1 / 40

FINE 3010-01 Financial Management

FINE 3010-01 Financial Management. Instructor: Rogério Mazali Lecture 14: 11/08/2010. FINE 3010-01 Instructor: Rogério Mazali. Fundamentals of Corporate Finance Sixth Edition Richard A. Brealey Stewart C. Myers Alan J. Marcus McGraw Hill/Irwin. Chapter 11:

derora
Download Presentation

FINE 3010-01 Financial Management

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. FINE 3010-01Financial Management Instructor: RogérioMazali Lecture 14: 11/08/2010

  2. FINE 3010-01Instructor: RogérioMazali Fundamentals of Corporate Finance Sixth Edition Richard A. Brealey Stewart C. Myers Alan J. Marcus McGraw Hill/Irwin Chapter 11: Introduction to Risk, Return, and the Opportunity Cost of Capital

  3. Agenda • Rates of Return: A Review • A Century of Capital Market History • Market Indices • The Historical Record • Using Historical Evidence to Estimate Today’s Cost of Capital • Measuring Risk • Variance and Standard Deviation • Measuring the Variation in Stock Returns • Risk and Diversification • Diversification • Asset vs. Portfolio Risk • Market Risk vs. Idiosyncratic Risk • Thinking About Risk • Message 1: Some risks Look Big and Dangerous but really are Diversifiable • Message 2: Market Risks are Macro Risks • Message 3: Risk can be Measured

  4. Summary Two factors move investor’s appetite: • How much they can eat – Expected Return • How long they can sleep - Risk In this set of lectures, we are trying to find proxies for these metrics…

  5. The Issue: The Discount Rate The questions we will (try to) answer are: • How can we measure risk? • How can we incorporate risk in an expected return expression?

  6. Total Annual Returns in the Past Century (in %) * * Risk Premium = Mean Returns – U.S. T-Bills Returns

  7. Introducing “Uncertainty” Finance is inherently concerned about the future. We can take two approaches to handle the problem: • Historical Approach: Future returns can be forecasted from or approximated by historical returns. Then, use historical returns! • Model Future Uncertainty: Scenario Analysis, and the determination of States of the World, Future Returns, and Probabilities.

  8. Expected Return & Variance: An Example

  9. Expected Return Calculations: Stock A Reminder: E(RA) = 0.25 * (-0.2) + 0.25 * 0.1 + 0.25 * 0.3 + 0.25 * 0.5 = 0.175

  10. Variance Calculations: Stock A 0.25 * (-0.2 – 0.175)^2 = 0.03515 Reminder: Var(RA) = 0.25 * (-0.2 – 0.175)^2 + 0.25 * (0.1 – 0.175)^2 + 0.25 * (0.3 – 0.175)^ 2 + 0.25 * (0.5 – 0.175)^2 = 0.066875

  11. Summary Results

  12. Mean – Variance Analysis

  13. Formulas • Expected returns & variance for a single security Expected Mean: E(R) = μ= p1R1 + p2R2 + …. psRs Expected Variance: σ2 = Σpi * (Ri – E(R))2 Standard Deviation = σ = • In practice if we do not know all of the possible states of the world or their corresponding probability of occurrence, so we may use historical data to form expectations

  14. Portfolio Risk • So far we’ve been examining risk from the perspective of an individual asset • So what happens when we have a portfolio of assets? Definition: A portfolio is a combination of securities. Basic Ingredients: - 2 or more securities - Some money invested in each security, i.e. the Weights

  15. Portfolio Illustration

  16. Portfolio’s Weights: An Example Imagine that you want to make a portfolio of Security A and Security B. You have $100,000, and you want to invest 30,000 in Security A and the rest in Security B. The weights of your portfolio will be: WA= 30,000 / 100,000 = 0.3 WB = 70,000 / 100,000 = 0.7

  17. Portfolio Rate of Return • Two-asset portfolio E(RPort) = wA * E(RA) + wB * E(RB) Expected Returns are just a linear combination of the returns of each security in the portfolio • N-asset portfolio

  18. Portfolio Variances • Two-asset portfolio Var(RPort) = wA2 * Var(RA) + wB2 * Var(RB) + 2 * wA* wB * Cov(RA, RB) The Variance formula has to account also for the co-movements of the two sets of data!

