1. SYNOPSIS
๏ผ Efficient Market Theory
๏ผ Portfolio Analysis โ Markowitz theory
๏ผ Sharpeโs optimum portfolio construction
๏ผ Capital Asset Pricing Model (CAPM)
2. Efficient Market Theory
๏ Efficient Market theory states that the share price fluctuations are
random and do not follow any regular pattern.
Features of Efficient Market
๏ All instruments are correctly priced as all available information is
perfectly understood and absorbed by all the investors.
๏ No excess profits are possible.
๏ In a perfectly efficient market, analysts immediately compete away any
chance of earning abnormal profits.
๏ The forces of demand and supply move freely and in an independent
and random manner.
3. The three forms of market efficiency
Weak form: Market pricing information includes only past prices
Semi-strong form: includes public information
Strong form: includes public and private information
4. Portfolio Analysis
๏ Portfolio is a combination of securities such as
stocks, bonds, etc.
๏ The process of blending together these securities
so as to obtain optimum return with minimum
risk is called portfolio construction.
๏ A rational investor always attempts to minimize risk
and maximize return on his investment.
๏ Investing in more than one security is a strategy to
attain this goal.
5. Markowitz Theory
๏ Markowitz is considered the father of modern portfolio
theory, mainly because he is the first person who gave a
mathematical model for portfolio optimization and diversification.
๏ Modern portfolio theory (MPT) is a theory of finance that attempts
to maximize portfolio expected return for a given amount of
risk, or minimize the risk for a given level of expected return.
๏ Markowitz theory' advise investors to invest in multiple securities
rather than pulling all eggs in one basket.
6. Markowitz model โ Portfolio
The portfolio return can be calculated with the help of the
following formula:
= return on the portfolio
= proportion of total portfolio investment in security 1
= expected return on security 1
7. Markowitz model โ Portfolio risk
The portfolio risk can be calculated with the help of the following formula:
ฯ p = โ X1
2 ฯ1
2 + X2
2 ฯ2
2 + 2 X1 X2 ( r12 ฯ1 ฯ2)
ฯ p = Portfolio standard deviation
X1 = Percentage of total portfolio value in stock X1
X2 = Percentage of total portfolio value in stock X2
ฯ1 = Standard deviation of stock X1
ฯ2 = Standard deviation of stock X2
r12 = correlation co-efficient of X1 and X2
r12 = Covariance of X 12
ฯ1 ฯ2
8. Sharpeโs optimum portfolio construction
๏ William Sharpe, tried to simplify the process of data inputs and reaching a
solution, by developing a simplified variant of the Markowitz model.
๏ In the Sharpeโs model the desirability of any securities' inclusion in the
portfolio is directly related to its excess return-to-beta ratio. Then they
are ranked from highest to lowest order.
๏ The number of securities selected depends on a unique Cut- off rate such
that all securities with higher ratios will be included.
๏ Percentage of investment in each of the selected security is then decided
on the basis of respective weights assigned to each security.
9. Constructs of Sharpeโs single index model
ฮฒ =
Correlation Coefficient
Between Market and Stock
ร
Standard Deviation of Stock
Returns
Standard Deviation of Market
Returns
10. Cut- off Point
๏ = variance of the market index
๏ = variance of a stockโs movement that is not
associated with the movement of market index i.e.
stockโs unsystematic risk.
17. Capital Asset Pricing Model (CAPM)
CAPM is used to determine a theoretically appropriate required rate of
return of an asset, if that asset is to be added to an already well-
diversified portfolio, given that asset's non-diversifiable risk.
18. Let us say that stock A has a beta (Bi = .5%), the risk free rate of return (Rf = 4%)
and the expected rate of return for the market (Rm = 10%).
Calculate the expected rate of return for the asset?
19. Assumptions of CAPM
All investors:
๏ Aim to maximize economic utilities and are rational and risk-averse.
๏ Are broadly diversified across a range of investments.
๏ Are price takers, i.e., they cannot influence prices.
๏ Can lend and borrow unlimited amounts under the risk free rate of interest.
๏ Trade without transaction or taxation costs.
๏ Deal with securities that are all highly divisible into small parcels.
๏ Assume all information is available at the same time to all investors.
๏ Further, the model assumes that standard deviation of past returns is a perfect
proxy for the future risk associated with a given security