Financial Management MGT201
STOCK BETA, PORTFOLIO BETA AND INTRODUCTION TO SECURITY MARKET LINE
After going through this lecture, you would be able to have an understanding of the following
· Stock Beta
· Portfolio Beta
· Introduction to SML (CAPM)
First, we would recap some of the concepts which we have studied in the previous lectures.
It is mentioned in the efficient capital markets the investors would take on extra risk only if they are
compensated in the form of extra return. The market only compensates the investor to the extent that he
will receive extra return for extra market risk he takes on by investing in a new stock. However, the
market will not pay the investor any extra return for taking on unnecessary risk in the form of
company's own risk. Therefore, it is best for investors to act rationally and to maintain diversified
portfolios of many stocks and in this manner they can eliminate the company's own risk and they can
make investments in stocks at a lower required rate of return. Market portion of risk can be represented
through the `Beta' coefficient and it is the corner stone for Capital Asset Pricing Model (CAMP).
It is a tendency of a Stock to move with the Market (or Portfolio of all Stocks in the Stock
Market).it is the building block of CAPM.
Total Risk = Diversifiable Risk + Market Risk
Total Stock Return = Dividend Yield + Capital Gain Yield
Stock Risk Vs Stock Beta:
It is a statistical spread of possible returns (or Volatility) for that Stock
It is a statistical spread of possible returns (or Volatility) for that Stock relative to the
market spread i.e. spread (or Volatility) of the fully diversified market portfolio or index.
Beta Coefficients of Individual Stocks are published in "Beta Books" by Stock Brokerages & Rating
It is the overall Stock Market. For Example, Karachi Stock Exchange. KSE 100 Index represents Value
of "Portfolio" of Highest Volume Stocks but NOT ALL stocks. Therefore it is not fully perfect
Market carries Risk. It moves up and down because of macroeconomic factors (inflation,
general interest rates) and political changes. Therefore the market has some expected rate of return
which changes with time because of this there is possibility of different outcomes. There are no fully
diversified portfolios in reality. The CAMP based on the promise market Beta to be Equal to + 1.0. We
can then look at the different beta and compare them with the markets.
Meaning of Beta for Share ABC in Karachi Stock Exchange (KSE):
· If Share A's Beta = +2.0 then that Share is Twice as risky (or volatile) as the KSE Market i.e. If
the KSE 100 Index moved up 10% in 1 year, then based on historical data, the Price of Share B
would move up 20% in 1 year.
· If Share B's Beta = +1.0 then that Share is Exactly as risky (or volatile) as the KSE Market
· If Share C's Beta = +0.5 then that Share is only Half as risky (or volatile) as the KSE Market
· If you could find a Share D with Beta = -1.0 then that share would be exactly as volatile as the
KSE Market BUT in the opposite way i.e. If the KSE 100 Index moved UP 10% then the price
of the Share D would move DOWN by 10%!
· The Beta of most Stocks ranges between + 0.5 and + 1.5
· The Average Beta for All Stocks = Beta of Market = + 1.0 Always.
Our approach for calculating the beta will be straight forward. Let us assume that we analyze he
movements in KSE index for period of three years and we also analyze the price movements for the
Stock A in KSE for the same period of time of three years. We look at the change in the price of the
Financial Management MGT201
stock and compare it to the change in price in the market for each one of the three years separately.
And then we plot those points on a graph where the expected return on the stock on the y- axis and
the expected return on the market on x-axis. We are using the price of the stock and value of the
index as representative measures for the expected return.
Calculating Stock Beta Graphically
Linear Regression or Least Squares Fit through Experimental
Data Collected for 3 Years
Slope = Beta = Y / X =
% rA* / % rM =
A=Risk Relative to Market =
rA* - rRF
(rA* - rRF) / (rM* - rRF)
Company Specific Risk
rM* - rRF
Expected Return on KSE 100 Market Index
If you look at the graph, we have plotted three years of data for the changes in the Karachi stock
exchange 100 market index and the expected return on the stock A. The expected return on A is on y-
axis and it is represented by rA* and the expected return on stock in KSE 100 market index is
represented by rM* the `*' represented the expected part of the rate of return. In both cases the expected
returns have been benched marked against the risk free rate of return. That is because we pick the risk
free rate of return as the starting point for the changes in the expected return. Three points are shown on
the graph on for each year in the analysis and after plotting these points on the graph we can then do
what is known as the linear regression of straight line which best fit through points. You have studied
this concept in the course of "Statistics and Probability" .The slope of the line represents the beta
Slope = Beta = Δ Y / Δ X = % Δ rA* / % Δ rM*
= A =Risk Relative to Market = (rA* - rRF) / (rM* - rRF)
Beta represents the risk of stock relative to the return of the market and in terms of risk free rate
of return we can define the Beta as the expected rate of return for stock A minus risk free rate of return
divided by the expected rate of return for the market minus risk free rate of return. We use historical
data of expected rate of return and we graphed it against changes in the overall market index
Calculating Portfolio Beta (CAPM):
There are two ways of calculating portfolio beta
· Analyze Historical Data for Portfolio Returns and Market Index Returns like in the case of
Stock Beta, plot Least Squares Fit Line, and compute Portfolio Line Slope or Beta directly.
