The Basics of Investments

1. The Basics of Investments • Time Value of Money • The Risk/Return Tradeoff • The Impact of Inflation F303 Intermediate Investments

2. Equity Returns • Investors earn returns in the equity markets one of two ways • Through dividends • Through Capital Gain • What is the preferred method? • Dividends are taxed as received • Capital gains are taxed at lower rates and can be deferred F303 Intermediate Investments

3. Equity Returns – An example • An investor has a choice between two stocks, both of which are expected to provide a 10% return • Stock A expects no capital growth but pays a large dividend • Stock B pays no dividend but is expected to provide a return through capital appreciation • Which of these 2 equities will provide more dollars in the end? • What if the return is a mix of capital gain and dividends? • Will one always be preferred over the other? • Investor goals • Risk F303 Intermediate Investments

4. Risk and Return • There are four methods to measure return • Holding Period Returns • The Arithmetic Average • The Geometric Average (a/k/a Time Weighted Average) • Dollar Weighted Average F303 Intermediate Investments

5. Holding Period Return • HPR = Ending Price – beginning price + dividend Beginning Price • This method is most effective for only 1 year or one period. If measuring over multiple periods, best to use one of the other methods F303 Intermediate Investments

6. Holding Period Return - Example • Assume that on August 17, 2000, you bought a share of Target stock trading at $26.25. On August 17, 2001, the stock had risen to $36.62. If at the end of the period, the stock also paid a dividend of $.24, what is the Holding Period Return?? F303 Intermediate Investments

7. Other Methods(we will use the following data) F303 Intermediate Investments

8. Other Methods Defined • Arithmetic Average – The sum of multiple HPRs divided by the number of periods • This is the best forecast for future returns • (HPR1+HPR2+HPR3)/3 • Geometric Average – The single per period return that gives the same cumulative performance as the sequence of actual returns • Mutual funds are required to report this return because it ignores the dollar amount of funds managed • [(1+HPR1)*(1+HPR2)*(1+HPR3)]1/3 - 1 F303 Intermediate Investments

9. Other Methods Defined • Dollar Weighted Return – The Internal Rate of Return (IRR) that gives the interest rate that sets the present value of the cash flows equal to the initial cost of establishing the portfolio • Used to account for varying dollar amounts under management • 0 = -CF0 + CF1/(1+IRR) + CF2/(1+IRR)2 + CF3/(1+IRR)3 F303 Intermediate Investments

10. Quoted Rates of Return • APR – the annual percentage rate • Most typically quoted • Equal to the per period rate * the number of periods in a year • Simple interest approach • 1 + EAR = (1 + APR/n)n F303 Intermediate Investments

11. Rates of Return and Inflation • Growth in money vs. growth in purchasing power • Definitions • Nominal interest rate: The growth rate of money, R • Real interest rate: growth rate of purchasing power, r • Consumer Price Index (CPI): measure of inflation, i • Quick calculation of real rate: r = R-i • More accurately: (1+r) = (1+R)/(1+i) F303 Intermediate Investments

12. US Stocks, Bonds and Inflation • Compare a year of high inflation (1980) to a year with low inflation (1993) • Disparity between the “quick” and more precise measures of real v. nominal growth rates F303 Intermediate Investments

13. Understanding Risk • Fear v. understanding • Concepts of risk capacity and risk tolerance • Risk of individual securities v. the risk of the overall portfolio • The risk free rate of return = 90 day Treasury Bill Rate • Risk Premium is the difference the expected HPR and the risk free rate • Risk is measured by finding the expected return for a security and then finding the variance and standard deviation • Concept Check: Text p. 158 F303 Intermediate Investments

14. Measuring Risk - An example • A share of stock is currently selling for $23.50. According to analysts the following three scenarios are possible by year end F303 Intermediate Investments

15. Measuring Risk - An example • Given the data on the previous slide, what are: • HPR = Ending Price – beginning price + dividend Beginning Price • Expected Return = HPR * Probabilities • Variance = Probabilities * (Actual returns - Expected return) • Standard deviation = Square root of the variance F303 Intermediate Investments

16. Asset Allocation Across Risky and Risk Free Assets • Risk is controlled by the allocation between Risky and Risk Free assets • Once accomplished, assets are then allocated within the risky class • AN EXAMPLE F303 Intermediate Investments

17. Asset Allocation Example • Assume you have a $100,000 portfolio • You decide to invest $20K in a risk-free asset • That means $80K goes into a risky portfolio made up of the Dolphin Environmental Equity Fund and the Bush Oil Equity Fund • The Optimal allocation within the risky asset is 60% in the Dolphin Fund/ 40% in the Bush Fund • What is the Dollar Value of each fund in the $100,000 portfolio? • What is we are more risk averse and decide to invest 40% in a risk free asset? F303 Intermediate Investments

18. The Risk/Reward Trade-off: CAL and the Sharpe Ratio • Sharpe Ratio = Risk Premium / Standard Deviation • This represents the slope of the CAL. It indicates how much additional return you can expect for each additional unit of risk as measured by the standard deviation F303 Intermediate Investments

19. The Sharpe Ratio - an Example • Assume the following: • The expected return on a portfolio = 26.55% • The standard deviation of the portfolio = 36.5% • Risk-free rate = 4.5% • What is the risk premium on the risky asset? (Expected return - risk free return) • Next, assume you create a portfolio that invests 50% in the risky portfolio and 50% in the risk free asset • What is the expected return and risk premium of this portfolio? • What is the standard deviation of this portfolio? • What is the Sharpe Ratio of this portfolio? F303 Intermediate Investments

20. The Sharpe Ratio - an Example • What happens if you change the weight of the Risky Portfolio from 50% to 60%? • What is the expected return and risk premium of this portfolio? • What is the standard deviation of this portfolio? • How many additional units of risk (Std Dev) are being added? • Show that the new expected return is = Sharpe Ratio * the Additional Units of risk! F303 Intermediate Investments