File282611043.pptx

Risk and Rates of Return   

Stand-alone risk Portfolio risk Risk & return: CAPM / SML

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Lecture Overview • • • • •

Concept Calculating a return Measuring Risk: part I Reproducing Risk through Diversification Measuring Risk: part II Beta

• Capital Asset Pricing Model Risk free + Risk premium

• Summary

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Motivating the topic: Risk and Return The relationship between risk and return is fundamental in Finance theory. If given choice between:  Investing in a low-risk opportunity that says it will pay you a 10% return on your money, or  Investing in a high-risk opportunity that says it will pay you a 10% return on your money  Most people would the lower risk opportunity

The principle we follow in finance is that investors need the inducement of higher reward to take perceived higher risk.

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Investment returns The rate of return on an investment can be calculated as follows: (Amount received – Amount invested)

Return =

________________________ Amount invested

For example, if $1,000 is invested and $1,100 is returned after one year, the rate of return for this investment is: ($1,100 - $1,000) / $1,000 = 10%.

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Defining a Return on an Investment • We invest in a stock with the hope of earning a positive return on our investment. • We need a way to measure this return. • Example with stock, we have two components that contribute to our return:  We can received a dividend payment  The stock-price itself can appreciate

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Calculating a Return on a Stock • Stocks have 2 “returns” components;  Dividend  Stock price appreciation

Percentage return

=

End. Price-Beg. price Beg. Price

+

Dividend Beg. Price

Percentage return = Capital Gains Yield + Dividend Yield

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Calculating a Return on a Stock • Example :  Assume we purchased one share of stock at $25 and received $2 in dividends during the year. After one year the stock price increase to $31 . So what is the percentage return we achieved? Percentage return = Capital Gains Yield + Dividend Yield Percentage return=(31-25)/25 + 2/25 = 24% + 8% = 32%

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Historic vs. Required Returns • The previous example calculated what actually happened. We call this a “historic” return. • However prior to making the investment we may have the expected return of 50%  In this case, what actually happened fell short our expectations.

• Alternatively, maybe our expectations were to earn only 10%  In this case, the actual returns exceeded our expectations.

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What is investment risk? • Two types of investment risk • Stand-alone risk • Portfolio 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. 5-9

Measure Risk: part I - Volatility • It’s useful to have mathematical tool so that we can measure risk. • A common approach is to look at a distribution of either historic or projected returns and calculate volatility (either the standard deviation or variance) of the returns. • The following slide shoes two different “distributions” superimposed.

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Probability distributions • A listing of all possible outcomes, and the probability of each occurrence. • Can be shown graphically. Firm X

Firm Y -70

0

15

Expected Rate of Return

100

Rate of Return (%)

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Standard deviation as a measure of risk • Standard deviation (σi) measures total, or stand-alone, risk. • The larger σi is, the lower the probability that actual returns will be closer to expected returns. • Larger σi is associated with a wider probability distribution of returns.

• Difficult to compare standard deviations, because return has not been accounted for.

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Formula for Standard Deviation and Variance σ= Standard Deviation σ^2= Variance

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Coefficient of Variation (CV) A standardized measure of dispersion about the expected value, that shows the risk per unit of return.

Std dev  CV   ^ Mean k

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Illustrating the CV as a measure of relative risk Prob.

A

B

0

Rate of Return (%)

σA = σB , but A is riskier because of a larger probability of losses. In other words, the same amount of risk (as measured by σ) for less returns. 5-17

Diversifying risk: Portfolios  In the beginning of the lecture we saw that higher risks must come with (the potential for) higher returns.  More volatile stocks should have on average higher returns.  We can reduce Volatility for given level of return by grouping assets into portfolios.  This is known as “ Diversifying Risk”

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Diversifying risk: Example  In a given year a particular pharmaceutical company may fail in getting approval of a new drug, those causing its stock price to drop.  But unlikely that every pharmaceutical company will fail major drug trials in the same year.  On average, some are likely to be successful while others will fail  Therefore the returns for portfolio comprised of all drugs companies will have much less volatility than that a single drug company.

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Diversifying risk: Example (continuation)

 By holding stocks in the entire sector of pharmaceutical we have eliminated quite a bit risk as just described.  But it’s possible that there is a sector-level risk that may impact all drug companies.  For example if FDA changes it’s drug approval policy and requires all new drugs to go through more strict testing we would expect the entire sector and our portfolio comprised all pharmaceutical companies to “suffer”.  But what if we held a portfolio of not just pharmaceuticals but also computer companies, manufacturing companies, service companies and even real estate, commodities and other major assets? 5-20

Diversifying risk: Example (continuation)

 We would expect this expanded portfolio to be even less risky than a portfolio of just one sector.  Such market portfolio would still have uncertainty and risk but it would be greatly reduced compare to just one asset or even a group of related assets.  So there is two components of risk  Firm-specific risk (or asset specific risk) also called diversified risk, unsystematic risk.  Market risk (or systematic risk, non diversifiable risk)

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Breaking down sources of risk Stand-alone risk = Market risk + Firm-specific risk

• Market risk – portion of a security’s stand-alone risk that cannot be eliminated through diversification. Measured by beta. • Firm-specific risk – portion of a security’s standalone risk that can be eliminated through proper diversification.

