Risk and Return Holding Period Return Distribution Historical

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

Single Period Return q Holding Period Return: Ø Percentage gain during a period q q q P 0 P 1+D 1 t=0 t=1 HPR: holding period return P 0: beginning price P 1: ending price D 1: cash dividend Example q Investments 7 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? 2

Return (Probability) Distribution q Moments of probability distribution Ø Ø Ø q Mean: measure of central tendency Variance or Standard Deviation (SD): measure of dispersion – measures RISK Median: measure of half population point Return Distribution Ø Describe frequency of returns falling to different levels Investments 7 3

Risk and Return Measures You decide to invest in IBM, what will be your return over next year? q Scenario Analysis vs. Historical Record q Ø Scenario Analysis: Investments 7 4

Risk and Return Measures q Scenario Analysis and Probability Distribution Ø Expected Return Ø Return Variance Ø Standard Deviation (“Risk”) Investments 7 5

Risk and Return Measures q More Numerical Analysis Ø Using Excel Investments 7 6

Risk and Return Measures q Example Ø Ø Current stock price $23. 50. Forecast by analysts: q q q Ø 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? Investments 7 7

Historical Record q Annual HPR of different securities Ø Ø Ø 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 Investments 7 8

Real vs. Nominal Rate q Real vs. Nominal Rate – Exact Calculation: q q q R: nominal interest rate (in monetary terms) r: real interest rate (in purchasing powers) i: inflation rate q Approximation (low inflation): q Example Ø 8% nominal rate, 5% inflation, real rate? Investments 7 q Exact: q Approximation: 9

Risk and Horizon q S&P 500 Returns 1970 – 2005 Daily Mean 0. 0341% Std. Dev. 1. 0001% q Yearly Mean 8. 9526% Std. Dev. 15. 4574% How do they compare* ? Ø Ø Mean Std. Dev. 0. 0341*260 = 8. 866% 1. 0001*260 = 260. 026% SURPRISED? ? ? * There is approximately 260 working days in a year Investments 7 10

Consecutive Returns It is accepted that stock returns are independent across time q q q Consider 260 days of returns r 1, …, r 260 Means: E(ryear) = E(r 1) + … + E(r 260) Variances vs. Standard Deviations: s(ryear) ¹ s(r 1) + … + s(r 260) Var(ryear) = Var(r 1) + … + Var(r 260) Investments 7 11

Consecutive Returns Volatility Daily volatility seems to be disproportionately huge! q S&P 500 Calculations Ø Ø Ø 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! q Investments 7 12

Accounting for Risk - Sharpe Ratio q Reward-to-Variability (Sharpe) Ratio Ø Ø q E[r] – rf r – rf - Risk Premium - Excess Return Sharpe ratio for a portfolio: or Investments 7 13

Wrap-up What is the holding period return? q What are the important moments of a probability distribution? q How do we measure risk and return? q Investments 7 14