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Financial Management MGT201

Lesson 26

SML GRAPH AND CAPITAL ASSET PRICING MODEL

Learning Objectives:

After going through this lecture, you would be able to have an understanding of the following

topics.

· SML Graph & CAPM

We will continue our discussion on risk. It is very important in our daily life .we are always

concerned with risky situation. There is risk that you can not watch this lecture due to the power failure.

We have to know that how we can measure and control the risk in every day life. We are going to see

that how we can use required rate of return that we calculated by using the SML equation and use that

required rate of return for the calculation we have been doing in the first two parts of this course. In first

part we did capital budgeting and NPV calculations and in the NPV formula the `r' we are using is the

required rate of return not he expected rate of return. We can use the value of required return from SML

equation in stock or bond pricing. We have studied that in the efficient markets the required rate of

return is come from the market return. There are two methods for the calculation of risk.

First approach the experimental cost base in this approach we use expected rate of return and market

index. Then we plot these points on the graph and we join them with a straight line called regression line

and slope of this line is called beta co- efficient.

The second approach for its calculation is called theoretical beta of stock:

Beta Stock A = σ A σ M ρ AM / σ 2 M

= σ A ρ AM / σ M

Extent to which Actual Stock Return Data lies on Regression Line

Total Risk = Market Risk + Random Company Specific Risk If the experimental data points

All lies exactly on the regression line then this particular stock has only market risk.

Theoretical Market Risk of a Stock:

Market Risk of Stock A = β A σ M = σ A ρ AM

Extent to which Actual Stock Return Data lies on Regression Line

The third formula which we discussed is very important and cornerstone of the CAPM.

Security Market Line (SML) and Required Rate of Return (rA):

It allows us that the value which we have calculated for the beta and from that calculate

the required rate of return of the stock and then we use for stock pricing. So, then the required rate of

return for any stock A is equal to

rA = rRF + (rM - rRF ) β A .

In Efficient Markets, Stock Price (and Value) depends on Required Return which depends on Market

Risk (not the Total Risk).

The required rate of return in efficient markets depends upon the risk premium which depends only

upon the market risk and not on the total risk. We do not have to worry about company's risk because

we assume that investors are rational and maintain diversified portfolio. Now, let's take a look at the

security market line graphically .It is important to understand this graph and many things that it tells us.

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Security Market Line (SML)

For Efficient Stocks

rA = rRF + (rM - rRF )

yA .c + mx where x = and m = Slope =

Required

(rM - rRF) / ( M - 0) = (rM - rRF) /1

Return (r*)

rA= 30%

Risky Stock A's

Security Market Line

Risk Premium =

rM= 20%

Market Risk

30-10 = 20.

Premium for

Based on Market

Avg Stock =

rRF= 10%

Risk (not Total

10%

Risk)

A =+ 2.0

M =+ 1.0

RF = 0

Beta Risk (

)

The graph represents the SML in the efficient stock market. On y axis we have required rate of

return r* for the stock A for and risk free rate of return and on the x- axis is beta risk which represents

the market risk. SML is straight line and it tells us the relationship between the market risk and the

required return. it starts on the left hand side from risk free rate of return and it passes through a point

ion the middle which is the overall market point. This point is located at the beta of +1.0 and at the

required return of 20%.This means that the market offers a rate of return which is higher then the risk

free rate of return. Because the market fluctuates it has a risk of 1.0 and not 0. if we extend the line it

passes through the point where the beta is +2.0 and the required return is 30%.because this point lies on

the SML it means that stock A has no company risk & what is the risk premium ?

Risk premium=rA-rRF=30%-10%=20%.

It is directly proportion to market risk of stock.

