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Financial Management ­ MGT201
VU
Lesson 25
STOCK BETAS &RISK, SML& RETURN AND STOCK PRICES IN EFFICIENT MARKS
Learning Objectives:
After going through this lecture, you would be able to have an understanding of the following
topics.
·  Stock Betas and Risk
·  SML & Required Returns (CAPM)
·  Stock Prices in Efficient Markets
In the previous lecture, we have mentioned that the risk that is relevant in efficient markets where
the investors are sensible and rational is the market risk. This is because rational investors maintain
many stocks and they maintain diversified portfolio which contain stocks from different sectors and they
manage to eliminate their diversifiable risk and the only risk they faced is the market component of the
risk. However, this market component can not be eliminated and it will remain because markets do
fluctuate. Fluctuation in the Market Index (KSE 100 index) is a measure of Market Risk. This
fluctuation is caused by macro economic and socio political factors. Rational Investors in Efficient
Markets eliminate the Random Company-Specific Risk through Portfolio Diversification.  So, in
Efficient Market the only Risk that remains is Market Risk. And so, the Price of Efficient Stocks is
based on Market Risk only. But the CAPM based on the fundamental principal that the rate of return for
the stock is directly proportional to the risk premium and the risk premium dependent on market risk
alone and not the total risk. Before going into details of SML we first go through the remaining topics
related to beta and its theoretical calculation based on standard deviation and covariance. We have
mentioned that beta of the stocks have tendency of stock to move with the market. It is experimentally
possible to calculate beta of the stock by monitoring the price or rate of return of the stock and at the
same time monitoring the market index in the same period of time & comparing that how the changes in
the stock market price relate to the changes in the stock market index. If you plot them on the graph
where you have expected return for stock on Y- axis and expected return from the stock market index
slope of the line from these points represent the beta
Stock Beta measures the Risk of a Stock Relative to the market.
Beta Stock A
= %  Δ rA* / % Δ rM*  = Slope of Regression Line. Regression Line uses
Experimental Data.
The formula that relates beta of the stock to the standard deviation is as follows
Beta Stock A = Covariance of Stock A with Market / Variance of Market
= σ A σ M ρ AM /  σ  2  M
(Covariance Formula based on Probability & Statistical Portfolio Theory)  Links Stock Beta
(Market Portion of Risk) to Stock Standard Deviation (Total Single Stock Risk).
Simplified formula:
= σ A  ρ AM /  σ M = market risk
Theoretical Beta ­ Example:
Suppose you have Analyzed the Historical Time Data for (1) Movements of the Price (or Return) of
a Stock A and (2) Movements in the Value of the Stock Index.
You then Apply Simple Probability Formulas to compute the following Standard Deviations:
σ A = 30% (Stock A's Total Risk or Standard Deviation)
σ M  = 20% (Stock Market Index Standard Deviation or Risk)
ρ AM = + 0.8 (Correlation between Stock A and the Market Index)
Compute the Theoretical Beta of Stock A:
Stock A Beta = 30% (0.8) / 20% = 24% / 20% = 1.2
108
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Financial Management ­ MGT201
VU
Calculating Stock Beta Graphically
Linear Regression through Annual Data Points for 3 Years.
CALCULATION OF BETA
Year 2
BASED ON EXPERIMENTAL
Expected
DATA OR OBSERVATION
Return on
Slope = Beta = Y /  X
Stock A
=  %  rA*  / %  rM* =
(Historical) %
A =Risk Relative to Market =
rA* - rRF
(rA* - rRF) / (rM* - rRF)
Y-Intercept =
Year 1
Alpha =
Company Specific Risk
rM* - rRF
Expected Return on KSE 100 Market Index
Year 3
(Historical) %
The beta of 1.2 shows that stock is relatively more risky then the market and if the market
moves up by 10% this stock will move up by 12%.
If all the points of the stock lie on the straight line then stock does not have any diversifiable risk. The
difference between the actual data point and the point which vertically lies above or below the point is
representative of the error which is representative of the company's risk attached to any stock.
Now we can put together the two concepts which we studied up till now that is company's
specific risk and the second concept of regression line and the distance between data line and actual
point of the company's risk. Now, we can come up with the total definition of total risk variances.
Total variance risk formula:
Total Risk of Stock A in terms of Variance (= Std Dev 2)
Total Risk = Market Risk + Random Specific Unique Risk
σ2A
β2A   σ2  M
+  σ  2 A-Error
=
Visualizing the Variance Risk Formula on the Regression Line
If a Stock is Part of a Totally Diversified Portfolio then its Company Risk = 0. Therefore Total Risk
= Market Risk. And the Stock points will lie exactly on the Regression line.
If a Stock is a Single Investment then it carries Company Specific or Diversifiable or Random Risk.
This means that its points will not lie on the Regression line. The extent to which the points are
scattered away is a measure of the Variance Error Term (last term in the formula)
109
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Financial Management ­ MGT201
VU
How Efficiently Priced is Stock A?