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Illustrating diversification effects of a stock portfolio p (%) 35

Company-Specific Risk Stand-Alone Risk, p

20 Market Risk 0

10

20

30

40

2,000+

# Stocks in Portfolio 5-24

Creating a portfolio: Beginning with one stock and adding randomly selected stocks to portfolio • σp decreases as stocks added, because they would not be perfectly correlated with the existing portfolio. • Expected return of the portfolio would remain relatively constant. • Eventually the diversification benefits of adding more stocks dissipates (after about 10 stocks), and for large stock portfolios, σp tends to converge to  20%. 5-25

Failure to diversify  If an investor chooses to hold a one-stock portfolio (exposed to more risk than a diversified investor), would the investor be compensated for the risk they bear?

 NO!  Stand-alone risk is not important to a well-diversified investor.  Rational, risk-averse investors are concerned with σp, which is based upon market risk.  There can be only one price (the market return) for a given security.  No compensation should be earned for holding unnecessary, diversifiable risk. 5-26

Measuring Risk: part II-Beta • Measures a stock’s market risk, and shows a stock’s volatility relative to the market. • Indicates how risky a stock is if the stock is held in a welldiversified portfolio.

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Calculating betas  Run a regression of past returns of a security against past returns on the market.  The slope of the regression line (sometimes called the security’s characteristic line) is defined as the beta coefficient for the security.  Finding betas:  The easiest way to find betas is look them up. Many companies provide betas:     

Value Line Investment Survey Hoovers MSN Money Yahoo! Finance Zacks

 You can also calculate beta for yourself 5-29

Illustrating the calculation of beta _ ki 20

.

15

.

10

Year 1 2 3

kM 15% -5 12

ki 18% -10 16

5

-5

.

0 -5 -10

5

10

15

_

20

kM

Regression line:

^ ^ k = -2.59 + 1.44 k i

M

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Comments on beta • If beta = 1.0, the security is just as risky as the average stock. • If beta > 1.0, the security is riskier than average. • If beta < 1.0, the security is less risky than average. • Most stocks have betas in the range of 0.5 to 1.5.

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Can the beta of a security be negative? • Yes, if the correlation between Stock i and the market is negative (i.e., ρi,m < 0). • If the correlation is negative, the regression line would slope downward, and the beta would be negative. • However, a negative beta is highly unlikely.

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

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What is the market risk premium? • Additional return over the risk-free rate needed to compensate investors for assuming an average amount of risk. • Its size depends on the perceived risk of the stock market and investors’ degree of risk aversion. • Varies from year to year, but most estimates suggest that it ranges between 4% and 8% per year. 5-34

Capital Asset Pricing Model (CAPM) • Model based upon concept that a stock’s required rate of return is equal to the risk-free rate of return plus a risk premium that reflects the riskiness of the stock after diversification. • Primary conclusion: The relevant riskiness of a stock is its contribution to the riskiness of a welldiversified portfolio.

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Capital Asset Pricing Model (CAPM) example: • The CAPM equation allows us to estimate any stock’s beta, risk-free rate and market-risk premium. Let’s say we expect the market portfolio to earn 12%, and treasury bond yield are 3.5%. If Home Depot has beta of 1.08 we can calculate the required return for holding the stock as follows:

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Verifying the CAPM empirically • The CAPM has not been verified completely. • Statistical tests have problems that make verification almost impossible. • Some argue that there are additional risk factors, other than the market risk premium, that must be considered.

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More thoughts on the CAPM • Investors seem to be concerned with both market risk and total risk. Therefore, the SML may not produce a correct estimate of ki. ki = kRF + (kM – kRF) βi + ??? • CAPM/SML concepts are based upon expectations, but betas are calculated using historical data. A company’s historical data may not reflect investors’ expectations about future riskiness. 5-38

Summary • We need the expectation of the extra reward for taking on more risk. • An asset’s risk premium is the additional compensation required above the risk-free rate for holding the asset. • At the market level, the market risk premium is the additional return above the risk-free rate to hold the market portfolio • For a given asset, the CAPM will tell us how much return we will require for holding the asset relative to the risk-free rate and market portfolio.

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