- Portfolio management involves determining the optimal mix of assets to achieve an investor's objectives while balancing risk and return. The key objectives include capital growth, security, liquidity, consistent returns, and tax planning.
- Modern portfolio theory, developed by Harry Markowitz, introduced the concept of efficient portfolios which maximize return for a given level of risk. The theory uses statistical measures like variance and standard deviation to quantify risk.
- Variance and standard deviation are commonly used to measure the risk of individual assets and portfolios. The variance of a portfolio is calculated using the covariance between asset returns to determine the portfolio's total risk.
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Portfolio Management
1. PORTFOLIO MANAGEMENT
SERIAL CONTENTS
1 WHAT IS PORTFOLIO MANAGEMENT?&OBJECTIVES
2 RISK AVERSION
3 MARKOWITZ PORTFOLIO THEORY
4 ALTERNATIVE MEASURES OF RISK
5 WHAT IS EXPECTED RETURN?
6 VARIANCE (STANDARD DEVIATION) OF RETURNS FOR AN
INDIVIDUAL
7 VARIANCE (STANDARD DEVIATION) OF RETURNS FOR A
PORTFOLIO
2. WHAT IS PORTFOLIO
MANAGEMENT?
Portfolio management is the art and science of making decisions about investment
mix and policy, matching investments to objectives, asset allocation for individuals
and institutions, and balancing risk against performance. Portfolio management is
all about determining strengths, weaknesses, opportunities and threats in the
choice of debt vs. equity, domestic vs. international, growth vs. safety, and many
other trade-offs encountered in the attempt to maximize return at a given appetite
for risk.
3. OBJECTIVES OF PORTFOLIO MANAGEMENT
Objectives
Capital
Growth
Security of
Principal
Amount
Invested
Liquidity
Marketability
of Securities
Invested in
Consistent
Returns
Diversification
of Risk
Tax
Planning
4. RISK AVERSION
People are risk averse:
Portfolio theory also assumes that investors are basically risk averse, meaning that, given a
choice between two assets with equal rates of return, they will select the asset with the lower
level of risk.
Evidence that people are risk averse:
Most investors purchase various types of insurance, including life insurance, car insurance, and health
insurance.
Another evidence of risk aversion is the difference in promised yield (the required rate of return) for
different grades of bonds with different degrees of credit risk.
5. Everybody is not Risk Averse:
Everybody is not risk averse and same people is not risk averse for
all investment.
Some people have no insurance against anything, either by choice
or because they cannot afford it.
We assume that most investors with a large investment portfolio are
risk averse but with small investment they are not risk averse.
6. MARKOWITZ PORTFOLIO THEORY
• Markowitz model is a theoretical framework for analysis of risk and
return and their inter-relationships. He used the statistical analysis for
measurement of risk and mathematical programming for selection of
assets in a portfolio in an efficient manner. His framework led to the
concept of efficient portfolios. An efficient portfolio is expected to
yield the highest return for a given level of risk or lowest risk for a
given level of return.
7. THE MARKOWITZ MODEL ASSUMPTIONS
Investors consider each investment alternative as being represented by a probability
distribution of expected returns over some holding period.
Investors maximize one-period expected utility, and their utility curves demonstrate
diminishing marginal utility of wealth.
Investors estimate the risk of the portfolio on the basis of the variability of expected
returns.
Investors base decisions solely on expected return and risk, so their utility curves are a
function of expected return and the expected variance (or standard deviation) of returns only.
For a given risk level, investors prefer higher returns to lower returns. Similarly, for a
given level of expected return, investors prefer less risk to more risk.
8. ALTERNATIVE MEASURES OF RISK
One of the best-known measures of risk is the variance, or standard deviation of
expected returns. It is a statistical measure of the dispersion of returns around the
expected value whereby a larger variance or standard deviation indicates greater
dispersion. The idea is that the more dispersed the expected returns, the greater the
uncertainty of future returns.
Another measure of risk is
The Range Of Returns.
9. Although there are numerous potential measures of risk, we will use
the variance or standard deviation of returns because :
this measure is somewhat intuitive,
it is a correct and widely recognized risk measure, and
it has been used in most of the theoretical asset pricing models
10. WHAT IS EXPECTED RETURN?
The expected return on an investment is the expected value of the
probability distribution of possible returns it can provide to investors. The
return on the investment is an unknown variable that has different values
associated with different probabilities. Expected return is calculated by
multiplying potential outcomes (returns) by the chances of each outcome
occurring, and then calculating the sum of those results (as shown below).
11. (ERR OF INDIVIDUAL ASSET)
Probability Possible Rate of
Return (percent)
0.35 .08
.30 .10
.20 .12
.50 .14
Probability
(Pi)
Possible Rate of
Return (percent)
(Ri)
Expected
security return
(percent)
(Pi*Ri)
0.35 .08 .0280
.30 .10 .0300
.20 .12 .0240
.50 .14 .0210
Total .1030
10.3%
12. Expected Return of portfolio refers to the expected rate of return on
investments and is often calculated by applying the weights of all
the Investments in the portfolio with their respective returns and
then doing the sum total of results.
13. ( PORTFOLIO EXPECTED RATE OF RETURN)
Securities
Amount of
investment
Expected
security
return E(Ri)
A 20000 .10
B 30000 .11
C 30000 .12
D 20000 .13
Securities Weight(Wi)
Expected
security return
E(Ri)
Expected
Portfolio
Return(Wi*Ri)
A .20 .10 .0200
B .30 .11 .0330
C .30 .12 .0360
D .20 .13 .0260
0.1150
E(Rport
) =
𝑖=1
𝑛
𝑊𝑖𝑅𝑖
where:
Wi = The weight of an individual asset in the portfolio, or the percent of
the portfolio in Asset I
Ri = The expected rate of return for Asset I
Company X Want To Invest 100000 In 4 Security As Per Following:
15. VARIANCE (STANDARD DEVIATION) OF
RETURNS FOR PORTFOLIO
Two basic concepts in statistics, Covariance and Correlation, must be
understood before we discuss the formula for the variance of the rate of
return for a portfolio.
Covariance: Covariance is a measure of the degree to which two
variable move together relative to their individual mean values over
time.
Correlation: Correlation analysis is a statistical tool we can use to
describe the degree to which one variable is linearly related to another.
16. CALCULATE VARIANCE & COVARIANCE OF THE
PORTFOLIO?
Date ‘’X” COMPANY
Monthly rate of return
‘’Y’’ COMPANY
Monthly rate of return
JAN -04
FEB-04
MAR-04
APR-04
MAY-04
JUN-04
JUL-04
AUG-04
SEP-04
OCT-04
NOV-04
DEC-04
2.23
1.46
-1.07
-2.13
1.38
2.08
-3.82
0.33
1.78
1.71
4.68
3.63
Mean=1.02
1.77
2.00
1.50
-5.59
-0.54
0.95
1.73
3.74
0.84
1.51
-2.19
2.31
Mean= 0.67
18. Calculation of variance of X company
𝜎𝑖
2
=
1
11
62.36 = 5.67
Calculation of variance of Y company
𝜎𝑗
2
=
1
11
66.56= 6.05
Calculation of Standard deviation of X company
𝜎𝑖= 5.67=2.38
Calculation of Standard deviation of X company
𝜎𝑗= 6.05=2.46
