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Financial Management ­ MGT201
VU
Lesson 22
PORTFOLIO RISK ANALYSIS AND EFFICIENT PORTFOLIO MAPS
Learning Objectives:
After going through this lecture, you would be able to have an understanding of the following
topics
·  Portfolio Risk Analysis & Efficient Portfolio Maps
Before starting the new concepts we should recap what we have studied in the previous lecture.
Recap:
Portfolio is a Collection of Investments in different Stocks, Bonds, other Securities or a mix of
all. Its objective is to invest in Different Un-Correlated Stocks in order to minimize overall Risk &
Maximize Portfolio Return. It is mentioned that individuals and companies maintain the portfolio in
order to reduce to reduce the risk
There are 2 Types of Stock Risk
Total Stock Risk = Diversifiable + Market Risk
Diversification means expanding the number of investments which cover different kinds of
stocks. We can reduce the risk as random events in one industry can be off set by the random effects in
the other industry. This way you can reduce the company pacific or unique risk. The market risk arises
because of micro economic or large scale factors such as market interest rate, inflation etc. These factors
have virtually identical effect on the share prices. For example, in event of a war stick market go down
in value which means almost every share went down.7 Stocks are a good number for diversification. 40
Stocks are enough for Minimizing Total Risk
Calculating Expected 2-Stock Portfolio Return & Risk
Expected Portfolio Return = rP * = xA rA + xB rB
Portfolio Risk is generally not a simple weighted average.
Up to this point we only look at the portfolio which has only two stocks.
Interpreting 2-Stock Portfolio Risk Formula:
= XA2 σ A 2 +XB2 σ B 2 + 2 (XA XB σ A σ B
AB)
is coefficient of correlation which states that how muck the investments are correlated.
Here,
The risk of investing in any one share can be reduced if we invest in other shares also. There have been
several experiment studies that show that if you invest in approximately 40 different uncorrelated
different shares of different companies then you can entirely eliminate the company pacific portion of
the risk. Even if you can not diversify across 40 different companies but if you diversify just across 7
different shares from different companies then you can still you can reduce most of the diversifiable risk.
No matter what we do we can not eliminate the market risk that market risk become the minimum risk
we have to live with in our portfolio. The important thing then to remember is that how this risk will
effected when we talk about portfolio of two stocks or more. The Correlation coefficient needs to be
understood in order to understand the risk and return.
Correlation Coefficient (
AB or "Ro"):
Risk of a Portfolio of only 2 Stocks A & B depends on the Correlation between those 2 stocks.
The value of Ro is between -1.0 and +1.0
If Ro = 0 then Investments are Uncorrelated & Risk Formula simplifies to Weighted Average
Formula.
If  Ro = + 1.0 then Investments are Perfectly Positively Correlated and this means that
Diversification does not reduce Risk.
If Ro = - 1.0, it means that Investments are Perfectly Negatively Correlated and the Returns (or Prices
or Values) of the 2 Investments move in Exactly Opposite directions. In this Ideal Case, All Risk can be
diversified away. For example, if the price of one stock increases by 50% then the price of another stock
goes down by 50%.
In Reality, Overall Ro for most Stock Markets is about Ro = + 0.6.it is very rough rule of thumb. It
means that correlations are not completely perfect and you should remember that if the correlation
coefficient is +1.0 then it is not possible to reduce the diversifible risk.
This means that increasing the number of Investments in the Portfolio can reduce some amount of risk
but not all risk
94
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Financial Management ­ MGT201
VU
Portfolio Risk - Example Recap
Complete 2-Stock Investment Portfolio Data:
Value (Rs) Exp Return (%)  Risk (Std Dev)
Stock A
30
20
20%
Stock B
70
10
5%
Total Value = 100
Correlation Coeff Ro = + 0.6
2-Stock Portfolio Risk Calculation:
= XA2 σ A 2 +XB2 σ B 2 + 2 (XA XB σ A σ B
AB)
= {0.0036 + 0.001225 + 0.00252} 0.5 = 0.0857= 8.57%
·  2-Stock Portfolio Return Calculation:
rP* = x A r A + x B r B = 6 + 7 = 13%
Interpretation of Result:
The Portfolio Risk for our Basket of 2 Investments is
+8.57 % (if Ro = + 0.6). What does this
mean?
Bell Curve Assumption: If we assume a Normal Probability Distribution, then there is a 68.26%
chance that our future Portfolio Return will be somewhere between (rP*- σ  ) and (rP*+ σ  ) i.e.
between (13% -8.57%) and (13% +8.57%) or between +4.43% and +21.57%
Portfolio Risk lies between the Individual Risks of the 2 Investments i.e
σ Stock B <  σ P
<
σ Stock A or 5% < 8.57% < 20% (if Ro = +0.6)
You can also come up with more accurate outcome about the actual value of the return on the portfolio
after 1 year if you take a larger range for the standard deviation. So, if you are taking about the range
from -2 sigma to +2 sigma towards then there is likelihood that actual rate of return of the portfolio is
somewhere in between the two standard deviation.
