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Portfolio managementPortfolio management

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“ Never tell people how to do things. Tell them what to do and they will surprise you with their ingenuity”

General George Patton

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How Finance is organizedHow Finance is organized

Corporate finance

Investments

International Finance Financial Derivatives

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Risk and ReturnRisk and Return

The investment process consists of two broad tasks:

• security and market analysis

• portfolio management

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Risk and ReturnRisk and Return

Investors are concerned with both:

Expected return: comes from a valuation model

Risk

As an investor you want to maximize the returns for a given level of risk.

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Return: Calculating the expected return Return: Calculating the expected return for each alternativefor each alternative

occurs outcomeeach y that probabilit p

outcomeeach for return expected k

outcomes ofnumber n where

kP....kP k

return of rate expected k

nn11

^

^

Outcome Prob. of outcome Return in 1(recession) .1 -15%2 (normal growth) .6 15%

3 (boom) .3 25%

k^ =expected rate of return = (.1)(-15) + (.6)(15) +(.3)(25)=15%

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What is investment risk?What is investment risk? Investment risk is related to the probability of earning a low or negative

actual return. The greater the chance of lower than expected or negative returns, the riskier

the investment.

Expected Rate of Return

Rate ofReturn (%)100150-70

Firm X

Firm Y

Firm X (red) has a lower distribution of returns than firm Y (purple) though both have the same average return. We say that firm X’s returns are less variable/volatile (lower standard deviation ) and thus X is a less risky investment than Y

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Selected Realized Returns, Selected Realized Returns, 1926 – 20061926 – 2006

Average Standard Return Deviation

Small-company stocks 18.4% 36.9%Large-company stocks 12.2 20.2L-T corporate bonds 5.8 9.4L-T government bonds 5.6 8.1U.S. Treasury bills 3.7 3.1

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Investor attitude towards risk:Investor attitude towards risk:Does it matter?Does it matter?

Risk aversion – assumes investors dislike risk and require higher rates of return to encourage them to hold riskier securities.

Some individuals are risk lovers, meaning that they purchase/ invest in instruments with negative expected rate of return

Ex:

Risk premium – the difference between the return on a risky asset and less risky asset, which serves as compensation for investors to hold riskier securities

Very often risk premium refers to the difference between the return on a risky asset and risk-free rate (ex. a treasury bond)

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Top Down Asset AllocationTop Down Asset Allocation

1. Capital Allocation decision: the choice of the proportion of the overall portfolio to place in risk-free assets versus risky assets.

2. Asset Allocation decision: the distribution of risky investments across broad asset classes such as bonds, small stocks, large stocks, real estate etc.

3. Security Selection decision: the choice of which particular securities to hold within each asset class.

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TerminologyTerminology Investment (portfolio) management: professional

management of a collection (i.e. portfolio) of securities to meet specific goals for the benefit of investors

Asset management is similar to Investment or Portfolio Management

Wealth manager is more of a broker , financial manager or investment advisor for wealthy clients

Portfolio management involve a long investment horizon Trading focuses on securities selection with a short term

horizon

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Top Down Asset allocationTop Down Asset allocation Capital Allocation decision: the choice of the proportion of

the overall portfolio to place in risk-free assets versus risky assets

Asset Allocation decision: the distribution of risky investments across broad asset classes such as bonds, small stocks, large stocks, real estate etc.

Security Selection decision: the choice of which particular securities to hold within each asset class.

90% of the portfolio performance is determined by the first two steps

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Portfolio ManagementPortfolio Management A properly constructed portfolio achieves a given level of

expected return with the least possible risk

Portfolio management primarily involves reducing risk rather than increasing return

The investment horizon is intermediate to long term

Portfolio managers have a duty to create the best possible collection of investments for each customer’s unique needs and circumstances

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Tactical Asset AllocationTactical Asset Allocation Also known as Market Timing

Shifting the relative proportion of the asset classes in the portfolio

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Portfolio ManagementPortfolio Management