A
Regression (Beta) Line for Stock
IF STOCK A WERE
Expected Return
EFFICIENT, ALL
on Stock A
Error =
POINTS WOULD LIE
(Historical) %
Measure of
ON A STRAIGHT LINE
Company -
AND TOTAL RISK =
rA* - rRF
Specific Risk
MARKET RISK ONLY
Error =
of Stock A
Measure of
Company -
Specific Risk
of Stock A
rM* - rRF
Expected Return on KSE 100 Market Index (Historical) %
Variance Risks ­ Example:
If the Market Risk = 20% and Stock A's Beta = 1.5 then what is the Relevant Market Risk
Component of Stock A?
Stock A's Market Variance = Beta A2 x Market Variance = 1.52 x (20%) 2 = 2.25 x 400% =
900% (Variance)
So the Stock A's Market Risk (in Standard Deviation terms) = Square Root of Variance = 30%
= Beta A σ M
Note that Total Risk of Stock A can be calculated directly by calculating the Standard Deviation of
the Possible Future Returns. That was the first Risk Formula we studied in Risk Theory.
Suppose Total Risk = 35%. Then Company Specific or Diversifiable or Random Risk of Stock A =
Total Risk - Market Risk = 35% - 30% = 5%.
So 86% (= 30/35 x 100) of Stock A's Total Risk is Market Risk - quite likely that Stock A is Part of
a well Diversified Portfolio or Mutual Fund.
Security Market Line (SML) :
Straight Line Model is for Beta Risk and Required Return. Similar to the Relationship for the 2-
Stock Portfolio with Ro>0 Beta Risk is Directly Proportional to Required Return. The Investors require
an extra Return which exactly compensates them for the extra Risk of the Stock relative to the Market.
SML Linear Equation for the Required Return of any Stock A:
rA = rRF + (rM - rRF ) β A
In the above formula
rA = Return that Investors Require from Investment in Stock A.
rRF = Risk Free Rate of Return (i.e. T-Bill ROR).
rM = Return that Investors Require from Investment in an Average Stock (or the Market
Portfolio of All Stocks where β M = + 1.0 always).
β A = Beta for Stock A. (rM - rRF )  β A = Risk Premium or Additional Return Required in
Excess of Risk Free ROR to compensate the Investor for the Additional Market Risk of the Stock
Required Rate of Return,
Risk Premium & Market Risk:
SML Model for Efficient Markets establishes a Straight Line relationship (or Direct Proportionality)
between a Stock's Required ROR and its Risk Premium.
rA = rRF + (rM - rRF )  A
A Stock's Risk Premium depends on its Market Risk Portion (and not the Total Risk)
110
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Financial Management ­ MGT201
VU
In Efficient Markets, Market Price of a Stock is based on Required Return which depends on
Risk Premium which depends on Stock's Market Risk Component (and not the Total Risk).
Stock Prices in Efficient Markets:
A Single Stock Investor who owns No Stocks and wants to buy a Share A will have to face
more Risk (Market Risk + Specific Risk) than a Rational Fully Diversified Investor. The Single
Stock Investor will want to buy the Stock at a lower price to compensate him for the higher risk.
However, Efficient Markets do not price stocks based on Single Stock Investors who want
compensation for taking on Unnecessary Company-Specific Risk which they should have
diversified away.
Efficient Markets price the Stocks based on their Market Risk Component only. So, Efficient Stock
Prices are based on Rational Investors holding Diversified Portfolios of many stocks.
SML - Numerical Example:
Calculate the Required Rate of Return for Stock A given the following data:
β A = 2.0 (i.e. Stock A is Twice as Risky as the Market)
rM = 20% pa (i.e. Market ROR or ROR on a Portfolio consisting of All Stocks or ROR on
the "Average Stock")
rRF = 10% pa (i.e. T-Bill ROR)
SML Equation (assumes Efficient Stock Pricing, Risk, and Return)
rA = rRF + (rM - rRF ) β A .
= 10% + (20% - 10%) (2.0) = 30%
Interpretation of Result:
Investors require a 30% pa Return from Investment in Stock A. This is higher than the
Market ROR because the Stock (Beta = 2.0) is Riskier than the Market (Beta = 1.0 always).
If Required Return (30%) is higher than Expected Return (20%) it means that Stock A is
Unlikely to Achieve the Investors' Requirement and Investors will NOT invest in Stock A.
Security Market Line (SML)
For Market of Efficient Stocks
rA = rRF + (rM - rRF ) x
A
Required
y = c + mx where x =  and  m = Slope =
(rM - rRF) / (  M - 0) = (rM - rRF) /1
Return (r*)
rA= 30%
Security Market Line
rM= 20%
Market Risk
Premium for
Risky Stock A's
Avg Stock =
rRF= 10%
Total Risk
10%
Premium =
30-10 = 20%
A =+ 2.0
M =+ 1.0
Beta Risk (
)
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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