2- STOCK PORTFOLIO THEORY, RISK AND EXPECTED RETURN:Diversification, Definition of Terms

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Financial Management MGT201

Lesson 21

2- STOCK PORTFOLIO THEORY, RISK AND EXPECTED RETURN

Learning Objectives:

After going through this lecture, you would be able to have an understanding of the following

topics

· 2-Stock Portfolio Theory

· Risk & Expected Return

In this lecture, we will continue our discussion on the risk. One of the easiest way of calculating risk

using probability is by understanding the chance that are embedded in the game of cards and the

fundamentals of probability are very easily understood. We discuss in this lecture calculation of risk

using probability. But first we recap the previous concepts formula and

Recap of Risk Basics:

Risk: It arises because of Uncertainty, Volatility, and Spread in possible out comes. There are many

possible outcomes (pi) for Expected Rate of Returns (r.i).

It is measured using Standard Deviation or Variance.

Risk = Std Dev = σ =

√ ( r i - < r i > )2 p i . = "Sigma"

Bell Curve Assumption: In this it is assumed that the forecasted outcome of events will be distributed

in the shape of a Normal Probability Distribution. The advantage we gain from using this that after

calculating the standard deviation for any particular investment we have an idea that what the

distribution or the spread of possible outcomes is going to be like. If you use normal distribution that we

are sure that 68.26% of the times the Actual Future Rate of Return will lie within -1σ and +1 σ range

Coefficient of Variation: Investment Comparison Criterion used to simultaneously account for Risk &

Return

CV = σ/ < r >.

Our Objective is to minimize Risk & maximize Return.

< r > = Exp or Weighted Avg ROR =

pi ri

Graphical Standard Deviation

Expected (or Mean)

Return = <r> = 10%

+/- 1 Std Dev covers

68.26% of the Area

under the Normal

Curve always

ilit

(p)

Return ( r ) %

-2

-1

-13.24%

+33.24%

Our Example

Portfolio Risk & Return:

Portfolio:

Portfolio is defined as a Collection of Multiple Investments. Most organization maintains large

collection or portfolio of investments and when we talk about the risk and return then we have to

consider overall risk and return for the entire portfolio. Portfolios may have 2 or more stocks, bonds,

other securities and investments or a mix of all. We will focus on Stock Portfolios.

Financial Management MGT201

Risk is Relative:

The RISK from investing in Stock of Company ABC usually decreases as you make more

Investments in other stocks of different unrelated companies. This is a logical fact because when you

talk about one business which is earning you Rs 100,000 a month then you not look only on this

business when you are running another business that is losing you Rs 200,000 a month,. You have to

look at all the business and the overall rate of return you are generating, Similarly if you are investing in

the bonds or stocks then you are need to look at the overall risk and return of the portfolio. The

important thing to remember is that risk of particular share of company ABC will change if you are

investing in that share after you have portfolio of many other stocks. If you already have large number

of investments which you have made and then if you invest in particular share in company ABC will be

different

Diversification:

The important thing to remember is that risk of particular share of company ABC will change if

you are investing in that share after you have portfolio of many other stocks. If you already have large

number of investments and then you invest in particular share in company ABC then the risk will be

different. Investing in many Different Shares and Bonds and Projects of Different Companies in

Different Countries can reduce risk. Diversified portfolios can reduce risk. The level of risk generally

reduces as the size of the portfolio increase.

Portfolio Risk & Return:

What matters is the Overall Risk & Return on the entire Portfolio (or Collection) of Investments.

The Risk & Return of an Individual Investment in a Stock or Bond should be seen in terms of its

Incremental Effect on the Overall Portfolio

Investment Rule:

Investor will try to Maximize Portfolio Return and Minimize Portfolio Risk. Investor will NOT

take on Additional Portfolio Risk UNLESS compensated with Additional Portfolio Return.