The heart of the Portfolio Management is the concept of diversification

The empirical evidence shows that the markets are quite efficient

Passive (Indexing) vs. Active Investing

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Expected Portfolio Rate of ReturnExpected Portfolio Rate of Return

- Weighted average of expected returns (Ri) for the individual investments in the portfolio

- Percentages invested in each asset (wi) serve as the weights

E(Rport) = wi Ri

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Portfolio Risk (two assets only)Portfolio Risk (two assets only)

When two risky assets with variances 12 and 2

2, respectively, are combined into a portfolio with portfolio weights w1 and w2, respectively, the portfolio variance is given by:

p2

= w121

2 + w222

2 + 2W1W2 Cov(r1r2)

Cov(r1r2) = Covariance of returns for Security 1 and Security 2

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Correlation between the returns of two securitiesCorrelation between the returns of two securities

Correlation, : a measure of the strength of the linear relationship between two variables

21

21 ),cov(

RR

-1.0 < < +1.0 If= +1.0, securities 1 and 2 are perfectly positively

correlated If= -1.0, 1 and 2 are perfectly negatively correlated If= 0, 1 and 2 are not correlated

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Efficient Diversification Efficient Diversification

Let’s consider a portfolio invested 50% in an equity mutual fund and 50% in a bond fund.

Equity fund Bond fundE(Return) 11% 7%Standard dev. 14.31% 8.16%Correlation -1

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Portfolo Risk and Return Combinations

5.0%

6.0%

7.0%

8.0%

9.0%

10.0%

11.0%

12.0%

0.0% 2.0% 4.0% 6.0% 8.0% 10.0% 12.0% 14.0% 16.0%

Portfolio Risk (standard deviation)Po

rtfol

io R

etur

n

% in stocks Risk Return0% 8.2% 7.0%5% 7.0% 7.2%10% 5.9% 7.4%15% 4.8% 7.6%20% 3.7% 7.8%25% 2.6% 8.0%30% 1.4% 8.2%35% 0.4% 8.4%40% 0.9% 8.6%45% 2.0% 8.8%

50.00% 3.08% 9.00%55% 4.2% 9.2%60% 5.3% 9.4%65% 6.4% 9.6%70% 7.6% 9.8%75% 8.7% 10.0%80% 9.8% 10.2%85% 10.9% 10.4%90% 12.1% 10.6%95% 13.2% 10.8%

100% 14.3% 11.0%

100% bonds

100% stocks

Note that some portfolios are “better” than others. They have higher returns for the same level of risk or less. We call this portfolios EFFICIENT.

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The Minimum-Variance FrontierThe Minimum-Variance Frontierof Risky Assetsof Risky Assets

E(r)

Efficientfrontier

Globalminimum

varianceportfolio Minimum

variancefrontier

Individualassets

St. Dev.

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Two-Security Portfolios with Various Two-Security Portfolios with Various Correlations Correlations

100% bonds

retu

rn

100% stocks

= 0.2

= 1.0

= -1.0

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The benefits of diversificationThe benefits of diversification

Come from the correlation between asset returns

The smaller the correlation, the greater the risk reduction potential greater the benefit of diversification

If= +1.0, no risk reduction is possible

Adding extra securities with lower corr/cov with the existing ones decreases the total risk of the portfolio

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Estimation IssuesEstimation Issues Results of portfolio analysis depend on accurate statistical inputs Estimates of

- Expected returns - Standard deviations- Correlation coefficients

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Portfolio Risk as a Function of the Number of Portfolio Risk as a Function of the Number of Stocks in the PortfolioStocks in the Portfolio

Nondiversifiable risk; Systematic Risk; Market Risk

Diversifiable Risk; Nonsystematic Risk; Firm Specific Risk; Unique Risk

n

Portfolio risk

Thus diversification can eliminate some, but not all of the risk of individual securities.

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M

E(rp)

CAL (Globalminimum variance)

CAL (A)CAL (O)

O

A

rf

O M

A

G

O

M

p

Optimal Risky Portfolios and a Risk Free AssetOptimal Risky Portfolios and a Risk Free Asset