SAPM -2 - Portfolio Management

7/30/2019 SAPM -2 - Portfolio Management

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PORTFOLIO

MANAGEMENTLecture 1


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Portfolio Perspective

What is a Portfolio?

Diversification

Evaluate how individual securities contribute to risk/return

of a portfolio?

Markowitz framework: Standard deviation as a measureof risk


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Types of Clients

Individual Investors

Institutional Investors

Banks

Insurance Companies

Investment companies

Others

Characteristics

Time horizon

Risk tolerance

Income needs

Liquidity needs


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Asset Classes

Equities

Fixed Income / Bonds

Commodities

Real Estate


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Portfolio Management Process

Planning

Analyse investors objectives and constraints

Create Investor Policy Statement (IPS)

Execution

Asset Allocation

Security Analysis and Selection

Portfolio Construction

Feedback

Monitoring and rebalancing

Measurement and reporting (Evaluation)


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Pooled Investments

Mutual Funds

Open-ended / Closed Ended

Types of Fund (Stock, Bond, Index Fund)

Active/Passive

Hedge Funds

Absolute returns, high leverage, large investors

Strategies: shorting, derivatives

Private Equity Funds

Buy-out funds, Venture capital funds


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Portfolio Risk & Return

Expected Returns - E(R)

Risk Standard Deviation -

Example

Stock A Stock B+ = Portfolio

E(RA)

A

E(RB)

B

E(RP)

P

Return

Risk


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Expected Return and Standard Deviation

Excel Example

State ofEconomy Probability Return onStock A Return onStock B Return onPortfolio

1 20% 15% -5% 5%2 20% -5% 15% 5%3 20% 5% 25% 15%4 20% 35% 5% 20%5 20% 25% 35% 30%

ExpectedReturns 15.00% 15.00% 15.00%Variance 0.0200 0.0200 0.0090Standard Deviation 14.14% 14.14% 9.49%


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Diversification and Risk

Total Risk = Systematic Risk + Unsystematic Risk

Market Risk Unique Risk


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Portfolio Expected Return

()

=1

Two Securities: A and B

+

Weight (w) Expected Return (E(R)Stock A 0.6 20%Stock B 0.4 12%

Expected Return 16.80%


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Covariance and Correlation

Covariance reflects the degree to which two securitiesvary or change together.

Excel Example

Correlation () Standardized Measure

( , )

( , ) ( , )


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Correlation

Value between -1 and 1


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Portfolio Risk

Standard deviation of portfolio


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Portfolio Risk

Example

Weight Expected Return Standard DeviationStock A 0.6 20% 40%Stock B 0.4 12% 16%Correlation -1

Expected Return 16.80%Standard Deviation 17.60%


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Three Asset Portfolio

Expected Returns:

Variance:


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Matrix Multiplication


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Three Asset Example - MMULT

Portfolio weights are w' = (.3, .4, .3)

Variance-covariance matrix:


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Efficient Frontier

A portfolio of two securities

Security A Security BExpectedReturns 12% 20%StandardDeviation 20% 40%Correlation -0.2

Portfolio AProportion BProportionExpectedReturn StandardDeviation1 1 0 12.00% 20.00%2 0.9 0.1 12.80% 17.64%3 0.76 0.24 13.92% 16.27%4 0.5 0.5 16.00% 20.49%5 0.25 0.75 18.00% 29.41%6 0 1 20.00% 40.00%


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Efficient Frontier

0.00%

5.00%

10.00%

15.00%

20.00%

25.00%

0.00% 5.00% 10.00% 15.00% 20.00% 25.00% 30.00% 35.00% 40.00% 45.00%


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Efficient Frontier

Benefit of diversification

Minimum Variance

Portfolio (Portfolio C)

Feasible set oropportunity set

represented by the

curved line AB

The curve bends

backwards.

Investors invest above

MVP.


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Effect of Correlation on Diversification

A

B

r = 1r = -1

r=0O


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Effect of Correlation on Diversification


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Markowitz Efficient Frontier (Multiple

Securities)

The efficient frontier represents the set of portfolios that will give the

highest return at each level of risk or the lowest risk for each level of

return.


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Efficient Portfolio

A portfolio is efficient if there is no alternative with:

Higher expected return with same level of risk

Same expected return with lower level of risk

Higher expected return for lower level of risk


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Adding Risk-free Asset

Adding a risk-free asset can change the efficient frontier as it has no risk/variance.


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Capital Allocation Line

R

Rf

E(Rm)

CAL

+

P


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Capital Allocation Line

Y = MX + C

R

Rf

E(Rm)

CAL

P

+()


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Risk Aversion

Risk aversion refers to the behaviour of investor to prefer

less risk to more risk.

Risk averse investors:

Prefer lower to higher risk for a given level of expected return

Accept high risk investment only if expected returns are greater


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Risk Aversion (Different Investors)

Risk

E(R)

Risk Neutral

Investor


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Risk

E(R)

Risk Neutral

Investor

IP IQ

Risk Averse Investors


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Risk

E(R)

Risk Neutral

Investor

IP IQ

Risk Averse Investors

Risk Lovers


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Utility Indifference Curve

U = E(R) A * Variance U is a given level of happiness

A is the level of risk averseness

E(R) = A * Variance +U

Happiness

increases as

we move

towards left.


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Optimal Investor Portfolio

Combine Indifference curve with CAL/Efficient Frontier


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CAL Vs. CML

CML is a special case of CAL

Homogeneity of expectations

Market portfolio

R

Rf

E(Rm)

CML

M

M


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Lending vs. Borrowing portfolio

R

Rf

E(Rm)

CML

M

M


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Lending vs Borrowing portfolio

R

Rf

M

Borrowing rate > Lending rate


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Beta

A measure of volatility of a portfolio or a security in

comparison to the market.

Formula

Market Beta = 1

(,)() ,2

,


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Capital Asset Pricing Model

Investors are risk-averse, utility maximizing and rational

Frictionless markets

Single holding period

Homogenous expectations Investments are infinitely divisible

Investors are price takers


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CAPM Equation

+


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Security Market Line

1

0.8 1.2


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Question

The risk-free rate is 5%. The return on Sensex is 12%.

XYZ Corp. is 20% less volatile than the market.

Calculate the required rate of return on XYZ Corp.


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Question

The stock market is expected to generate 11% return. The

standard deviation of the market returns is 15%. ABC

Corp. is 20% more volatile than the market. Risk-free rate

is 4%.

Calculate the expected return on XYZ Corp.


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Return Generating Models

Single-factor Models

Multi-factor Models

Documents

SAPM -2 - Portfolio Management