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Financial Management ­ MGT201
VU
Lesson 20
RISK FOR A SINGLE STOCK INVESTMENT, PROBABILITY GRAPHS AND CO-
EFFICIENT OF VARIATION
Learning Objectives:
After going through this lecture, you would be able to have an understanding of the following
topics
·  Risk for Single Stock Investment
·  Probability Graphs and Coefficient of variation
In this lecture, we will continue our discussion on risk and return. This is very important area of
financial management.
In previous lecture, we have mentioned an example for the investment in share and after one
year the share price has 3 possible outcomes. This uncertainty in future price of the share that leads to
the certain distribution in forecasted share price and this distribution is source of the uncertainty which
allow us to calculate risk.
3 Possible Outcomes Example Continued:
Measuring Stand Alone Risk for Single Stock Investment
Std Dev = δ =
√ ∑ (r i - < r i >) 2 p i.
=
((r i - < r i >) 2 p i.)) 0.5.
=  {[(40-10)2 (0.3)] + [(10-10)2 (0.4)] + [(-20-10)2 (0.3)] } 0.5 .
=  {270 + 0 + 270} 0.5 = {Var} 0.5.
=  {540} 0.5 = 23.24
How do we interpret this Result for Risk?
Standard Deviation Interpretation
What are the units of Standard Deviation?
For our example where Return is being estimated in % terms, the units of
Standard Deviation will also be %.
It tells us that if we assume a Normal Probability Distribution and symmetric about expected rate of
return, then we conclude that 68.26% of the time, the Actual Return will lie within -1 Standard
Deviation and +1 Standard Deviation of the Expected (or Mean) Return.
Expected (or Mean) Return = 10%
+/- 1 Standard Deviation = 10% +/- 23.24% which means from (10% - 23.24%) to (10% + 23.24%) i.e.
from -13.24% to 33.24%.
There is a 68.26% chance that the Actual Return on our Stock Investment after 1 year will be
somewhere between -13.24% and 33.24%. It is important thing to remember that in normal distribution
the area under the curve from -1 standard deviation to +1 standard deviation is 68.28%. So, we can be
sure that two thirds of the time the actual value for the return will be in between -13.68% and +33.24 %.
-13.24% is not a good sign as it indicates that we are making loss but remember that required rate of
return is 10%.
Graphical Standard Deviation
Expected (or Mean)
Return = <r> = 10%
+/- 1 Std Dev covers
68.26% of the Area
Prob
under the Normal
abili
Curve always
ty
(p)
Return (r) %
-2
-1
+1
+2
-13.24%
+33.24%
Our Example
87
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Financial Management ­ MGT201
VU
In the figure the probability is written on y-axis and the rate of return is mentioned on the x-axis.
It shows that higher the standard deviation the higher the risk.
Now, lets take a look another example in which we raw comparing three different investments
which we want to compare in terms of risk and return.
Example:
Comparison of 3 Investments in terms of Risk & Return. Which is the best Investment?
Risk (Std Dev)
Expected Return
Stock A
23.24%
10%
T-Bill/Bond B
5%
10%
Project C
30%
30%
T-Bill is Least Risky (lowest Std Dev =5%) and Project C has Highest Return (=30%).
Given 2 Investments with Identical Expected Return, choose the Investment with the Lower
Risk (or Spread or Volatility or Standard Deviation)
Given 2 Investments with Identical Risk, choose the Investment with the Higher Expected Return
If you compare first two investments, both have the same rate of return but the T-bills have less
risk. Clearly, T-Bill B is a better investment than Stock A because their Returns are identical (10%) but
the T-Bill is less risky (10%) than the Stock (23.24%).
But, which is better? T-Bill B or Project C? T-Bill B is Less Risky but Project C promises Higher
Return.
Now, we conceptually visualize these two types of investment
Combined Risk & Return
Graphical Comparison of Investments
T-Bill B: Low
Risk & Low
Proba
Return
bility
(p)
Project C: High
Risk B
Risk & High Return
Risk C
Exp Return C
Exp Return B
Rate of Return (r) %
In the figure, we are showing both investments on the same graph. Left hand shows the
probability distribution for the T- bills and on the right hand side shows the broader and shorter
probability graph for project C. How to visualize which project have higher expected rate of return.
Project C is on right hand side and therefore it has higher return as to project B.The other thing is that
project B form a probability distribution which have a sharp hill or spread of the curve is much narrower
as to project C. The standard deviation for project B is much narrower then the standard deviation for
project C .In project B has less risk whereas Project C has a higher expected rate return. We have to
look at risk and return simultaneously to answer that which option is better. We can derive the answer
with the help of the coefficient of variation
Comparison of Different Investments
Coefficient of Variation:
Coefficient of Variation (Risk per unit Return)
88
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Financial Management ­ MGT201
VU
It is defined as the CV = Standard Deviation / Expected Return. Coefficient of Variation tells us
about the Risk per unit Return. The project which offers lowest per unit risk is the best investment. Now
we calculate the CV for both the projects.
Compare the CV's of the Projects:
CV T-bill = 5% / 10% = 0.5
CV Project C = 30% / 30% = 1.0
Choose the Project with the Lowest CV. Choose the T-Bill because it carries the lowest Risk per unit
Return
Risk Aversion Assumption
Most Investors are psychologically Risk Averse. If two investments offer the same Expected
Return, most Investors would choose the one with the lower Risk (or Standard Deviation or Spread
or Volatility). In other words, most Investors are not major gamblers. Note that gamblers would
choose Project C which appeals to investor greed by offering an upside return of 30%+10% = 40% !
Consequences on Share Price: The Higher the Risk of a Share, the Higher its Rate of Return and the
Lower its Market Price.
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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