fin352 vicentiu covrig 1 risk and return (chapter 4)

FIN352Vicentiu Covrig

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Risk and ReturnRisk and Return(chapter 4)(chapter 4)


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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 risk

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

The relationship between the returns for assets in the portfolio is important.


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Risk AversionRisk Aversion

Portfolio theory assumes that investors are averse to risk Given a choice between two assets with equal expected rates of

return, risk averse investors will select the asset with the lower level of risk

It also means that a riskier investment has to offer a higher expected return or else nobody will buy it


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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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Components of ReturnComponents of Return

Required Return- The return required to compensate for the amount of risk

expected. Nominal risk-free rate

- Risk-free rate- Inflation

Required risk premium- Return that varies with the risk entailed

PremiumRisk Required Inflation Expected Rate free-Risk

PremiumRisk Required Rate free-Risk NominalReturn Required


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Computing ReturnsComputing Returns Arithmetic average return

- Example 1: (0.10+0.08-0.04)/3 = 0.0467 or 4.67%

- Example 2: (0.50-0.50)/2 = 0 or 0%

Geometric mean return

- Example 1: (1.1×1.08×0.96)1/3 – 1 = 0.0448 or 4.48%

- Example 2: (1.5×0.5)1/2 – 1 = -0.134 or -13.4%

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N

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1

Return return average Arithmetic

1)100

Return1( return mean Geometric

1

1

NN

t

t


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RiskRisk Variation, or volatility of return

- Most investors probably are more interested the chance of losing money

- Standard deviation

- Example 1: {[(0.10-0.0467)2 + (0.08-0.0467)2 + (-0.04-0.0467)2] / (3-1) }1/2 = 0.0757 or 7.57%

1N

Return AverageReturn Deviation Standard

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1t

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Risk and ReturnRisk and Return Risk/Return relationship

- The greater the risk, the more return should be demanded.

- Coefficient of Variation

CoV = 7.57% / 4.67% = 1.62

Return Average

Deviation Standard Variation oft Coefficien


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Annual data, 1950 to 2007Annual data, 1950 to 2007

Long-Term Short-term

Common Treasury Treasury Inflation

Stocks Bonds Bills Rate

Arithmetic average 13.15% 6.37% 4.89% 3.87%

Median 15.40% 3.65% 4.85% 3.19%

Geometric mean 11.84% 5.92% 4.89% 3.83%

Standard deviation 17.24% 10.51% 2.71% 2.99%

Coefficent of variation 1.30 1.64 0.55 0.77


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More ReturnsMore Returns

Total Return- Includes dividends, interest, income, and capital

gains (losses) Inflation

- Reduces future buying power- Nominal return

Return with inflation included

- Real returnReturn with inflation removedReturn as a buying power measurement


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Impact of TaxesImpact of Taxes

Capital Gains- Only realized gains are taxed

- Short-term (less than one year)taxed at marginal income tax rate

- Long-term (over one year)Taxed at 20%

Dividends- Taxed at 15%

Interest Income- Taxed at marginal income tax rate


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Forming a PortfolioForming a Portfolio

Don’t put all your eggs in one basket!

The purpose of owning different types of stocks and different asset classes is diversify.

The main goal of diversification is to reduce overall investment risk.


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Statistical MeasuresStatistical Measures

The risk of a portfolio is determined by how the individual securities co-move over time.

Covariance is a measure of that co-movement:

However, the standardized measure of correlation is more popular:

- Between -1 and 1

ji

ijijij Dev. Std.Dev. Std.

CovariancenCorrelatio


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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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Portfolio Risk and ReturnPortfolio Risk and Return Expected Portfolio Return

Standard Deviation of Portfolio Returns

N

1iiiP REWRE

N

i

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iji

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ijj

jiiiP RRCOVWWRVARWRSD1 1 1

2


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Combining these investments allows for the possibility Combining these investments allows for the possibility of risk reductionof risk reduction

The goal of the investor is to form a portfolio the moves to the upper-left corner of the risk/return graph.

The very highest level of return for each level of risk desired is the efficient portfolio.

All the efficient portfolios make up the efficient frontier.

The optimal portfolio for you is the one that maximizes your utility (given your risk aversion)


2020


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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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Investor Perceptions of RiskInvestor Perceptions of Risk Portfolio theory is based on the statistics of how

investment returns co-move over time. Do people really view risk from this statistical

perspective?- No, people tend to see high returns as safe. When the markets

go up, people jump in. - Risk is felt after returns turn negative- Myopic view (short-term perspective)

After 3-years of losses, long-term investors become 3-year investors—they want out!

- House Money EffectAfter experiencing a gain, or profit, gamblers become willing to

take more risk.


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Investor Risk Perceptions Make the Use of Portfolio Investor Risk Perceptions Make the Use of Portfolio Theory Difficult for Real InvestorsTheory Difficult for Real Investors

People mentally keep track of things in separate mental “file folders,” called mental accounting. - The profits, losses, return of each investment are

considered separately.

- This makes thinking in terms of the interaction between investments difficult.

The result, is that people frequently fail to diversify.


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Learning objectivesLearning objectives

Know the concepts of risk and return.Know the components of return.Know how to calculate average and geometric meanKnow how to calculate standard deviation and the coefficient of variationFirm and market specific risksKnow the concepts of correlation and diversificationDiscuss the efficient frontier and portfolio; optimum portfolioDiscuss the investors perception of risk: myopic, house money effect and mental accountingEnd of chapter ST4.1; questions 4.1 to 4.6; CFA problems 4.1 to 4.5

fin352 vicentiu covrig 1 risk and return (chapter 4)

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