The Trade-off Between Risk and Return
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© 2009 Cengage Learning/South-Western The Trade-off Between Risk and Return Chapter 6
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© 2009 Cengage Learning/South-Western
The Trade-off Between Risk and Return
Chapter 6
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The Trade-off Between Risk and Return
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The Trade-off Between Risk and Return
Risk represents the marginal cost of investing.
A trade-off always arises between expected risk and expected return.
The return earned on investments represents the marginal benefit of investing.
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Valuing risky assets is a task fundamental to financial management
1. Determine the asset’s expected cash flows2. Choose discount rate that reflects asset’s
risk3. Calculate present value (PV cash inflows -
PV outflows)This three-step procedure is called
discounted cash flow (DCF) analysis.
The Trade-off Between Risk and Return
Three-step procedure for valuing a risky asset
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Total return: the total gain or loss experienced on an investment over a given
period of time
Component
s of the total
return
Income stream from the investment
Capital gain or loss due to changes in asset prices
Total return can be expressed either in dollar terms or in percentage terms.
Understanding Returns
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Total dollar return = income + capital gain or loss
Terrell bought 100 shares of Micro-Orb stock for $25
A year later:Dividend = $1/shareSold for $30/share
Dollar return
= (100 shares) x ($1 + $5)
= $600
Owen bought 50 shares of Garcia Inc. stock for $15
A year later:No dividends paidSold for $25/share
Dollar return
= (150 shares) x ($15)
= $500
Dollar Returns
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Terrell’s dollar return exceeded Owen’s by $100. Can we say that Terrell was better off?
No, because Terrell and Owen’s initial investments were different: Terrell spent $2,500 in initial
investment, while Owen spent $750.
investment initialreturndollar total
return percentage Total
Percentage Returns
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%2424.0
500,2$
5$1$100returnpercentage sTerrell'
%6767.0
750$
10$50return percentage sOwen'
In percentage terms, Owen’s investment performed better than Terrell’s did.
Percentage Returns
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The History of Returns: Nominal ReturnsThe Value of $1 Invested in Stocks, Treasury Bonds, and Bills
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The History of Returns: Real ReturnsThe Real Value of $1 Invested in Stocks, Treasury Bonds, and Bills
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Risk premium: the additional return that an investment must offer, relative to some
alternative, because it is more risky than the alternative.
The Risk Dimension
Percentage Returns on Bills, Bonds, and Stocks, 1900 - 2006
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Percentage Returns on Bills, Bonds, and Stocks, 1900–2006
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Percentage Returns on Stocks, Treasury Bonds and Bills, 1900 - 2006
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Table 6.2 Risk Premiums for Stocks, Bonds, and Bills, 1900–2006
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Asset classes with greater volatility pay higher average returns.
• Average return on stocks is more than double the average return on bonds, but stocks are 2.5 times more volatile.
Volatility and Risk
Average Returns and Standard Deviation for Equities, Bonds, and Bills, 1900 - 2006
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We can approximate the unknown probability distribution for future stock returns by assuming a normal distribution.
The Distribution of Historical Stock Returns1900 - 2006
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Normal distribution can be described by its mean and its variance.
• Variance (2) – a measure of volatility in units of percent squared
1
)(Variance 1
2
2
N
RRN
tt
The Variability of Stock Returns
• Standard deviation – a measure of volatility in percentage terms
Variancedeviation Standard
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Table 6.3 Estimating the Variance of Stock Returns from 1994–2006
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Table 6.4 Average Returns and Standard Deviation for Equities, Bonds, and Bills, (1900–2006)
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Fig. 6.6 The Relationship Between Average (Nominal) Return and Standard Deviation for Stocks, Treasury Bonds, and Bills, 1900 - 2006
• Investors who want higher returns have to take more risk.• The incremental reward from accepting more risk is constant.
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From 1994 – 2006, the standard deviation of the typical stock in the U.S. was abut 60% per year, while the standard deviation of the entire stock market was only 19.8%!
The Power of DiversificationAverage Returns and Standard Deviations for 11 Stocks, 1994-2006
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Most individual stock prices show higher volatility than the price volatility of a portfolio of all common
stocks.
How can the standard deviation for individual stocks be higher than the standard deviation of the portfolio?
Diversification: The act of investing in many different assets rather than just a few, so as to
reduce volatility.
The ups and downs of individual stocks partially cancel each other out.
The Power of Diversification
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Annual Returns on Coca-Cola and Wendy’s International
• The two stocks did not always move in sync. • The net effect is that the portfolio is less volatile than either
stock held in isolation.
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Average Returns and Standard Deviations of Portfolios of Stocks and Bonds, 1972 - 2006
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The Relationship Between Portfolio Standard Deviation and the Number of Stocks in the Portfolio
• The risk that diversification eliminates is called unsystematic risk.• The risk that remains, even in a diversified portfolio, is called
systematic risk.
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Diversification reduces portfolio volatility, but only up to a point. Portfolio of all stocks still
has a volatility of 19.8%.
Systematic risk: the volatility of the portfolio that cannot be eliminated through
diversification.
Unsystematic risk: the proportion of risk of individual assets that can be eliminated
through diversification
What really matters is systematic risk….how a group of assets move together.
Systematic and Unsystematic Risk
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Risk and Return Revisited
• For the various asset classes, a trade-off arises between risk and return.
Does this trade-off hold for individual securities?
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No obvious pattern here!
Average Returns and Standard Deviations for 11 Stocks, 1994-2006
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Anheuser-Busch had a higher average return than Archer Daniels Midland, and with smaller volatility.
American Airlines had a much smaller average return than Wal-Mart, with similar volatility.
The tradeoff between standard deviation and average returns that holds for asset classes does
not hold for individual stocks!
Because investors can eliminate unsystematic risk through diversification, market rewards only
systematic risk.
Standard deviation contains both systematic and unsystematic risk.
Risk and Return Revisited
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Risk Premiums Around the World
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• Investment performance is measured by total return.
• Trade-off between risk and return for assets: historically, stocks have higher returns and volatility than bonds and bills.
• One measure of volatility: standard deviation
• Systematic risk: risk that cannot be eliminated through diversification
The Trade-off Between Risk and Return
