Post on 15-Jan-2016
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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%
N
N
tt
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
N
1t
2t
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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
N
iji
N
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)
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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