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)

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Presentation transcript:

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

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

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 = = 60 Capital gain = 975 – 950 = 25 Total dollar return = = $85 Total percentage return = 85/950 = 8.95% 12-3

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 = (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% % = 17.86% 12-4 Financial Market Returns: The Case of Stocks

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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Average Returns, Download and open up Annual financial market returns, Annual financial market returns,

Average Returns, 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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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

Example: Variance and Standard Deviation YearActual Return Average Return Deviation from the Mean Squared Deviation Totals Variance =.0045 / (4-1) =.0015 Standard Deviation =

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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 appear to be at least roughly normally distributed… 12-13

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