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Risk and Return

Explore the concepts of risk and return in finance, including holding period return, return distribution, historical record, and risk measures. Learn how to calculate and analyze returns using probability distributions and scenario analysis.

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Risk and Return

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  1. Risk and Return Holding Period Return Return Distribution Historical Record Risk and Return

  2. Single Period Return • Holding Period Return: • Percentage gain during a period • HPR: holding period return • P0: beginning price • P1: ending price • D1: cash dividend • Example • You bought a stock at $20. A year later, the stock price appreciates to $24. You also receive a cash dividend of $1 during the year. What’s the HPR? P0 P1+D1 t = 0 t = 1

  3. Return (Probability) Distribution • Moments of probability distribution • Mean: measure of central tendency • Variance or Standard Deviation (SD): measure of dispersion – measures RISK • Median: measure of half population point • Return Distribution • Describe frequency of returns falling to different levels

  4. Risk and Return Measures • You decide to invest in IBM, what will be your return over next year? • Scenario Analysis vs. Historical Record • Scenario Analysis:

  5. Risk and Return Measures • Scenario Analysis and Probability Distribution • Expected Return • Return Variance • Standard Deviation (“Risk”)

  6. Risk and Return Measures • More Numerical Analysis • Using Excel

  7. Risk and Return Measures • Example • Current stock price $23.50. • Forecast by analysts: • optimistic analysts (7): $35 target and $4.4 dividend • neutral analysts (6): $27 target and $4 dividend • pessimistic analysts (7): $15 target and $4 dividend • Expected HPR? Standard Deviation?

  8. Historical Record • Annual HPR of different securities • Risk premium = asset return – risk free return • Real return = nominal return – inflation • From historical record 1926-2006 Risk Premium and Real Return are based on APR, i.e. arithmetic average

  9. Real vs. Nominal Rate • Real vs. Nominal Rate – Exact Calculation: • R: nominal interest rate (in monetary terms) • r: real interest rate (in purchasing powers) • i: inflation rate • Approximation (low inflation): • Example • 8% nominal rate, 5% inflation, real rate? • Exact: • Approximation:

  10. Risk and Horizon • S&P 500 Returns 1970 – 2005 • How do they compare* ? • Mean 0.0341*260 = 8.866% • Std. Dev. 1.0001*260 = 260.026% SURPRISED??? * There is approximately 260 working days in a year

  11. Consecutive Returns It is accepted that stock returns are independent across time • Consider 260 days of returns r1,…, r260 • Means: E(ryear) = E(r1) + … + E(r260) • Variances vs. Standard Deviations: s(ryear) ¹s(r1) + … + s(r260) Var(ryear) = Var(r1) + … + Var(r260)

  12. Consecutive Returns Volatility Daily volatility seems to be disproportionately huge! • S&P 500 Calculations • Daily: Var(rday) = 1.0001^2 = 1.0002001 • Yearly: Var(ryear) = 1.0002001*260 = 260.052 • Yearly: • Bottom line: Short-term risks are big, but they “cancel out” in the long run!

  13. Accounting for Risk - Sharpe Ratio • Reward-to-Variability (Sharpe) Ratio • E[r] – rf - Risk Premium • r – rf - Excess Return • Sharpe ratio for a portfolio: or

  14. Wrap-up • What is the holding period return? • What are the important moments of a probability distribution? • How do we measure risk and return?

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