The Trade-off between Risk and Return Professor XXXXX Course Name / Number

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.

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.

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.

Total dollar return = income + capital gain / loss 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 = (150 shares) x ($15) = $500

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

Percentage Returns In percentage terms, Owen’s investment performed better than Terrell’s did.

Value of $1 Invested in Equities, Treasury Bonds and Bills, 1900 - 2003 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

Percentage Returns on Bills, Bonds, and Stocks, 1900 - 2003 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

Distribution of Historical Stock Returns, 1900 - 2003 <-30 -30 to -20 to -10 to 0 to 10 to 20 to 30 to 40 to >50 -20 -10 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.

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 Units of variance (%-squared) - hard to interpret, so calculate standard deviation, a measure of volatility equal to square root of 2

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.

Average Returns and St. Dev. for Asset Classes, 1900-2003 Stocks Bills Bonds Standard Deviation (%) Investors who want higher returns have to take more risk The incremental reward from accepting more risk seems constant

Average Return and St. Dev. for 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?

Average Return and St. Dev. for Individual Securities, 1994-2003 Wal-Mart Anheuser-Busch American Airlines Archer Daniels Midland Standard Deviation (%) No obvious pattern here

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.

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

Systematic and Unsystematic Risk 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 Anheuser Busch stock had higher average returns than Archer-Daniels-Midland stock, with smaller volatility. 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.

Risk and Return 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