Note: If Ro = - 0.6 (Negative Correlation) then Portfolio Risk = + 4.8% which is lower than both
Individual Investments!!
Now, we consider the case of negatively correlated investments.
Negatively Correlated Investments
2-Stock Investment Portfolio Data:
Exp Indiv Return (ri)  Indiv Risk (Std Devi )
Stock A 20%
20%
Stock B
10%
5%
Correlation Coeff Ro = - 0.6
Portfolio Risk & Return Table (for Different Portfolio Mixes):
Fraction of Stock A
Portfolio Risk Exp Portfolio Return (rP*)
100%
20%  20%
80%
15%  18% = 0.8(20) + 0.2(10)
50%
9%
15% = 0.5(20) + 0.5(10)
30%
4.8%  13%
15%
3.4%  11.5%
0%(i.e. 100% Stock B) 5%
10%
Efficient Portfolio Map
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Financial Management ­ MGT201
VU
Efficient Portfolio Map
Shows All Combinations of 2-Stock Portfolio
Negative Correlation (Ro = -0.6)
rP*
Point of Minimum
Portfolio
20%
Risk
Stock A
Return
(100% A &
15%
80%A
50%A
0% B)
13%
30%A
11.5%
15%A
10%
Stock B
(0% A &
100% B)
3.4% 5%
20%
9%
15%
P
Portfolio Risk
4.8%
Efficient Portfolio Interpretation
Efficient Portfolio Map for 2-Stock Portfolio shows all possible Efficient Combinations (Mixes)
of stocks.
Efficient Portfolios:
Efficient Portfolios are those whose Risk & Return values match the ones computed using
Theoretical Probability Formulas. The Incremental Risk Contribution of a New Stock to a Fully
Diversified Portfolio of 40 Un-Correlated Stocks will be the Market Risk Component of the New Stock
only. The Diversifiable Risk of the New Stock would be entirely offset by random movements in the
other 40 stocks. Adding a New Stock to the existing Portfolio will create more Efficient Portfolio
Curves. The New Stock will contribute its own Incremental Risk and Return to the Portfolio.
rP * = xA rA + xB rB + xC rC (3 Stocks)
Efficient Portfolio Maps
3-Stock Portfolio
Negative Correlation
rP*
Efficient Frontier for
Portfolio  30%
3-Stock Portfolio
Stock C
Return
20%
Stock A
10%
Stock B
Old Efficient Frontier for
2-Stock Portfolio of A & B
40%
2.5% 5%
20%
P
Portfolio Risk
3.4%
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Financial Management ­ MGT201
VU
Now, if we add another stock in the portfolio we can take a look
3-Stock Portfolio Risk Formula
3x3 Matrix Approach
Stock A
Stock B
Stock C
XA2
2
Stock
XA XB
XA XC
A
A
B
AB
A
C
AC
A
XB2
2
Stock
XB XA
XB XC
B
A
BA
B
B
C
BC
B
XC2
2
Stock
XC XA
XC XB
C
A
CA
C
B
CB
C
C
To compute the Portfolio Variance for a 3-Stock Portfolio, just add up all the terms in every
box. To compute the Portfolio Risk (Standard Deviation), simply take the Square Root of the Variance.
You can extend this Matrix Approach to calculate the Risk for a Portfolio consisting of any
number of stocks.
Terms in Boxes on Diagonal (Top Left to Bottom Right) are called "VARIANCE" terms associated
with individual magnitude of risk for each stock.
Terms in all other (or NON-DIAGONAL) Boxes are called "COVARIANCE" terms which account for
affect of one stock's movement on another stock's movement.
