# Financial Management

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Financial Management ­ MGT201
VU
Lesson 23
EFFICIENT PORTFOLIOS, MARKET RISK AND CAPITAL MARKET LINE (CML)
Learning Objectives:
After going through this lecture, you would be able to have an understanding of the following
topics.
·  Efficient Portfolios,
·  Market Risk & CML
First we recap the important concepts which we have studied in previous lectures. Portfolio theory
is looking at the relationships between the risk and return for portfolios, especially for diversified
portfolios.
Total Stock Return = Dividend Yield + Capital Gain Yield
You should recall this from the Gordon formula that we learnt in the share valuation.
We spoke about the total risk for the stock and we said that it is equal to the company's risk plus the
market risk.
Total Risk = Diversifiable Risk + Market Risk
We mentioned that on the basis of experimental studies that if we invest in many stocks which are
not correlated to each other then it is possible to reduce overall risk for your investment as a whole. We
called this portfolio or collection of stocks. 7 Stocks are a good number for diversification & 40 Stocks
are enough for eliminating Company Risk & Minimizing Total Risk.
Now, in the portfolio theory model which we are going to discuss the major assumption is that the
rational investors in the market place maintain diversified portfolios. We discuss in the previous lecture
about calculating expected return on the portfolio and we mentioned that it is simply the weighted
average of return of each stock in the portfolio. The formula
2-Stock Portfolio's Expected Return = rP * = xA rA + xB rB
2-Stock Portfolio Risk Formula
Sd= X A2 σ A 2 +XB2 σ B 2 + 2 (XA XB σ A σ B
AB)
It is mentioned in the previous lecture that we can calculate the risk of larger portfolio using the
matrix approach
Matrix for Calculating Portfolio Risk: Covariance Terms (Non-Diagonal Boxes) measures (1)
Magnitude of movement (Standard Deviation) and (2) Closeness of movement (Correlation
Coefficient) between any two stocks in the portfolio.
3-Stock Portfolio Risk Formula
3 x 3 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.
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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. These represent the magnitude or size
of the movement between the two stocks. There are two parts for this covariance terms
·One of the two covariance terms for two stock portfolios is XA XB σ A σ B
AB.
Both standard deviation and covariance are important to calculate the size of the movement of
both stock A and B. In other words, if covariance is large then a pair of stock moves a lot and they also
move together. Correlation coefficient is the measure that how closely they move Standard deviation
tells us that how much they move.
We have discussed in the previous lecture about the efficient portfolio map and the efficient
frontier. If we plot the risk and return for the portfolio whose correlation coefficient is negative then we
come up with a hook shape curve and it tells us that it is possible to increase the return on portfolio & at
same time reduce the risk which is ideal because the objective is to maximize the return and to minimize
the risk. But in conclusion of last lecture we said that there is a whole line with infinite number of points
that represents an efficient frontier and every single combination or mix of the portfolio on this line
represents an efficient combination. But this does not help us very much why because we do not know
which one of these mix is the best. So, the first ting we are going to figure out is that what optimal mix
of the portfolio is. The starting point to figure out this is to realize that if you have a portfolio of stocks
then every investor have access to another portfolio and that portfolio is the portfolio of T bills and we
are going to assume that every body have the option of investing in the T-Bills that give them the risk
free rate of return. For Pakistan, we consider that figure to be 10%.So; this is the starting point to figure
out that what is the optimal portfolio mix is. The realization that if your portfolio is giving you the
return which is less then risk free rate of return then why would you investing in that portfolio and you
would choose to invest in T-bills. By using this understanding, let's take another look on risk and return
portfolio frontier model and see that how we can use this fact to find the optimal portfolio mix and we
take look at 3 stock portfolio consisting of stock A, B and C and added to that we will give ourselves the
option of investing in a T-bill portfolio wherever stocks are not providing sufficient return. So, if we
look at the e efficient portfolio map you will see that Portfolio risk is on X- axis and the portfolio
return on Y- axis.
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Picking Most Efficient Portfolio
Capital Market Line (CML) & T-Bill Portfolio
P Efficient Frontier
rP* = rRF + [ (rM - rRF) / M ]
rP*
for 3-Stock Portfolio
Portfolio
Capital Market Line
Stock C
Return 30%
"The Parachute"
Stock A
20%
Optimal Portfolio Mix
(50%A, 30% B, 20%C) if
10%=
Stock B
rRF
Risk Free T-Bill ROR = 10%
40%
20%
2.5%
P
Portfolio with Negative
3.4%
Portfolio Risk
or Zero Correlation
Coefficient
The efficient frontier for the 3 stock portfolio is the overarching largest hook shaped curve and
also remember that closed combination of the all the hook shaped curves forms a parachute like
shape and any one of the points inside that parachute is a possible mix or combination of different
stocks that you can have in your portfolio. However, the most efficient combinations lie on the
efficient frontier line and the next logical step we are going to take is to figure out what is the best
point on the efficient frontier. As it is mentioned that we will assume that we have access to T- bill
portfolio which offers a risk free rate of return of 10% and that will be the starting point of our
capital market line (CML).wherever this line if you extend from the 10 % point from y-axis touches
the efficient frontier line and is tangent to it is the point for the "Optimal Portfolio Mix." This point
is shown as a large dot in the above figure. If you look at the location of this large dot on the
efficient frontier you can see that it lies closer to the Stock B and Stock A. Therefore, there is larger
percentage of stock A and B in this optimal portfolio mix. Approximately, the optimal portfolio mix
consist of 50% Stock A, 30% Stock B, and 20% Stock C. It is important to remember that we have
the option of investing in the T-bill portfolio which offers a risk free rate of return
And the expected rate of return is 10%.Therefore, if the returns on this portfolio decrease 10%
then the investor will invest in the risk free T ­bills portfolio. Whichever portfolio offers lowest
coefficient of variation is the better portfolio. The CML represents different combinations that you
can pick in the risk free as well as stock portfolio. Thus CML represents combination of efficient
portfolio in the capital market. It is the important point remembers that According to the Portfolio
Theory, Efficient Portfolios are Fully Diversified and they must lie on the CML Line. Now, it is
also possible simply come up with the equation for the CML.
