 20%Arithmetic Average: [0.10

+ (-0.05) + 0.20] / 3 = 8.33% - usual

Слайд 7Общий риск: стандартное отклонение

Слайд 82. Risk and return relationship Общий риск: стандартное отклонение

Слайд 9Return (actual), mean return, %CAPM-return (model return), %Risk-free return, %Excess

return, %Abnormal return, % Total risk (sigma), % Systematic risk (beta), t Unsystematic

Слайд 10Measuring Risk: ERR Expected return: The return for an asset is

the probability weighted average return in all scenarios.

Слайд 11 Variance: A measure of the dispersion of a set of

data points around their mean value. Variance measures the variability

Слайд 12 Standard deviation: Square root of Variance. A measure of the

dispersion of a set of data from its mean. The

Слайд 13Measuring Risk: ERR Example: Calculating ERR, Variance, and Standard deviation

Слайд 14Measuring Risk: Historical RR Variance: The variance of an asset’s historical

returns is the sum of the squared deviations divided by

Слайд 15Measuring Risk: Historical RR Example: Calculating Mean, Variance, and

Standard deviation

Слайд 16Risk and Return Relationship Coefficient of Variation (CV) = Standard deviation

/ Expected (historical) rate of return. Measures risk-return relationship, i.e.,

Слайд 17Risk and Return characteristics, World, 2009

Слайд 181234Return, %Sigma, %• 2 vs. 1; return is higher• 2

vs. 3; risk is lower• 4 vs. 3; return is

Слайд 19World Stock Indices, 2009

Слайд 20Stock Behavior: Beta and Alpha

Слайд 21SCL, Beta and Alpha

Слайд 22Beta Beta: A measure of systematic risk, of a security (or a

portfolio) in comparison to the market (market index, proxy). Measure

Слайд 23Total Risk: Components Systematic Risk - The risk inherent to the

entire market, or market segment. Also known as “non-diversifiable risk"

Слайд 24Total Risk: Components

Слайд 25Безрисковая доходность

Слайд 26Безрисковая доходность

Слайд 27Correlations of indices with S&P500 2010 2009North America: 0,80 – 0,95 0,88

– 0,99South America: 0,70 – 0,76 0,83 – 0,88Western Europe: 0,80 –

Слайд 28Markets: Correlations in 2010

Слайд 29Security Market Line (SML) Return,%.rfRisk-free rate Market PortfolioBeta1.0SMLSML equation

= rf +  ( rm - rf ) =

Слайд 30rm = 13%, rf = 3%x = 1.20, then: E(rx) = 3%

+ 1.2*(13%-3%) = 15%y = 0.80, then: E(ry) = 3% +

Слайд 31AlphaAlpha (abnormal return; excess return) = ract - rfrp =

rf + p ( rm - rf ) (+/- alpha)

Слайд 32SML, 2009, DJIA

Слайд 33Beta, 2009, DJIA

Слайд 34Markowitz’ Efficient Frontier

Слайд 35Coefficient of Determination

Слайд 36Stock BEHAVIOUR – from the SCL equationFind and describe:BetaAlpha Correlation

coef. Sigma Mean returnCV

Слайд 37ClassRisk and ReturnAdditional materials (Advanced level)

Слайд 38Capital Allocation Line (CAL) A line created in a graph of

all possible combinations of risky and risk-free assets. The graph displays

Слайд 39Portfolio risk and return: Return The rate of return on a

portfolio is a weighted average of the rates of return

Слайд 40Portfolio risk and return: Covariance Covariance is a measure of the

linear association between the 2 variables. A measure of the

Слайд 41Portfolio risk and return: Covariance Covariance between Stock 1 and Stock

2 = = Cov 1,2 = ρ1,2 σ 1 σ

Слайд 42Portfolio risk and return: Correlation Correlation is a measure of the

linear association between the 2 variables. In the world of

Слайд 43Portfolio risk and return: Sigma When two risky assets with variances

 12 and  22, respectively, are combined into a

Слайд 44Portfolio risk and return: Sigma Rule: When a risky asset is

combined with a risk-free asset, the portfolio standard deviation equals

Слайд 45DIVERSIFICATION Coca ColaReebokStandard Deviation35% in Reebok, 65% in Coca-Cola

Expected Returns and Standard Deviations vary given different weighted combinations

Слайд 46Efficient FrontierExample

Correlation Coefficient = 0.4Stocks s % of Portfolio Avg

Слайд 47Efficient FrontierExample

Correlation Coefficient = 0.4Stocks s % of Portfolio Avg

Слайд 1Class
Risk and Return
Historical returns in the USA.
Sigma. CV. Security Characteristic

Слайд 3Risk and Return
Risk - The chance that an investment's actual

Слайд 5Risk and Return
P1 – P0 (+ ∑D)
HPR, % =

P0

Return, % = P1 / P0 - 1

CV

Слайд 6
Measuring Returns

Historical returns:
X1=10%, X2= (-5%), X3 = 20%

Arithmetic Average:
[0.10

Слайд 82. Risk and return relationship
Общий риск: стандартное отклонение

Слайд 9Return (actual), mean return, %
CAPM-return (model return), %
Risk-free return, %
Excess

return, %
Abnormal return, %
Total risk (sigma), %
Systematic risk (beta), t
Unsystematic