97
Table of Contents:
  1. INTRODUCTION TO FINANCIAL MANAGEMENT:Corporate Financing & Capital Structure,
  2. OBJECTIVES OF FINANCIAL MANAGEMENT, FINANCIAL ASSETS AND FINANCIAL MARKETS:Real Assets, Bond
  3. ANALYSIS OF FINANCIAL STATEMENTS:Basic Financial Statements, Profit & Loss account or Income Statement
  4. TIME VALUE OF MONEY:Discounting & Net Present Value (NPV), Interest Theory
  5. FINANCIAL FORECASTING AND FINANCIAL PLANNING:Planning Documents, Drawback of Percent of Sales Method
  6. PRESENT VALUE AND DISCOUNTING:Interest Rates for Discounting Calculations
  7. DISCOUNTING CASH FLOW ANALYSIS, ANNUITIES AND PERPETUITIES:Multiple Compounding
  8. CAPITAL BUDGETING AND CAPITAL BUDGETING TECHNIQUES:Techniques of capital budgeting, Pay back period
  9. NET PRESENT VALUE (NPV) AND INTERNAL RATE OF RETURN (IRR):RANKING TWO DIFFERENT INVESTMENTS
  10. PROJECT CASH FLOWS, PROJECT TIMING, COMPARING PROJECTS, AND MODIFIED INTERNAL RATE OF RETURN (MIRR)
  11. SOME SPECIAL AREAS OF CAPITAL BUDGETING:SOME SPECIAL AREAS OF CAPITAL BUDGETING, SOME SPECIAL AREAS OF CAPITAL BUDGETING
  12. CAPITAL RATIONING AND INTERPRETATION OF IRR AND NPV WITH LIMITED CAPITAL.:Types of Problems in Capital Rationing
  13. BONDS AND CLASSIFICATION OF BONDS:Textile Weaving Factory Case Study, Characteristics of bonds, Convertible Bonds
  14. BONDS’ VALUATION:Long Bond - Risk Theory, Bond Portfolio Theory, Interest Rate Tradeoff
  15. BONDS VALUATION AND YIELD ON BONDS:Present Value formula for the bond
  16. INTRODUCTION TO STOCKS AND STOCK VALUATION:Share Concept, Finite Investment
  17. COMMON STOCK PRICING AND DIVIDEND GROWTH MODELS:Preferred Stock, Perpetual Investment
  18. COMMON STOCKS – RATE OF RETURN AND EPS PRICING MODEL:Earnings per Share (EPS) Pricing Model
  19. INTRODUCTION TO RISK, RISK AND RETURN FOR A SINGLE STOCK INVESTMENT:Diversifiable Risk, Diversification
  20. RISK FOR A SINGLE STOCK INVESTMENT, PROBABILITY GRAPHS AND COEFFICIENT OF VARIATION
  21. 2- STOCK PORTFOLIO THEORY, RISK AND EXPECTED RETURN:Diversification, Definition of Terms
  22. PORTFOLIO RISK ANALYSIS AND EFFICIENT PORTFOLIO MAPS
  23. EFFICIENT PORTFOLIOS, MARKET RISK AND CAPITAL MARKET LINE (CML):Market Risk & Portfolio Theory
  24. STOCK BETA, PORTFOLIO BETA AND INTRODUCTION TO SECURITY MARKET LINE:MARKET, Calculating Portfolio Beta
  25. STOCK BETAS &RISK, SML& RETURN AND STOCK PRICES IN EFFICIENT MARKS:Interpretation of Result
  26. SML GRAPH AND CAPITAL ASSET PRICING MODEL:NPV Calculations & Capital Budgeting
  27. RISK AND PORTFOLIO THEORY, CAPM, CRITICISM OF CAPM AND APPLICATION OF RISK THEORY:Think Out of the Box
  28. INTRODUCTION TO DEBT, EFFICIENT MARKETS AND COST OF CAPITAL:Real Assets Markets, Debt vs. Equity
  29. WEIGHTED AVERAGE COST OF CAPITAL (WACC):Summary of Formulas
  30. BUSINESS RISK FACED BY FIRM, OPERATING LEVERAGE, BREAK EVEN POINT& RETURN ON EQUITY
  31. OPERATING LEVERAGE, FINANCIAL LEVERAGE, ROE, BREAK EVEN POINT AND BUSINESS RISK
  32. FINANCIAL LEVERAGE AND CAPITAL STRUCTURE:Capital Structure Theory
  33. MODIFICATIONS IN MILLAR MODIGLIANI CAPITAL STRUCTURE THEORY:Modified MM - With Bankruptcy Cost
  34. APPLICATION OF MILLER MODIGLIANI AND OTHER CAPITAL STRUCTURE THEORIES:Problem of the theory
  35. NET INCOME AND TAX SHIELD APPROACHES TO WACC:Traditionalists -Real Markets Example
  36. MANAGEMENT OF CAPITAL STRUCTURE:Practical Capital Structure Management
  37. DIVIDEND PAYOUT:Other Factors Affecting Dividend Policy, Residual Dividend Model
  38. APPLICATION OF RESIDUAL DIVIDEND MODEL:Dividend Payout Procedure, Dividend Schemes for Optimizing Share Price
  39. WORKING CAPITAL MANAGEMENT:Impact of working capital on Firm Value, Monthly Cash Budget
  40. CASH MANAGEMENT AND WORKING CAPITAL FINANCING:Inventory Management, Accounts Receivables Management:
  41. SHORT TERM FINANCING, LONG TERM FINANCING AND LEASE FINANCING:
  42. LEASE FINANCING AND TYPES OF LEASE FINANCING:Sale & Lease-Back, Lease Analyses & Calculations
  43. MERGERS AND ACQUISITIONS:Leveraged Buy-Outs (LBO’s), Mergers - Good or Bad?
  44. INTERNATIONAL FINANCE (MULTINATIONAL FINANCE):Major Issues Faced by Multinationals
  45. FINAL REVIEW OF ENTIRE COURSE ON FINANCIAL MANAGEMENT:Financial Statements and Ratios