CML Equation: rP* = rRF + [(rM - rRF) / σM]  σP
rRF= risk free rate of return
rM = expected rate of return for the market of all possible stock
σM = risk of the market
σP = risk of stock portfolio
The Expected Return on an Investment in a Common Share is not guaranteed or certain. The
Price and Dividend can vary so we can guess what the Possible future Returns (or Outcomes) might
be and assign probabilities to each. Uncertainty about Future Expected Return on Investment gives
rise to Probability Distribution of Possible Outcomes. This gives rise to a Spread of Possible Future
Returns which is a measure of the Risk or Uncertainty or Standard Deviation. We can apply this
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concept to the single stock or a portfolio of a many stocks. When we talk about the expected return
on a single stock then we are saying that it is the combination of the dividend gain yield and the
capital gain yield. When we talk about the expected return for the portfolio then we consider
expected return for each stock in that portfolio and assign proportionate amount of weightage based
on the fraction of the investment in a particular stock compare to the total value of the portfolio.
Furthermore, the individual risk of every investment affects the risk of every other investment in the
portfolio! The Overall Portfolio Risk decreases as the number of investments increase up to the
point that the Company Specific or Unique Risk has been totally eliminated i.e. About 40
uncorrelated stocks. In this Range it is possible to Increase Return and Reduce Risk! After that,
the Portfolio is assumed to be Fully Diversified and any additional investment will only contribute
to the Market Risk which can not be eliminated.
Market Risk & Portfolio Theory:
We can measure that how market risk varies from one stock to another based on the Beta's. It is
mentioned that when you add newly stock to the fully diversified portfolio then the only contribution
this new stock is made to the risk of the existing portfolio is the market risk because we are considering
that company's unique risk has entirely wiped out by diversification. If the correlation between different
stocks is negative or Zero then risk and return profile graph takes on a hook shaped curve and this hook
shaped curve is important to understand because it means that it is possible for certain combinations of
the portfolio to both reduce risk and increase return.
Hook Shaped Curve
Negative Correlation Coefficient
Possible to Get Higher Return AND LOWER RISK
rP*
Point of Minimum Risk
Portfolio
20%
Return
Stock A
(100% A)
80%A
15%
50%A
13%
30%A
11.5%
15%A
10%
Stock B
(100% B)
3.4% 5%
20%
9%
15%
P
Portfolio Risk
However, if the correlation coefficient is +ve then the risk return relationship is that of
continuous function which is continuously rising as return rises the risk also rises with it. It is the
fundamental concept in risk and return that the investor will not take on any additional risk unless
they compensated by additional return. It is important to under stand that when we are talking about
efficient capital markets and talking about the capital market line we are saying that efficient
portfolios in the market all lie on the capital market line. It means that if one investor is only
investing in the stock A and the other has a diversified portfolio of 40 stocks and now he is also
investing in Stock A then the amount of risk for both investors will be different the investor who is
only investing in stock A is taking on the Market risk of the stock as well as the company's risk
whereas the other investor is only taking on the market component risk for that stock.  Rational
Investors with Diversified Portfolios expect to be compensated by extra return in exchange for
taking on Extra Market Risk.
You can NOT expect to receive extra return (or compensation) for taking on Company-Specific
Risk which Rational Investors have eliminated! The Efficient Market will only offer you a Return
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(and a Share Price) which is the bare minimum acceptable to Rational Diversified Investors. This is
the Basis of the Capital Asset Pricing Model (CAPM).
Beta Concept & CAPM:
Beta:
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.
Stock Risk vs. Stock Beta:
Stock Risk:
It is a statistical spread of possible returns (or Volatility) for that Stock
Stock Beta:
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
Agencies
CAPM: Capital Asset Pricing Model.
It is developed by Professors Sharpe & Markowitz. He won Nobel Prize in 1990
Market Risk is the only risk that is relevant to a Rational Investor with a Diversified Portfolio of
Investments. The Company Specific (or Unique) Risk is Diversified Away! Market Risk is measured
in terms of the Standard Deviation (or Volatility) of the Market Portfolio or Index. Every Stock Market
develops an Index comprising of a weighted average of the highest-volume shares in that market. This
Index represents the relative strength of that Stock Exchange and is considered to be close to a Totally
Diversified Portfolio. In reality, no such Portfolio exists anywhere in the world. For example the
Karachi Stock Exchange has the KSE 100 Index.
Return, Risk, and Beta
Stock B's Possible
Stock A's Possible
Future Returns
Future Returns
Stock B's Weighted
Stock A's Weighted
Average Return or
Average Return or
Expected Mean Return
Expected Mean Return
Stock A's Risk or
Stock A's Risk or
Standard Deviation
Standard Deviation
Weightage of
Weightage of
Stock A in
Stock B in
Correlation
Portfolio
Portfolio
between 2 Stocks
Portfolio's
Expected Return
Portfolio Risk
Beta
Market Risk
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