Please note that slope of this line is = (rM-rRF)/ (betaM-0) = (rM-rRF)/1. This is the measure

tendency of the average investors in the market to take risk. If the SML line is steeper the investors will

not take unnecessary risk. In other words they are risk aversive as the slope increase the avoidance for

the risk also increases in the market as whole. It is very important to formulate the equation for SML

You should be able understand the various points that lie on the SML line including the risk free rate of

return or T-BILL return as well as the market point and you should also understand that the slope of

SML line is=(rM-rRF)/(betaM-0)=(rM-rRF)/1.Beta coefficient was the slope of the line for different graph

that graph shows the stock rate of return on y-axis and market rate of return on x-axis. But over there

we are not talking about the required rate of return we were talking about the expected rate of return so;

do not confuse these two different graphs. SML exist for only the efficient markets or perfect capital

markets. SML tells us in detail that rational investor will eliminate the company's specific risk and the

total risk of the company will be equal to the market risk of the company. SML line is an ideal case and

in efficient markets all the stocks lie on the SML line. If stock is not on SML then according to market

equilibrium it will come back on SML. If any stock is not on SML then forces of market equilibrium

will bring it on the security market line. If risk and return combination of any stock is above SML it

means that it is offering the higher rate of return as compare to efficient stock. The people will rush to

buy such stock when the demand will increase the return will decrease.

If any stock is lying below the SML line the price will come down it will offer as much

potential as the efficient stock offers. The supply for such stock will increase and it will offer higher

return in form of capital gain. So, the market forces will throw these points on the SML. Markets are not

risk free .markets index fluctuate .The investors expect that market return will be more than the average

expected return.

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Financial Management MGT201

Security Market Line (SML)

Slope & Risk Taking

Required

Steep Slope SML

Return (r*)

 Most Investors

Avoid Investors

rM= 20%

Low Slope SML 

Most Investors in

rRF= 10%

this Market are

Gamblers

M =+ 1.0

RF = 0

Beta Risk (

)

Even Markets and Market Returns Fluctuate because of Macro Systematic Factors. So the Fully

Diversified Market Portfolio consisting of all shares is NOT Risk Free. The Market has a Risk

Premium over the Risk Free ROR. This Market Risk Premium represents 100% Market Risk and No

Company-Specific or Diversifiable Risk. Efficient Stock combinations of Risk & Return in Efficient

Market Equilibrium must lie ON the SML.

Any Stock whose (Risk, Return) Pair lies ABOVE THE SML is offering Excessive Return (above the

Market). So, all rational investors will rush to Buy it. The present Price would Rise and the Return (as

measured by Capital Gain Yield = ( Pn -Po) / Po) would Fall until it comes back on SML Any Stock

whose (Risk, Return) Pair lies BELOW THE SML is offering a Return that is lower than the Market. So,

Rational Investors will rush to sell it. The Stock Price would Fall and the Return would Rise until it

comes back on the SML.

Now , we will calculate the required rate of return using GORDON FORMULA .so, we need to

calculate required rate of return to understand the risk so, let's use SML formula for required rate of

return by plugging it into the GORDON FORMUL A. price valuation formula by GORDON:

Share A is being traded in the Karachi Stock Exchange (KSE) at a Market Price of Rs 12. You need to

calculate the Expected Theoretical Fair Price of a Stock A before you can decide whether to buy it or

not. Given the following Data:

DIV1 = Rs 2 (i.e. Forecasted Dividends in the upcoming year on a share of Face Value = Rs 10)

g = 10% pa (i.e. Forecasted Constant Growth Rate in Dividends)

rRF = 10% pa (i.e. T-Bill Rate of Return or PLS Bank Account ROR)

rM = 20% pa (i.e. The Karachi Stock Exchange's historical average ROR based on the value of the

KSE 100 Index)

Beta of Stock A = 2.0 (i.e. Stock A has historically been twice as volatile or risky as the KSE 100

Index)

Use the Gordon-SML Equation to Estimate Fair Price of Stock A:

Po* = DIV1 / [ (rRF + (rM - rRF ) A ) - g]

= 2 / [10% + (20% - 10%) (2.0)) - 10%]

= 2 / [30% - 10%] = 2 / 20% = Rs 10

The Required Rate of Return for Stock A was calculated to be 30% which is higher than the

Market (20%). The Market is offering a 10% extra return as a Risk Premium because Stock A (Beta =

2.0) is twice as risky as the market (Beta = 1.0).