Types of Risks for a Stock:

Types of Stock-related Risks which cause Uncertainty in future possible Returns & Cash Flows:

Total Stock Risk = Diversifiable Risk + Market Risk

Diversifiable Risk:

It is known as Company-Specific or Unique or Non-Systematic Risk. It is associated with

random events associated with Each Company whose stocks you are investing in i.e. Winning major

contract, losing a court case, successful marketing campaign, losing a charismatic CEO,...Diversifiable

Risk can be Reduced using Diversification. The bad random events affecting one stock will offset the

good random events affecting another stock in your portfolio

Market Risk:

It is known as Non-Diversifiable or Systematic (Country-wide) or Beta Risk. It is associated

with Macroeconomic or Socio-Political or Global events that systematically affect Stock investments in

every Stock Market in the country i.e. Inflation, Macro Market Interest Rates, Recession, and War.

Market Risk can NOT be reduced by Diversification

Financial Management MGT201

Portfolio Size vs Risk Graph

Unique or Diversifiable or

rtf

Specific or Non-Systematic Risk

oli

tal

Market or Systematic or Non-

Diversifiable or Beta Risk =

Minimum Possible Portfolio Risk

Number of Investments (Stocks) in the Portfolio

Note: About 100% of the Diversifiable Risk (and 50% of the

Total Risk) can be removed by Diversification across 40 stocks.

Just 7 carefully chosen Un-Correlated Stocks might be enough

to remove 30% of the Total Risk.

Portfolio Rate of Return

Portfolio's Expected Rate of Return: ( rP ).

It is the weighted average of the expected returns of each individual investment in the portfolio.

Formula is similar to Expected Return for Individual Investment but interpretation is different:

Portfolio Expected ROR Formula:

rP * = r1 x1 + r2 x2 + r3 x3 + ... + rn xn .

Where there are "n" different investments (i.e. Stocks, Bonds, Projects,...) in your portfolio. r1

represents the expected return (in % pa) on Investment No. 1 and x1 represents the weight of Investment

No. 1 (fraction of the Rupee value of the total portfolio that Investment No. 1 represents).

Example:

Suppose that you hold a Portfolio of 2 Stock Investments:

Value of Investment (Rs)

Exp Individual Return (%)

Stock A

Stock B

Total Value =

100

Expected Portfolio Return Calculation:

rP * =

rA xA

rB xB

= 20% (30/100) + 10 %( 70/100)

13%

2 Stock" Investment Portfolio Risk

Portfolio Risk is generally not the weighted average risk of the Individual Investments. In fact, it is

usually less

Stock (Investment) Portfolio Risk Formula:

p = √ XA2 σ A 2 +XB2 σ B 2 + 2 (XA XB σ A σ B

AB)

Definition of Terms:

XA is Investment A's weight in the total value of the Portfolio. σ A is Investment A's

AB is the Correlation Coefficient that measures the

Individual Risk (or standard deviation).

correlation in the returns of the two investments. Last term is a Covariance term

Financial Management MGT201

Example

Complete 2-Stock Investment Portfolio Data:

Value (Rs) Exp Return (%) Risk (Std Dev)

Stock A 30

20%

Stock B

Total Value = 100

Correlation Coeff Ro = + 0.6

2-Stock Portfolio Risk Calculation:

p = √ XA2 σ A 2 +XB2 σ B 2 + 2 (XA XB σ A σ B

AB)

= {(30/100)2(20%)2 + (70/100)2(5%)2 +2[(30/100)(70/100)(20%)(5%)(0.6)]}0.5

= {(0.09)(0.04) + (0.49)(0.0025) + 2[ (0.0021) (0.6) ] } 0.5

= {0.0036 + 0.001225 + 0.00252} 0.5.

= {0.004825 + 0.00252} 0.5.

= {0.007345} 0.5.

= 0.0857=8.57%

XA2 σA2 + XB2 σB2 + 2 (XA XB σA σB

AB)

Risk vs. Return Graph

Example with 2-Stock Portfolio with Positive Correlation

rP*

20%

Portfolio

17%

Return

15%

As Risk INCREASES,

the Investors' Required

13%

Return INCREASES

10%

12% 15% 20%

Risk

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