  19. Statistics Review: Covariance • Measures how two random variables move in relation to one another • Positive: The two variables move together • Ex: Height and Weight • Negative: the two variables move opposite each other, when one is up the other is down • Ex: Sleep and Coffee consumption • Zero : the two variables are linearly independent • Strawberry-flavored ice-cream consumption and exchange rate

  20. Calculation • Cov (RA, RB) = σAB = p1*(RA1 – E(RA))*(RB1 – E(RB))+p2*(RA2 – E(RA))*(RB2 –E(RB)) +….+ps*(RAs – E(RA))*(RBs – E(RB)) =Σ pi * (RAi –E(RA)) * (RBi – E(RB)) where i = 1, 2, …, s are the states of the world Notice: Cov(RA, RA) = ∑ pi * (RA- E(RA)) * (RA - E(RA)) = ∑ pi * (RA- E(RA))2 = Var(RA)

  21. Covariance: Example 0.0005 = 0.25 * (- 0.375) * (-0.005) -0.375 = -0.2 – E(RA) = -0.2 – 0.175 Covariance = 0.0005 + (-0.0027) + (-0.0055) + 0.0028 = -0.0049 NEGATIVE covariance!

  22. Covariance Matrix: The Results

  23. Covariance interpretation • Covariance tells us the direction of the relationship, between two series, it is a difficult coefficient to interpret, since it is base free – that is, apart from its sign, there is not that much we can say. • Covariance does NOT tell us about the strength of the relationship • If I give the covariance for how series 1, and 2 are related to series 3 you cannot tell which one is more closely related to series 3

  24. Correlation Coefficient • Correlation Coefficient: Measures the strength of the relationship • The correlation coefficient is a standardization of covariance

  25. Possible Correlation Coefficients • The correlation coefficient can only take on values between -1 and +1 • -1 implies that the assets are perfectly negatively correlated • +1 implies that the assets are perfectly positively correlated • 0 implies that the assets are not related

  26. Comparing Strength • When trying to determine the strength of the correlation between two series all you care about is the absolute value of the correlation coefficient • So if the correlation coefficient between asset 1 & 3 is -0.8, and the correlation coefficient between asset 2 & 3 is 0.5, is series 1 or 2 more correlated to 3?

  27. The Correlation Coefficient

  28. Back to Portfolio Variance again… Using the definition of the correlation coefficient, we can re-write the formula of the portfolio variance as follows: Var(RPort) = wA2 * Var(RA) + wB2 * Var(RB) + 2 * wA* wB * Cov(RA, RB) = wA2 * Var(RA) + wB2 * Var(RB) + 2 * wA* wB * σA * σB * ρAB If this covariance/correlation is negative, the last term of our expression – the one in bold – becomes negative!

  29. Portfolios… A&B

  30. Remarks • Is the portfolio’s standard deviation greater or less than the weighted average of the stocks standard deviation? • What happens if AB = 1?

  31. Portfolio Mean – Variance Analysis Stock A Stock B

  32. The Efficient Frontier – Hypothetical Numbers ρ = -1 (pink) Stock A Stock B ρ = 1 (yellow) Actual ρ = - 0.164 (blue)

  33. Portfolios, Mean Returns, & Variance: Why? There is an advantage in putting stocks together in a portfolio As long as the stocks in a portfolio do not move perfectly together, then as one stock experiences an increase in price, the other may experiences a decrease in price, and the total volatility of the portfolio is less affected than the volatility of each security in the portfolio! DIVERSIFICATION!

  34. Components of Stock Risk • Diversifiable/Unsystematic/Unique risk • Risk factors affecting only affects individual stocks or a small group of stocks (industries) • Non-diversifiable/Systematic/Market risk • Economy-wide sources of risk that affect the overall stock market

  35. Diversification • A portfolio strategy designed to reduce exposure to risk by combining a variety of investments, which are unlikely to all move in the same direction • Intuition: “Don’t put all your eggs in one basket” • Stocks don’t move in exactly the same way. On a given day, while Boeing may yield positive 1% return, Microsoft may have gone down 1%. So, if you had invested a dollar each in Boeing and Microsoft, you would not have lost any money.

  36. How Diversification Works • Diversification can only reduce/eliminate unsystematic risk. • Unsystematic risk arises due to random events that only affect a single company or a small group of companies. • Examples: Lawsuits, Strikes, Technological innovations... • Why can’t we diversify away systematic risk?

  37. How Diversification Works • Systematic risk arises from economy-wide influences that affect all assets. • Examples: Business Cycle, Inflation Shocks, and Interest Rates... • This risk cannot be diversified away

  38. The Wonders of Diversifying

  39. Portfolio Variances N-asset portfolio

  40. Limitation of diversification • N-asset portfolio, each stock weight 1/N • What happens as N increases?

More Related