The Trade-off Between Risk and Return*

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.

The Trade-off Between Risk and Return*Valuing risky assets is a task fundamental to financial management1. Determine the assets expected cash flows2. Choose discount rate that reflects assets risk3. Calculate present value (PV cash inflows - PV outflows)This three-step procedure is called discounted cash flow (DCF) analysis. Three-step procedure for valuing a risky asset

Understanding Returns*Total return: the total gain or loss experienced on an investment over a given period of timeTotal return can be expressed either in dollar terms or in percentage terms.

Dollar Returns*

Percentage Returns*Terrells dollar return exceeded Owens by $100. Can we say that Terrell was better off?No, because Terrell and Owens initial investments were different: Terrell spent $2,500 in initial investment, while Owen spent $750.

Percentage Returns*In percentage terms, Owens investment performed better than Terrells did.

The History of Returns: Nominal ReturnsThe Value of $1 Invested in Stocks, Treasury Bonds, and Bills*

The History of Returns: Real ReturnsThe Real Value of $1 Invested in Stocks, Treasury Bonds, and Bills*

The Risk Dimension*Risk premium: the additional return that an investment must offer, relative to some alternative, because it is more risky than the alternative.

Percentage Returns on Bills, Bonds, and Stocks, 19002006*

Percentage Returns on Stocks, Treasury Bonds and Bills, 1900 - 2006*

Table 6.2 Risk Premiums for Stocks, Bonds, and Bills, 19002006*

Volatility and RiskAverage return on stocks is more than double the average return on bonds, but stocks are 2.5 times more volatile.*Asset classes with greater volatility pay higher average returns.

The Distribution of Historical Stock Returns1900 - 2006*We can approximate the unknown probability distribution for future stock returns by assuming a normal distribution.

The Variability of Stock ReturnsVariance (2) a measure of volatility in units of percent squared*Normal distribution can be described by its mean and its variance.Standard deviation a measure of volatility in percentage terms

Table 6.3 Estimating the Variance of Stock Returns from 19942006*

Table 6.4 Average Returns and Standard Deviation for Equities, Bonds, and Bills, (19002006)*

Fig. 6.6 The Relationship Between Average (Nominal) Return and Standard Deviation for Stocks, Treasury Bonds, and Bills, 1900 - 2006Investors who want higher returns have to take more risk.The incremental reward from accepting more risk is constant.*

The Power of DiversificationAverage Returns and Standard Deviations for 11 Stocks, 1994-2006*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 Diversification*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.

Annual Returns on Coca-Cola and Wendys InternationalThe two stocks did not always move in sync. The net effect is that the portfolio is less volatile than either stock held in isolation.*

Average Returns and Standard Deviations of Portfolios of Stocks and Bonds, 1972 - 2006*

The Relationship Between Portfolio Standard Deviation and the Number of Stocks in the PortfolioThe risk that diversification eliminates is called unsystematic risk.The risk that remains, even in a diversified portfolio, is called systematic risk.*

Systematic and Unsystematic Risk*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 diversificationWhat really matters is systematic risk.how a group of assets move together.

Risk and Return RevisitedFor the various asset classes, a trade-off arises between risk and return.*

Average Returns and Standard Deviations for 11 Stocks, 1994-2006*No obvious pattern here!

Risk and Return Revisited*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 Premiums Around the World*

The Trade-off Between Risk and ReturnInvestment 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*