# Berlin, 04.01.2006Fußzeile1 The Trade-off Between Risk and Return Professor Dr. Rainer Stachuletz International Markets and Corporate Finance Berlin School.

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Berlin, 04.01.2006Fußzeile1 The Trade-off Between Risk and Return Professor Dr. Rainer Stachuletz International Markets and Corporate Finance Berlin School of Economics and Law

Berlin, 04.01.2006Fußzeile2 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, 04.01.2006Fußzeile3 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 flows 2. Choose discount rate that reflects asset’s risk 3. Calculate present value (PV cash inflows - PV outflows) The three-step procedure is called discounted cash flow (DCF) analysis.

Berlin, 04.01.2006Fußzeile4 Financial Return Total return: the total gain or loss experienced on an investment over a given period of time Components 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, 04.01.2006Fußzeile5 Dollar Returns Total dollar return = income + capital gain / loss Terrell bought 100 shares of Micro-Orb stock for \$25 A year later: Dividend = \$1/share Sold 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 paid Sold for \$25/share Dollar return = (50 shares) x (\$10) = \$500

Berlin, 04.01.2006Fußzeile6 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

Berlin, 04.01.2006Fußzeile7 Percentage Returns In percentage terms, Owen’s investment performed better than Terrell’s

Berlin, 04.01.2006Fußzeile8 \$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, 04.01.2006Fußzeile9 Percentage Returns on Bills Bonds, 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

Berlin, 04.01.2006Fußzeile10 Distribution of Historical Stock Returns, 1900 - 2003 50 -20-1001020304050 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, 04.01.2006Fußzeile11 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 Variance (%-squared) - hard to interpret, so calculate standard deviation, a measure of volatility equal to square root of  2

Berlin, 04.01.2006Fußzeile12 Volatility of Asset 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, 04.01.2006Fußzeile13 Average Returns and St. Dev. for Asset Classes 1.Investors who want higher returns have to take more risk 2.The incremental reward from accepting more risk seems constant Bills Bonds Stocks Average Return (%) Standard Deviation (%)

Berlin, 04.01.2006Fußzeile14 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?

Berlin, 04.01.2006Fußzeile15 Average Return (%) Standard Deviation (%) Wal-Mart Anheuser-Busch Archer Daniels Midland American Airlines No obvious pattern here !!! Average Return / Standard Dev. Individual Securities, 1994-2003

Berlin, 04.01.2006Fußzeile16 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, 04.01.2006Fußzeile17 Number of Stocks Systematic Risk 1 2 3 11 Portfolio of 11 stocks AMD Unsystematic Risk AMD + American Airlines AMD + American Airlines + Wal-Mart The Impact of Additional Assets on the Risk of a Portfolio Portfolio Standard Deviation

Berlin, 04.01.2006Fußzeile18 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, 04.01.2006Fußzeile19 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, 04.01.2006Fußzeile20 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

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