1. We can examine returns in the financial markets to help us determine the appropriate returns on non-financial assets (e.g., capital investments by firms) Lessons from capital market history  There is a reward for bearing risk  The greater the risk, the greater the potential reward  This is called the risk-return trade-off 12-1 Risk and Return: Lessons from Financial Market History

2. How to calculate financial market returns The historical record on financial market returns Interpreting return and risk Arithmetic versus geometric average Capital market efficiency 12-2 Agenda for 27 July

3. Financial Market Returns: The Case of Bonds Total dollar return = income from investment + capital gain or loss due to change in price Example:  Suppose you bought a bond for $950 one year ago. You have received two coupons of $30 each. You can sell the bond for $975 today. What is your total dollar return? Income = 30 + 30 = 60 Capital gain = 975 – 950 = 25 Total dollar return = 60 + 25 = $85 Total percentage return = 85/950 = 8.95% 12-3

4. Suppose you bought a stock one year ago for $35, and you received dividends of $1.25. The stock is now selling for $40.  What is your dollar return? Dollar return = 1.25 + (40 – 35) = $6.25  What is your percentage return? Dividend yield = 1.25/35 = 3.57% Capital gains yield = (40 – 35)/35 = 14.29% Total percentage return = 3.57% + 14.29% = 17.86% 12-4 Financial Market Returns: The Case of Stocks

5. Ibbotson Associates maintains a database consisting of year-to-year historical rates of return on the following asset classes: The Historical Record

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7. Average Returns, 1925 - 2010 Download and open up Annual financial market returns, 1926-2010Annual financial market returns, 1926-2010 12-7

8. Average Returns, 1925 - 2013 InvestmentAverage Return Large Stocks12.1% Small Stocks16.9% Long-term (20 yr) Corporate Bonds 6.3% Long-term (20 yr) Government Bonds 5.9% 1 month U.S. Treasury Bills3.5% Inflation (CPI3.0% 12-8

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10. Variance and Standard Deviation Variance and standard deviation measure the volatility of asset returns The greater the volatility, the greater the uncertainty. Historical variance = sum of squared deviations from the mean / (number of observations – 1) Standard deviation = square root of the variance 12-10

11. Example: Variance and Standard Deviation YearActual Return Average Return Deviation from the Mean Squared Deviation 1.15.105.045.002025 2.09.105-.015.000225 3.06.105-.045.002025 4.12.105.015.000225 Totals.42.00.0045 Variance =.0045 / (4-1) =.0015 Standard Deviation =.03873 12-11

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13. Normal distribution The normal distribution is a symmetric, bell-shaped frequency distribution  It is completely defined by its mean and standard deviation The return distributions shown in Figure 12.10 appear to be at least roughly normally distributed… 12-13

14. Normal distribution Download and open the Standard Normal Distribution Function Table (“z” table)Standard Normal Distribution Function Table 12-14