Capital Market Line:
It shows the relationship between risk
(standard deviation) and return of risk free asset and market portfolio (All
the financial investment available in proportion of they are available in a
market). The slope of the Capital Market Line shows the price of market risk.
The efficient portfolio is a reward for waiting and bearing a risk of holding
that portfolio for specified period.
In the above diagram standard deviation is shown in X axis
and expected return and risk free asset. The curve shown in the diagram is
known as efficient frontier curve. If
the investors prefer less risk then they must lying between risk free asset points
to market portfolio point. Between these two points investor can lend money to
government by buying treasury bills, government bonds on risk. If the investors
are interested in taking more risk to earn high return, then those investors lying
beyond the market portfolio point. And beyond the market portfolio point the
investor can borrow funds on risk free rate for buying risky assets.
Difference between Capital Market Line and Security Market
Line:
·
The CML shows the total risk as standard
deviation while the SML shows market risk as beta.
·
The efficient frontier curve shown in CML only
while inefficient portfolio shown in SML.
·
The capital market line shows risk and return
relationship as a whole market while the relationship of risk and return of
single stock is shown by security market line.
Formula:
E(R_{p})
= R_{f} + Ïƒ_{p} ((R_{m}
– R_{f}) / Ïƒ_{m})
Where,
E(R_{p}) = Expected return of a portfolio
R_{f} = Risk free rate of return
Ïƒ_{p} = Standard deviation of a portfolio
Ïƒ_{m} = Standard deviation of market
R_{m} = Market rate of return
Example: Find out
the expected return of a portfolio if the market standard deviation is 23% and
risk free rate is 4%. The market return is 12% and the standard deviation of
portfolio is 5%.
Solution:
E(R_{p}) = R_{f} + Ïƒ_{p} ((R_{m} –
R_{f}) / Ïƒ_{m})
= 4 + 5 ((12 – 4) / 23
= 4 + 5*0.35
= 4 + 1.75
= 5.75%
Example: Find out
the expected return of given portfolio with the help of given information:
Portfolio

Standard
deviation of portfolio (in %)

Risk
free rate in %)

Expected
market return

Standard
deviation of market portfolio

A

2

3

13

5

B

8

3

18

4

C

4

3

9

8

D

6

3

11

2

Solution:
E (R_{p}) = R_{f} + Ïƒ_{p} ((R_{m} –
R_{f}) / Ïƒ_{m})
Portfolio A:
= 3 + 2 ((13 – 3) / 5)
= 3 + 2*2
= 3 + 4
= 7%
Portfolio B:
= 3 + 8 ((18 3) /4)
= 3 + 8*3.75
= 3 + 30
= 33%
Portfolio C:
= 3 + 4((9 – 3) / 8)
= 3 + 4*0.75
= 3 + 3
= 6%
Portfolio D:
= 3 + 6((11 3) / 2)
= 3 + 6*4
= 3 + 24
= 27%
Example: Find out which portfolio gives higher return from
the given information:
Portfolio

Standard
deviation of portfolio (in %)

Risk
free rate in %)

Expected
market return

Standard
deviation of market portfolio

P

6

4

11

3

Q

1

4

12

2

R

5

4

10

7

Solution: E (R_{p}) = R_{f} + Ïƒ_{p}
((R_{m} – R_{f}) / Ïƒ_{m})
Portfolio P:
= 4 + 6((11  4) / 3)
= 18%
Portfolio Q:
= 4 + 1((12  4) / 2)
= 8%
Portfolio R:
= 4 + 5((10 4) / 7)
= 8.29%
Portfolio P has higher expected return in comparison to
portfolio Q and R.
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