The Fair Price of Stock A (Rs 10) is LESS than the Market Price (Rs 12) which means that the Market

Speculators have Overvalued Stock A and you should NOT buy it.

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Financial Management MGT201

So, what does our answer mean? We see that expected fair price of the share is Rs.10 which is lower

than the market price which is Rs.12.keep in mind that price for the share is imperfect market depends

upon the investor psychology , speculation and gambling that is taking place in the stock market .so,

when fair price is lower as in our example and market price is higher it means that the shares price or

stock has been over valued and the rational investor will not purchase it .other thing to note is that we

calculated share premium and required rate of return in our formula is 30%.it is higher than the over all

market risk .because it is twice risky as the market beta A=+2.0therfore it is giving extra return to the

investors for the compensation.

NPV Calculations & Capital Budgeting:

Application of SML (CAPM):

In the beginning of this course while studying capital budgeting and investment criteria we used

the NPV and PV formulas for calculating required rate of return and not for expected rate of return.

Required rate of return is attached to the individual investors. we forecast our dividends and they are

not true cash flows so we discount them to the present .we calculate the standard deviation for over

all industry. NPV (and PV) Calculation which is the Heart of Investment Criteria and Capital

Budgeting uses required return (and NOT Expected ROR). This is why Share Pricing also uses

Required Rate of Return because Share Price was derived from the PV Equation for Dividend Cash

Flows.

We can apply our Probabilistic Risk Analysis to Entire Companies or Real Projects or Assets and

focus on the Volatility or Uncertainty of their Net Cash Flows. We can compare that to the

Volatility of the Cash Flows of the Industry that the Company is a part of to come up with a Beta

Coefficient for the Assets of a Company as a whole. We can then use the Asset Beta to calculate

the Overall Required Rate of Return for a Company (i.e. All Assets - both Equity and Debt).

Risk & Return - Must Consider both:

In Perfect Markets and Efficient Markets where Rational Investors have Diversified Away ALL

Company Specific Risk, Value (and Stock Price) depends on Required Return which depends on Market

Risk (and not Total Risk).In most Real Markets where Investors are not fully Diversified, Total Risk is

important. It can be calculated using the Sigma (Standard Deviation) Formulas, probabilities, and

Expected Return. Total Risk and expected Return must both be considered in Comparing Investments.

Market Risk and required return are related to one another in Efficient Markets according to the SML

equation. Required Return depends on the Individual Investor's Psychological Risk Profile and

Opportunity Cost of Capital.

Betas:

Stock Beta vs. Real Asset Beta

Objective in FM is to maximize stock holders' (or Owners') Wealth

Negative Side Effect - Treasury Managers of Listed Corporations in USA and Europe spend too

much time manipulating Stock Prices.

Real Assets have Risky Revenue Cash Flows:

Asset Beta = Revenue Beta x [1 + PV (Fixed Costs)/PV (Assets)]

A Stock's Beta or Risk Relative to the Market can change with time. If the Company's business

operations or environment change, its responsiveness to the Market can alter i.e. if it buys another

business, implements a Total Quality Management program, makes an R&D technological discovery,

takes on Debt, etc.

Notes on Measuring Uncertainty

Standard Deviation vs. Beta

For Example, Oil Drilling Companies: possible to have High Standard Deviations in Forecasted

Earnings and Returns but Low Betas or Stock Price volatility relative to Market

Volatility vs. Risk:

Seasonal or macro volatility in Earnings does NOT necessarily signify Risk BUT High Stock

Price volatility does signify Risk.

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