Upload
abraham-devereaux
View
219
Download
3
Tags:
Embed Size (px)
Citation preview
Berlin, 04.01.2006 Fußzeile 1
The Trade-off Between
Risk and Return
Professor Dr. Rainer Stachuletz
International Markets and Corporate Finance
Berlin School of Economics and Law
Berlin, 04.01.2006 Fußzeile 2
Risk and Return
The return earned on investments represents the marginal benefit of investing.
Risk represents the marginal cost of investing.
A trade-off always arises between expected risk and expected return.
Berlin, 04.01.2006 Fußzeile 3
Risk and Return
Valuing risky assets - a task fundamental to financial management
Three-step procedure for valuing a risky asset
1. Determine the asset’s expected cash flows2. Choose discount rate that reflects asset’s risk3. Calculate present value (PV cash inflows - PV
outflows)The three-step procedure is called
discounted cash flow (DCF) analysis.
Berlin, 04.01.2006 Fußzeile 4
Financial Return
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.
Berlin, 04.01.2006 Fußzeile 5
Dollar Returns
Total dollar return = income + capital gain / 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 = (50 shares) x ($10)
= $500
Berlin, 04.01.2006 Fußzeile 6
Percentage Returns
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 $750.
Percentage return: total dollar return divided by the initial investment
investment initial
return dollar totalreturn percentage Total
Berlin, 04.01.2006 Fußzeile 7
Percentage Returns
%2424.0
500,2$
5$1$100 '
returnpercentagesTerrell
%6767.0
750$
10$50 '
returnpercentagesOwen
In percentage terms, Owen’s investment performed better than Terrell’s
Berlin, 04.01.2006 Fußzeile 8
$1 Investment in Equities, Treasury Bonds and Bills
Year
$15,579
$148
$61
$22
10,000
100,000
1,000
100
10
1
Equities Bonds
Bills Inflation
1900 1920 1940 1960 1980 2000 2003
Berlin, 04.01.2006 Fußzeile 9
Percentage Returns on BillsBonds, and Stocks
Difference between average return of stocks and bills = 7.6%
Difference between average return of stocks and bonds = 6.5%
Risk premium: the difference in returns offered by a risky asset relative to the risk-free return
available
Nominal (%) Real (%)Asset Class Average Best Year Worst Year Average Best Year Worst Year
Bills 4.1 14.7 0.0 1.1 19.7 -15.1Bonds 5.2 40.4 -9.2 2.3 35.1 -19.4Stocks 11.7 57.6 -43.9 8.5 56.8 -38
Berlin, 04.01.2006 Fußzeile 10
Distribution of Historical Stock Returns, 1900 - 2003
Histogram of Nominal Returns on Equities 1900-2003
<-30 -30 to -20 to -10 to 0 to 10 to 20 to 30 to 40 to >50 -20 -10 0 10 20 30 40 50
Percent return in a given year
Probability distribution for future stock returns is unknown. We can approximate the unknown distribution by assuming a normal
distribution.
Berlin, 04.01.2006 Fußzeile 11
Variability of Stock Returns
Normal distribution can be described by its mean and its variance.
Variance (2) - the expected value of squared deviations from the mean
1
)(1
2
2
N
RRVariance
N
tt
Variance (%-squared) - hard to interpret, so calculate standard deviation, a measure of volatility equal to
square root of 2
Berlin, 04.01.2006 Fußzeile 12
Volatility of Asset Returns
Asset Average(%) Std. Dev. (%) Average(%) Std. Dev. (%)
Equities 11.7 20.1 8.5 20.4Bonds 5.2 8.2 2.3 10Bills 4.1 2.8 1.1 4.7
Nominal Returns Real Returns
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.
Berlin, 04.01.2006 Fußzeile 13
Average Returns and St. Dev. for Asset Classes
1. Investors who want higher returns have to take more risk2. The incremental reward from accepting more risk seems
constant
Bills Bonds
Stocks
Average Return (%)
Standard Deviation (%)
Berlin, 04.01.2006 Fußzeile 14
Average Return / Standard Dev.Individual Securities, 1994-2003
For various asset classes, a trade-off arises between risk and return. Does the trade-off appear to hold for all individual
securities?
Company Average Return(%) Std Deviation(%)
Anheuser-Busch 19.2 16.1Coca Cola 12.1 22.6Wendy's International 11.8 23.3Archer Daniels Midland 7.6 23.5General Motors 8.3 26.0General Electric 20.3 32.1Merck 17.8 32.7Nordstrom 14.3 38.1Wal-Mart 22.7 44.7American Airlines (AMR) 10.0 47.8Advanced Micro Devices (AMD) 17.6 56.4Average for all 11 stocks 14.7 33.0Average for U.S stocks 12.5 21.0
Berlin, 04.01.2006 Fußzeile 15
Average Return (%)
Standard Deviation (%)
Wal-MartAnheuser-Busch
Archer Daniels Midland
American Airlines
No obvious pattern here !!!
Average Return / Standard Dev.Individual Securities, 1994-2003
Berlin, 04.01.2006 Fußzeile 16
Diversification
Most individual stock prices show higher volatility than the price volatility of portfolio of all common stocks.
How can the standard deviation for individual stocks be higher than the standard deviation of the portfolio?
Diversification: investing in many different assets reduces the volatility of the portfolio.
The ups and downs of individual stocks partially cancel each other out.
Berlin, 04.01.2006 Fußzeile 17
Number of StocksNumber of Stocks
Systematic RiskSystematic Risk
1 2 3 111 2 3 11
Portfolio of 11 stocks
AMD
Unsystematic RiskUnsystematic Risk
AMD + American Airlines
AMD + American Airlines + Wal-Mart
The Impact of Additional Assets on the Risk of a Portfolio
Po
rtfo
lio
Sta
nd
ard
Dev
iati
on
Berlin, 04.01.2006 Fußzeile 18
Diversification reduces portfolio volatility, but only up to a point. Portfolio of all stocks still has a volatility of 21%.
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
Berlin, 04.01.2006 Fußzeile 19
Anheuser Busch stock had higher average returns than Archer-Daniels-Midland stock, with
smaller volatility.
Systematic and Unsystematic Risk
American Airlines had much smaller average returns 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.
Berlin, 04.01.2006 Fußzeile 20
• Investment performance is measured by total return.
• Trade-off between risk and return for assets: historically, stocks had higher returns and volatility than bonds and bills.
• One measure of risk: standard deviation (volatility)
• Unsystematic and systematic risk: risk that can (cannot) be eliminated through diversification, respectively
Risk and Return