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WHAT IS RISK?

“The Variability of Returns from those that are expected”

Total Risk = Systematic Risk + Unsystematic Risk

- Systematic Risk is the variability of return on stocks or portfolios associated with changes in return on the market as a whole. It is also called market or non-diversifiable risk.
- Unsystematic Riskis the variability of return on stocks or portfolios not explained by general market movements. It is avoidable through diversification. It is also called firm-specific or diversifiable.

Total Risk = Systematic Risk + Unsystematic Risk

UR = Factors involve lawsuit, strikes,

successful and unsuccessful marking

programs, The winning and losing of

major contracts.

STD DEV OF PORTFOLIO

Unsystematic risk

Total

Risk

Systematic risk

NUMBER OF SECURITIES IN THE PORTFOLIO

Stand-Alone Risk:

- The risk associated with a single investment when it is held by itself, or in isolation, not in combination with other assets.

Measuring Risk With The Help Of Standard Deviation

If only sample returns data over some past periods are available, than

Estimated

here denotes the past realized rate of return in period t, and Is the average annual return earned during the last n years.

Measuring Stand-Alone RiskThe Standard Deviation

Variance = =3,517.0

Standard Deviation = =

MCB=59.3%

Variance =

OGDC=3.6%

Coefficient of Variation

Another useful measure to evaluate risky investments is the coefficient of variation (CV).

Coefficient of variation = CV = =

WATEEN OGDC

CV = CV =

=3.95 =0.24

Diversification

- Definition - An investment strategy designed to reduce risk by spreading the funds invested across many securities.
- Since people hold diversified portfolios of securities, they are not very concerned about the risk and return of a single security. They are more concerned about the risk and return of their entire portfolio.

Portfolio Risk

- The risk associated with an investment when it is held in combination with other assets, not by itself.

Example: Portfolio Variance

- Assume the following Statistics for stock A and B.
- What is the expected return and variance of this two-security portfolio?

Example: Portfolio Variance (cont’d)

- Solution:
The expected return of this two security portfolio

= 0.018

Example: Portfolio Variance (cont’d)

- The variance of this two security portfolio is:

CORRELATION

- The Correlation Coefficient between the returns on two stocks can be calculated as follows:
Where:

- rA,B=the correlation coefficient between the returns on stocks A and B
- sA,B=the covariance between the returns on stocks A and B,
- sA=the standard deviation on stock A, and
- sB=the standard deviation on stock B

RETURN:

- The percentage change in value of the investment over a given period of time.

Expected Return

The rate of return expected to be realized from an investment; the mean value of the probability distribution of possible results.

Or

The return that an investors expects to earn on an asset, given its prices, growth potential.

Probability Distribution

- A listing of all possible outcomes, or events, with a Probability (chance of occurrence) assigned to each outcome.

Expected Return

Expected rate of return =

Here is the possible outcome, is the probability the outcome will occur, and n is the number of possible outcomes. Thus is a weighted average of the possible outcomes.

Expected Return

State of Probability Return

Economy (P) MCB KASB BANK

OPTIMISTIC .20 110% 20%

NORMAL .50 22% 16

PESSIMISTIC .30 -60% 10%

For MCB, the expected return on the stock is:

Portfolio Returns

The weighted average expected return on the stocks held in the portfolio.

Here are the expected returns on the individual stocks, the are weights, and there are N stocks in the portfolio.

Correlation Coefficient

- The “Correlation Coefficient” is a measure of the extent that two variables move or vary together.
- It ranges between –1.0 and +1.0
- Positive correlation: a high value on one variable is likely to be associated with a high value on the other.
- Negative correlation: a high value on one variable is likely to be associated with a low value on the other.
- No correlation: values of each are independent of the other

Correlation Coefficient:

- Rate of Return Distribution for two perfectly negatively correlated stocks (r = -1.0)

Portfolio WM

Stock W

25

15

0

0

0

-10

-10

Correlation Coefficient:- Rate of Return Distribution for two perfectly negatively correlated stocks (r = -1.0)
- a. Rates of Return

25

25

15

15

2000

2000

2000

-10

Correlation Coefficient:

- Rate of Return Distribution for two perfectly positively correlated stocks (r = 1.0)

Portfolio MM’

Stock M

25

25

25

15

15

15

0

0

0

-10

-10

-10

Correlation Coefficient:- Rate of Return Distribution for two perfectly positively correlated stocks (r = 1.0)
- a. Rates of Return

2000

2000

2000

Relationship b/w Risk & Return

- The Risk-Return relationship is characterized as being a "positive" or "direct" relationship .
- Greater degrees of risk must be compensated for with greater returns on investment.
- If an investment has relatively lower levels
of expected risk then investors are

satisfied with relatively lower return.

Investors Attitude towards Risk

- Investors are assumed to be risk averse
- Risk Aversion:
Assumes investors dislike risk and require higher rates of return to encourage them to hold riskier securities.

- Risk Premium:
It is the difference between the expected

rate of return on a given risky asset and

that on a less risky asset

Capital Asset Pricing Model

CAPM is a model that describes the relationship between risk and expected (required) return; in this model, a security’s expected (required) return is the risk-free rateplus a premium based on the systematic risk of the security.

rate of

return

Required

rate of

return

Risk

Premium

Market

Risk

Firm-specific

Risk

can be diversified

away

=

+

Risk and the CAPM:

The uses of the capital asset pricing model (CAPM) include:

- Trying to establish the ‘correct’ equilibrium market value of a company’s shares.
- Trying to establish the cost of a company’s equity, taking account of the risk characteristics of a company’s investment, both business and financial risk.

CAPM FORMULA :

Where

is the expected return from an individual security

is the risk- free rate of return

is the expected return from the market as a whole

is the beta factor of the individual security or project

is the market premium for risk

The Concept of Beta:

- Beta () measures a stock’s market (or systematic) risk. It shows the relative volatility of a given stock compared to the average stock. An average stock (or the market portfolio) has a beta = 1.0.
- Beta shows how risky a stock is if the stock is held in a well-diversified portfolio.

- The beta factor for a particular security can be calculated by plotting its return against the market return and drawing the line of best fit.
- The equation of this line can be derived by regression analysis.

Beta: a measure of market risk.

Specifically, it is a measure of how an individual stock’s returns vary with market returns.

It’s a measure of the “sensitivity” of an individual stock’s returns to changes in the market.

- A firm that has a beta = 1 has average market risk. The stock is no more or less volatile than the market.
- A firm with a beta > 1 is more volatile than the market (ex: computer firms).
- A firm with a beta < 1 is less volatile than the market (ex: utilities).

15

10

5

-15

-10

5

15

-5

10

-5

-10

-15

XYZ Co. returns

. . .

. . . .

. . . .

. . . .

. . . .

. . . .

S&P 500

returns

. . . .

. . . .

. . . .

. . . .

. . . .

15

10

5

-15

-10

5

15

-5

10

-5

-10

-15

Beta = slope

= 1.20

XYZ Co. returns

. . .

. . . .

. . . .

. . . .

. . . .

. . . .

S&P 500

returns

. . . .

. . . .

. . . .

. . . .

. . . .

Portfolio Beta Coefficients:

- Portfolio betas are equal to the weighed sum of individual security betas.
Here is the beta of the portfolio, and it reflects how volatile the portfolio is in relation to the market; is the fraction of the portfolio invested in the stock; and is the beta coefficient of the stock.

The equation for CAPM:The Security Market Line (SML):

- The line that shows the relationship between risk as measured by beta and the required rate of return for individuals securities.
= 6%+(14-6%)(0.5)

=6%+8%(0.5)

=10%

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