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Return, Risk, and the SML

Return, Risk, and the SML. RWJ-Chapter 13. Dividends. Ending market value. Time. 0. 1. Initial investment. Returns. Dollar Returns the sum of the cash received and the change in value of the asset, in dollars. Percentage Returns

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Return, Risk, and the SML

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  1. Return, Risk, and the SML RWJ-Chapter 13

  2. Dividends Ending market value Time 0 1 Initial investment Returns • Dollar Returns • the sum of the cash received and the change in value of the asset, in dollars. • Percentage Returns • the sum of the cash received and the change in value of the asset divided by the original investment.

  3. Holding Period Return (Simple Return) OR Capital Gain Dividend Yield

  4. HPR (Simple Return)-Example (1) • Suppose you bought 100 shares of Wal-Mart (WMT) one year ago today at $25. Over the last year, you received $20 in dividends (= 20 cents per share × 100 shares). At the end of the year, the stock sells for $30. How did you do? • What is your return on this investment?

  5. $20 $3,000 Time 0 1 -$2,500 $520 20.8% = $2,500 Dollar Return: $520 gain Percentage Return:

  6. HPR (Simple Period)- Example (2) • Let’s look at Ford Capital Gain=2.16%% Dividend Yield=0.54% Source=Yahoo Finance

  7. HPR- Multiple Periods • The holding period return is the return that an investor would get when holding an investment over a period of n years, when the return during year i is given as ri: • Compounding Return: The cumulative effect that a series of gains or losses on an original amount of capital over a period of time

  8. HPR (Multiple Periods)- Example (3) • Suppose your investment provides the following returns over a four-year period:

  9. HPR (Multiple Periods)- Example (4) • Let’s find compounded return for Ford

  10. Annualizing Return • How can I annualize my return over time? • Two ways: • Arithmetic Average • Geometric Average

  11. Example • Average (Arithmetic Return)? • Geometric Return? • Interpret the results

  12. Risk: • What is risk? • Webster’s dictionary: “exposing to loss or damage” • In finance: • Stand-alone basis • Portfolio basis

  13. Which one is more risky? Why?

  14. Risk and Return Relation: Is risk a bad?

  15. How to measure Risk? • Likelihood that investors will receive a return on an investment that is different from the return they expected to make • Two important key words in this definition • Expectations • Deviation from our expectations

  16. To measure Risk: We need to know two concepts? • TIME SERIES ARE GIVEN • Expected Return: • How much “actual return” deviates from “Expected Return”? Expected Return Variance

  17. To measure Risk: We need to know two concepts? • PROBABILITY DISTRIBUTION GIVEN • Probability: • The chance that event will occur • Probability Distribution: • If all possible events, or outcomes, are listed, and if probability is assigned to each event, the listing is called probability distribution.

  18. Then: • Expected Return: • How much “actual return” deviates from “Expected Return”? Expected Return Variance

  19. Example (5) • What is the expected return of Stock X?

  20. d4 d1 d3 d2 Standard Deviation

  21. Example (6) • What are the expected return for Stocks X and Y?

  22. Example (6)-cont’d • You have $10,000, what is your portfolio return if you invest $2000 in Stock X and $8000 in Stock Y

  23. Diversification and Systematic Risk • What is diversification? • Spreading a portfolio over many investments to avoid excessive exposure to any source of risk

  24. Diversifiable vs. Market Risk • To the extent that the firm specific influences on two stocks differ, diversification should reduce portfolio risk • With all risk sources independent, the exposure to any particular source of risk is reduced to a negligible level • Firm specific risk is called unsystematic, unique risk, idiosyncratic risk, or diversifiable risk • The risk remains even after extensive diversification. This risk is called market or systematic risk

  25. Factors Affecting Unsystematic and Systematic Risk • Unsystematic (Unique) Risk: • Successful or unsuccessful product or marketing program • Winning or loosing of a major contract • In particular: good or bad news for a firm • Systematic Risk: • Economic conditions; recession, boom, high inflation, high interest rates

  26. Diversification Unique Risk Systematic Risk

  27. Market Risk

  28. Summary: • Based on the studies on capital market history, we know that there is reward, on average, for bearing risk. • Since, unsystematic risk can be eliminated at virtually no cost (by diversifying), there is no reward for bearing it. Put another way, the market does not reward risks that are borne unnecessarily. • Implication: • The expected return on an asset depends only on that asset’s systematic risk • No matter how much total risk an asset has, only the systematic portion is relevant in determining the expected return

  29. How to measure systematic risk? • Because systematic risk is the crucial determinant of an asset’s expected return, we need some way of measuring the level of systematic risk for different investment. • β (Beta Coefficient) tells us how much systematic risk as an average asset • Market Beta=1 • Risk Free Rate Beta=0 • Stock A: Standard Deviation=40%, Beta=0.50 • Stock B: Standard Deviation=20%, Beta=1.50 • Ford: http://www.google.com/finance?q=ford&ei=pISCUtCmIoG20AH2PA

  30. Portfolio Beta and Security Market Line • Weighted average Betas of the stocks in the portfolio • SML: Expected Return and Systematic Risk Relation:

  31. Example (7) • Let’s assume that you have a market portfolio (S&P 500) and risk-free rate asset (T-bills). Expected rate of Market Portfolio is 10% and risk-free rate is 3% What is the expected return and Beta if you invest: • 100% in risk free rate • 75% in risk free rate and 25% in Market Portfolio • 50% in risk free rate and 50% in Market Portfolio • 25% in risk free rate and 75% in Market Portfolio • 100% in Market Portfolio

  32. Market Risk Premium

  33. The SML and the Cost of Capital: A Preview • Risk is an extremely important consideration in almost all business decisions. Therefore, we need to the find the relation between risk and return (the SML) • We also need to know what determines the appropriate discount rate for future cash flows: Market risk premium, risk free rate and Beta • Why is the SML important: • It tells us reward to risk in financial markets • In order to find the discount rate: we need to compare the expected return on that investment to what the financial market offers on an investment with the same beta. In other words, the SML line tells us the “going rate” for bearing risk in the economy.

  34. The SML and the Cost of Capital: A Preview • Cost of Capital: the appropriate discount rate on a new project is the minimum expected rate of return an investment must offer to be attractive • This minimum required rate of return is called “Cost of Capital” • We have a much better idea of what determines the required return on invesment.

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