1 / 15

Concepts: Return and Risk

Concepts: Return and Risk. Review key concepts that are central to portfolio theory Holding-period return, and probability distributions The historical record. A. Holding Period Return (HPR). HPR = Holding Period Return P 0 = Price at the beginning of the period

dima
Download Presentation

Concepts: Return and Risk

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. Concepts: Return and Risk • Review key concepts that are central to portfolio theory • Holding-period return, and probability distributions • The historical record

  2. A. Holding Period Return (HPR) • HPR = Holding Period Return • P0 = Price at the beginning of the period • P1 = Price at the end of the period • D1 = Dividend or interest received during the period

  3. HPR Example Ending Price = 48 Beginning Price = 40 Dividend = 2

  4. Characteristics of Probability Distributions Moments of a probability distribution e.g., distribution of stock returns 1) Mean: most likely value 2) Variance/standard deviation: dispersion from the mean 3) Skewness e.g., is the distribution centered? 4) Kurtosis e.g., fat tails? * If a distribution is “normal”, it can be completely described by its first two moments

  5. Measuring the Mean • Expected return • S = number of possible outcomes or “states of nature, i” • pi = probability that outcome ‘i’ will occur • ri = return if outcome ‘i’ occurs

  6. Numerical example E(r) = (.1)(-.05)+(.2)(.05)...+(.1)(.35) E(r) = .15 = 15%

  7. Measuring Variance or Dispersion of Returns • Standard deviation = variance 1/2 • Using our example: • 2= [(0.1)(-0.05 - 0.15)2+(0.2)(0.05 - 0.15)2+…] = 0.01199 •  = [0.01199]1/2 = 0.1095 = 10.95%

  8. Sample Statistics • What we just looked at were the moments of a probability distribution • Before any realizations (i.e., before the fact, or ex-ante) • Calculating moments from actual results, e.g., historical records of financial asset returns – we use sample statistics • Weights are no longer the probabilities, but a function of the sample size, N • AVERAGE and STDEV functions in Excel

  9. Skewness  = 0.06,  = 0.17 Excel function: SKEW

  10. Kurtosis = 0.1,  = 0.2 Excel function: KURT

  11. Annual HPRs, Canada, 1957-2009

  12. Relationship between nominal and real rates • Let R = nominal rate • r = real rate • i = rate of inflation r = ?

  13. Annual Risk Premiums and Real ReturnsCanada, 1957-2009

  14. Nominal and Real Equity Returns Around the World, 1900-2000

  15. Geometric vs. Arithmetic mean • Geometric mean • Example: 10% return in first year, 8% in second year • If arithmetic: mean = ? • If geometric: mean = √[(1+0.1)(1+0.8)] – 1 = 0.08995 Excel function: GEOMEAN (but must add one first to each return) • Relationship if distribution is normal can be approximated by: • Geometric mean = arithmetic mean – 0.52

More Related