Rationale Risk is as important to investors as expected Lecture 4: - - PowerPoint PPT Presentation

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

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Rationale

• 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
• bservable. 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.

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Rates of Return: Single Period

HPR = Holding Period Return P0 = Beginning price P1 = Ending price D1 = Dividend during period

• ne

Example: Ending Price = 48 Beginning Price = 40 Dividend = 2 HPR = (48 - 40 + 2)/40 = 25% HPR = capital gain yield + dividend yield = 8/40 + 2/40 = 20% + 5%

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Expected Return = p(s) = probability of a state r(s) = return if a state occurs 1 to s states

Expected Return and Standard Deviation

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State

• Prob. of State

r in State 1 .1

• .05 (or 5%)

2 .2 .05 3 .4 .15 4 .2 .25 5 .1 .35 E(r) = (.1)(-.05) + (.2)(.05)...+ (.1)(.35) E(r) = .15 = 15%

Expected Returns: Example

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Standard deviation = [variance]1/2

Variance or Dispersion of Returns

Var =[(.1)(-.05-.15)2+(.2)(.05- .15)2...+ .1(.35-.15)2] Var= .01199 S.D.= [ .01199] 1/2 = .1095 = 10.95% Using Our Example:

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Mean and Variance of Historical Returns

• In forward-looking analysis so far, we determine a

set of relevant scenarios and associated investment

• utcomes (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

• nly dates and associated holding period returns.
• Therefore, when we use historical data, we treat

each observation as an equally likely scenario.

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Mean and Variance of Historical Returns

Expected return is arithmetic average

• r arithmetic average of rates of return

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The Normal Distribution

A graph of the normal curve with mean of 10% and the standard deviation of 20%.

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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
• f 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…….

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Normal and Skewed Distribution (mean = 6% SD = 17%)

Positive (negative) skewness  SD overestimates (underestimate) risk.

Skewness measures the degree of asymmetry

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Normal and Fat Tails Distributions (mean = .1 SD =.2)

Kurtosis is a measure of the degree of “fat tails”.

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History of Rates of Returns of Asset Classes for Generations, 1926- 2005

• The asset classes with higher volatility (i.e., SD) provided

higher average returns  investors demand a risk premium to bear risk.

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Histograms of Rates of Return for 1926-2005

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Excess Returns and Risk Premiums

• 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 risk- free rate  “excess return”.

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History of Excess Returns of Asset Classes for Generations, 1926- 2005

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History of Excess Returns of Asset Classes for Generations, 1926- 2005

• The average excess return was positive for every sub-
• periods. 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, -0.62 and -0.70.

• Negative skews imply SD underestimates the actual level
• f risk.
• Fat tails are observed for five assets during 1926-2005.
• The serial correlation is practically zero for four of the

five portfolios, supporting market efficiency.

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