Return and Risk Returns Nominal vs Real Holding

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Return and Risk Returns – Nominal vs. Real Holding Period Return Multi-period Return Distribution

Return and Risk Returns – Nominal vs. Real Holding Period Return Multi-period Return Distribution Historical Record Risk and Return

Real vs. Nominal Rate q Real vs. Nominal Rate – Exact Calculation: q q

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: 2

Single Period Return q Holding Period Return: Ø Percentage gain during a period q

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? 3

Multi-period Return: APR vs. EAR q q APR – arithmetic average EAR – geometric

Multi-period Return: APR vs. EAR q q APR – arithmetic average EAR – geometric average Ø Ø q T: length of a holding period (in years) HPR: holding period return APR and EAR relationship Investments 7 4

Multi-period Return - Examples q Example 1 Ø q 25 -year zero-coupon Treasury Bond

Multi-period Return - Examples q Example 1 Ø q 25 -year zero-coupon Treasury Bond Example 2 Ø What’s the APR and EAR if monthly return is 1% Investments 7 5

Return (Probability) Distribution q Moments of probability distribution Ø Ø Ø q Mean: measure

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 6

Measuring Risk and Return You decide to invest in IBM, what will be your

Measuring Risk and Return You decide to invest in IBM, what will be your return over next year? q Scenario Analysis vs. Historical Record q Ø Scenario Analysis: Ø Historical Record: q What time period historical data should you use? Ø Investments 7 What data is relevant now? 1930 s? 1980 s? 2008? 7

Risk and Return Measures q Scenario Analysis and Probability Distribution Ø Expected Return Ø

Risk and Return Measures q Scenario Analysis and Probability Distribution Ø Expected Return Ø Return Variance Ø Standard Deviation (“Risk”) Investments 7 8

Risk and Return Measures q More Numerical Analysis Ø Using Excel Investments 7 9

Risk and Return Measures q More Numerical Analysis Ø Using Excel Investments 7 9

Risk and Return Measures q Example Ø Ø Current stock price $23. 50. Forecast

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 10

Accounting for Risk - Sharpe Ratio q Reward-to-Variability (Sharpe) Ratio Ø Ø Ø q

Accounting for Risk - Sharpe Ratio q Reward-to-Variability (Sharpe) Ratio Ø Ø Ø q E[r] – rf - Risk Premium r – rf - Excess Return rf - Risk-free rate, i. e. 1 month T-Bill rate Sharpe ratio for a portfolio: or Investments 7 11

Risk and Horizon q S&P 500 Returns 1970 – 2005 Daily Mean 0. 0341%

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 12

Consecutive Returns It is accepted that stock returns are independent across time q q

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 13

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

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 14

Normality Assumption q The normality assumption for simple returns is reasonable if the horizon

Normality Assumption q The normality assumption for simple returns is reasonable if the horizon is not too short (less than a month) or too long (decades). Investments 7 15

Other Measures of Risk - Value at Risk q q Term coined at J.

Other Measures of Risk - Value at Risk q q Term coined at J. P. Morgan in late 1980 s Alternative risk measurement to variance, focusing on the potential for large losses • Va. R statements are typically made in $ and pertain to a particular investment horizon, e. g. –“Under normal market conditions, the most the portfolio can lose over a month is $2. 5 million at the 95% confidence level” Investments 7 16

Wrap-up What is the holding period return? q What are the major ways of

Wrap-up What is the holding period return? q What are the major ways of calculating multi-period returns? q What are the important moments of a probability distribution? q How do we measure risk and return? q Investments 7 17

Comparative Constructions II Nominal Sentences Nominal Sentences NominalComparative Constructions II Nominal Sentences Nominal Sentences Nominal
Frase Nominal e Sintagma Nominal Frase Nominal SintagmasFrase Nominal e Sintagma Nominal Frase Nominal Sintagmas
HPR holding period return horizon return total returnHPR holding period return horizon return total return
Risk and Return Selected Realised Returns Average ReturnRisk and Return Selected Realised Returns Average Return
Risk and Return Holding Period Return Distribution HistoricalRisk and Return Holding Period Return Distribution Historical
Nominal versus Real Convergance Rozalia Pal Nominal ConvergenceNominal versus Real Convergance Rozalia Pal Nominal Convergence
THE NEW KENESIAN NOMINAL REAL RIGIDITY NOMINAL RIGIDITYTHE NEW KENESIAN NOMINAL REAL RIGIDITY NOMINAL RIGIDITY
Nominal GDP vs Real GDP Nominal GDP hasNominal GDP vs Real GDP Nominal GDP has
NOMINAL VERSUS REAL Nominal is the CURRENT valueNOMINAL VERSUS REAL Nominal is the CURRENT value
Risk and Return 5 1 Risk and ReturnRisk and Return 5 1 Risk and Return
Chapter 8 Risk and Return Risk and ReturnChapter 8 Risk and Return Risk and Return
Chapter 4 Return and Risk Return and RiskChapter 4 Return and Risk Return and Risk
Risk Return Risk and Return Both are positivelyRisk Return Risk and Return Both are positively
Return Risk and the SML RWJChapter 13 ReturnsReturn Risk and the SML RWJChapter 13 Returns
Chapter 11 Risk and Return 0 Expected ReturnsChapter 11 Risk and Return 0 Expected Returns
PORTFOLIO RISK AND RETURN Measuring Returns Converting DollarPORTFOLIO RISK AND RETURN Measuring Returns Converting Dollar