· Use the Published Data for Individual Stock Betas from the "Beta Book"
Portfolio beta can be calculated as the sample weighted average of the stock beta's in that portfolio.
Portfolio Beta = β P =
XA β A+
XB β B + XC β C +.....
In the formula
βA represents the Beta (or Market Risk) of Stock A.
XA represents the Weight of Stock (fractional value of investment in A to total
portfolio value).The simple formula for calculating the portfolio beta is as follows.
Portfolio Beta (or Market Risk) Formula is a Simple Weighted Average unlike the portfolio risk formula
Financial Management MGT201
XA2 σ A
+ 2 (XA XB σ Aσ B ρ AB )
· Complete 2-Stock Investment Portfolio Data:
Value Exp Return (r*) Tot Risk
Total Value =Rs 100
= + 0.6
Portfolio Mean Expected Return = 13% = rP*
Portfolio Risk (Total) = 8.57% = P (relative to rP*)
Now we can calculate the portfolio beta which is measure of the market portion of portfolio risk.
Portfolio Beta = XaBa + XbBb = (30/100) (2.0) + (70/100) (0.5) = 0.6 + 0.35
= +0.95 = β P (relative to Market Risk or Volatility)
It means that the Portfolio of A & B is slightly less risky than the totally diversified KSE 100
Market Portfolio whose Beta = +1.0
Effect of New Stock Investment on Portfolio:
Now we will see the case that what will happen to portfolio beta if we add another stock to it.
Suppose, you add a 3rd Investment Stock C, to your Old 2-Stock Portfolio.
Exp Return (r*)
3-Stock Portfolio Beta = β P = XaBa + XbBb + XcBc
= (30/100) (2.0) + (30/100) (0.5) + (40/100) (1.5)
= 0.6+0.15+0.6 = 1.35
The effect of adding a stock with a Beta higher than the Portfolio's is that it increases the Portfolio's
Beta or Risk. In this case we also increase the beta by adding new stock but the expected rate of return
also increases for the portfolio. So, the increase rate of return would compensate the increase in risk.
Required Rate of Return (CAPM)
Required ROR vs. Expected ROR
Expected ROR (r*):
The Most Likely (or Mean) ROR expected in the future. It is calculated using Weighted
Average Formula and Probabilities (what we have been calculating so far).It is basically the weighted
average or mean of the expected return of the individual investments in the portfolio.
Required ROR (r):
It is the minimum return that investors require from the stock to invest in it. It
varies from individual to individual. It is based on
1) Perceived Risk relative to the Market and Psychological Risk Profile of each Investor and
2) His personal Opportunity Cost of Capital preference.
We have mentioned earlier that ROR or opportunity cost varies from person to person because
every individual have a different preference for risk taking. Some people have tendency to be gamblers
whereas other people put their money at national saving schemes.
However, the ROR can be linked
to the Beta risk because based on the portfolio theory and CAPM where we mentioned there is direct
relationship between risk and return.
Average Required ROR for all rational investors in an Efficient Market can be estimated using
the CAPM Theory: Beta and Risk Free Rate of Return.
Total Rate of Return (ROR) for Single Stock = Dividend Yield + Capital Gain. GORDON'S
FORMULA FOR COMMON STOCK PRICING OR VALUATION USES REQUIRED RETURN r =
DIV/Po + g. In Efficient Markets, Price of Stocks is based on Market Risk (or Beta).
We can formulate the required rate of return in terms of Beta risk so how can we use beta coefficient to
calculate the required rate of return for the average investor in the market. The answer to it is the
Financial Management MGT201
Security Market line SML. It is the part of CAPM and it is the most critical part of CAPM. SML is
straight line relationship that contains all possible combinations of efficient stocks in the market. If the
combination of risk and return for any stock does not lie on the SML then that stock is not efficiently
priced. In other words, it means that for most of the investors in the market there ROR for investment in
stock A is directly proportional to Beta risk for that stock A. You will recall that we are not unfamiliar
with straight line relationship between risk and return when we are talking about the portfolio when we
calculate the portfolio risk with a +ve correlation coefficient we came up with a continuously increasing
relationship between portfolio risk and return. So that model is similar to SML.
Risk vs. Return Graph (Risk Theory)
2-Stock Portfolio with Positive Correlation Coefficient
12% 15% 20%
Risk vs. Return Graph (SML- CAPM)
EFFICIENT MARKETS WITH FULLY DIVERSIFIED
PORTFOLIOS AND EFFICIENTLY PRICED STOCKS
STOCKS IN EFFICIENT
MARKETS WILL LIE ON
THE STRAIGHT SML
Security Market Line (SML):
It is a Straight Line Model for Beta Risk and Required Return. It is Similar to the Relationship for
the 2-Stock Portfolio with ρ >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.
Financial Management MGT201
SML Linear Equation for the Required Return of any Stock A:
rA = rRF + (rM - rRF ) β A .
In the above equation
rA = Return that Investors Require from Investment in Stock A.
rRF = Risk Free Rate of Return (ie. 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 in Excess of Risk Free ROR to compensate the Investor for
the additional Risk.
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