Слайд 10
Measuring Risk: ERR

Expected return:
The return for an asset is

data points around their mean value.
Variance measures the variability

Слайд 12

Standard deviation:
Square root of Variance. A measure of the

Слайд 13
Measuring Risk: ERR

Example: Calculating ERR, Variance, and Standard deviation

Слайд 14
Measuring Risk: Historical RR

Variance:
The variance of an asset’s historical

Слайд 15
Measuring Risk: Historical RR

Example: Calculating Mean, Variance, and

Слайд 16
Risk and Return Relationship

Coefficient of Variation (CV) =
Standard deviation

/ Expected (historical) rate of return.
Measures risk-return relationship, i.e.,

Слайд 181
2
3
4
Return, %
Sigma, %
• 2 vs. 1; return is higher

• 2

vs. 3; risk is lower

• 4 vs. 3; return is

Слайд 22
Beta
Beta: A measure of systematic risk, of a security (or a

Слайд 23
Total Risk: Components

Systematic Risk - The risk inherent to the

entire market, or market
segment. Also known as “non-diversifiable risk"

Слайд 27Correlations of indices with S&P500

2010 2009
North America: 0,80 – 0,95 0,88

– 0,99
South America: 0,70 – 0,76 0,83 – 0,88
Western Europe: 0,80 –

Слайд 28
Markets: Correlations in 2010

Слайд 29
Security Market Line (SML)

Return,%
.
rf
Risk-free rate
Market Portfolio
Beta
1.0
SML
SML equation

Слайд 30rm = 13%, rf = 3%

x = 1.20, then:
E(rx) = 3%

+ 1.2*(13%-3%) = 15%

y = 0.80, then:
E(ry) = 3% +

Слайд 31Alpha
Alpha (abnormal return; excess return) = ract - rf
rp =

Слайд 36Stock BEHAVIOUR – from the SCL equation
Find and describe:

Beta

Alpha

Correlation

coef.

Sigma

Mean return

CV

Слайд 37Class
Risk and Return
Additional materials (Advanced level)

Слайд 38Capital Allocation Line (CAL)

A line created in a graph of

all possible combinations of risky and risk-free assets.
The graph displays

Слайд 39
Portfolio risk and return: Return

The rate of return on a

Слайд 40
Portfolio risk and return: Covariance

Covariance is a measure of the

Слайд 41
Portfolio risk and return: Covariance

Covariance between Stock 1 and Stock

2 =
= Cov 1,2 = ρ1,2 σ 1 σ

Слайд 42
Portfolio risk and return: Correlation

Correlation is a measure of the

linear association between
the 2 variables. In the world of

Слайд 43
Portfolio risk and return: Sigma

When two risky assets with variances

Слайд 44
Portfolio risk and return: Sigma

Rule: When a risky asset is

Слайд 45
DIVERSIFICATION

Coca Cola
Reebok
Standard Deviation
35% in Reebok, 65% in Coca-Cola

Слайд 46Efficient Frontier
Example

Correlation Coefficient = 0.4
Stocks s % of Portfolio Avg

Слайд 47Efficient Frontier
Example

Correlation Coefficient = 0.4
Stocks s % of Portfolio Avg

Слайд 48Efficient Frontier
Example

Correlation Coefficient = 0.3
Stocks s % of Portfolio Avg

Слайд 49Efficient Frontier
Example

Correlation Coefficient = 0.3
Stocks s % of Portfolio Avg

Слайд 50
Diversification of Unsystematic Risk

Слайд 53ОНД, %
Стандартное отклонение, %
Stock B
Stock A
Corr = +1
Corr = -1
Corr

= 0
Portfolio diversification: 2 stocks

Слайд 54
Efficient Frontier

Standard Deviation
Each half egg shell represents the possible weighted

combinations for two stocks.
The composite of all stock sets constitutes

Слайд 55
Efficient Frontier

A
B
N
AB
ABN
Goal is to move up and left
Sigma
Return, %

Слайд 56
Efficient Frontier

Return, %
Low Risk
High Return
High Risk
High Return
Low Risk
Low Return
High Risk
Low

Return
Sigma
Goal is to move up and left

Слайд 57
Efficient (Markowitz) frontier

A line created from the risk-reward graph, comprised

Слайд 58
Political Risks: Mechel Story

“В четверг (25 июля) премьер-министр Владимир Путин

Слайд 59
Political Risks

Слайд 60
Political Risks: MICEX Index, 2008

Inauguration of president
Medvedev
Putin accuses
“Mechel” of

fishy business

Russian
intrusion into
Georgia
Putin’s speech in Sochi,
VII Economics Forum
Medvedev:

Слайд 61
Portfolio risk and return: Beta

Systematic Risk - The risk inherent

to the entire market, or market
segment. Also known as

Слайд 62
Portfolio risk and return: Beta

The Beta of a portfolio is