# Financial Management

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Financial Management ­ MGT201
VU
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
Pr
68.26% of the Area
ob
under the Normal
ab
Curve always
ilit
y
(p)
Return ( r ) %
-2
-1
+1
+2
-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.
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Financial Management ­ MGT201
VU
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
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
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Financial Management ­ MGT201
VU
Portfolio Size vs Risk Graph
P
Po
Unique or Diversifiable or
rtf
Specific or Non-Systematic Risk
oli
To
o
tal
Ri
Ri
M
Market or Systematic or Non-
sk
sk
Diversifiable or Beta Risk =
Minimum Possible Portfolio Risk
n
7
20
40
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
30
20
Stock B
70
10
Total Value =
100
Expected Portfolio Return Calculation:
rP * =
rA xA
+
rB xB
= 20% (30/100) + 10 %( 70/100)
=
6%
+
7%
=
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
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Financial Management ­ MGT201
VU
Example
Complete 2-Stock Investment Portfolio Data:
Value (Rs) Exp Return (%)  Risk (Std Dev)
Stock A 30
20
20%
10
5%
Stock B
70
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%
P
5%
9%
12% 15% 20%
Risk
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