Rationale Reference Nattawut Jenwittayaroje, Ph.D., CFA Expected Return and Standard Deviation Example: Ending Price =

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1 Rationale Lecture 4: Learning about return and risk from the historical record Reference: Investments, Bodie, Kane, and Marcus, and Investment Analysis and Behavior, Nofsinger and Hirschey Nattawut Jenwittayaroje, Ph.D., CFA NIDA Business School 1 Risk is as important to investors as expected return. Though we have CAPM, the level of risk faced by investors need to be estimated from historical experience. Neither expected returns nor risk are directly observable. Only realized rates of return and risk can be observed after the fact. Essential tools for estimating expected returns and risk from the historical record is needed. 2 Rates of Return: Single Period Expected Return and Standard Deviation HPR = Holding Period Return P 0 = Beginning price P 1 = Ending price D 1 = Dividend during period one Example: Ending Price = 48 Beginning Price = 40 Dividend = 2 HPR = ( )/40 = 25% HPR = capital gain yield + dividend yield = 8/40 + 2/40 = 20% + 5% Expected Return = p(s) = probability of a state r(s) = return if a state occurs 1 to s states 3 4

2 Expected Returns: Example Variance or Dispersion of Returns State Prob. of State r in State (or 5%) E(r) = (.1)(-.05) + (.2)(.05)...+ (.1)(.35) E(r) =.15 = 15% Standard deviation = [variance] 1/2 Using Our Example: Var =[(.1)( ) 2 +(.2)( ) ( ) 2 ] Var= S.D.= [.01199] 1/2 =.1095 = 10.95% 5 6 Mean and Variance of Historical Returns In forward-looking analysis so far, we determine a set of relevant scenarios and associated investment outcomes (i.e., rates of return) and probability. In contrast, asset and portfolio return histories come in the form of time series of past realized returns that do not explicitly provide the probabilities of those observed returns; we observe only dates and associated holding period returns. Therefore, when we use historical data, we treat each observation as an equally likely scenario. Mean and Variance of Historical Returns Expected return is arithmetic average or arithmetic average of rates of return 7 8

3 The Normal Distribution A graph of the normal curve with mean of 10% and the standard deviation of 20%. 9 The Normal Distribution Investment management is far more tractable when asset rates of return can be well approximated by the normal distribution. First, it s symmetric. Therefore, measuring risk as the SD of returns is adequate. Second, when assets with normally distributed returns are mixed, the resulting portfolio return is also normally distributed. Third, only two parameters (mean and SD) have to be estimated to obtain the probabilities of future scenarios. How closely actual return distributions fit the normal curve. 10 Normal and Skewed Distribution (mean = 6% SD = 17%) Normal and Fat Tails Distributions (mean =.1 SD =.2) Skewness measures the degree of asymmetry Kurtosis is a measure of the degree of fat tails. Positive (negative) skewness SD overestimates (underestimate) risk

History of Rates of Returns of Asset Classes for Generations, 1926-2005 Histograms of Rates of Return for 1926-2005 The asset classes with higher volatility (i.e., SD) provided higher average returns investors demand a risk premium to bear risk.

. How much of an expected reward is offered for the risk involved in investing money in a stock.

4 History of Rates of Returns of Asset Classes for Generations, Histograms of Rates of Return for The asset classes with higher volatility (i.e., SD) provided higher average returns investors demand a risk premium to bear risk Excess Returns and Risk Premiums History of Excess Returns of Asset Classes for Generations, How much should you invest in a risky asset (e.g., stocks).. How much of an expected reward is offered for the risk involved in investing money in a stock. We measure the reward as the difference between the expected holding-period return on the stock and the risk-free rate risk premium. The difference in any particular period between the actual rate of return on a risky asset and the riskfree rate excess return

5 History of Excess Returns of Asset Classes for Generations, The average excess return was positive for every subperiods. Average excess returns of large stocks in the last 40 years suggest a risk premium of 6%-8% The skews of the two large stock portfolios are significantly negative, and Negative skews imply SD underestimates the actual level of risk. Fat tails are observed for five assets during The serial correlation is practically zero for four of the five portfolios, supporting market efficiency. 17

Rationale. Learning about return and risk from the historical record and beta estimation. T Bills and Inflation

Rationale. Learning about return and risk from the historical record and beta estimation. T Bills and Inflation Learning about return and risk from the historical record and beta estimation Reference: Investments, Bodie, Kane, and Marcus, and Investment Analysis and Behavior, Nofsinger and Hirschey Nattawut Jenwittayaroje,