risk, return, and historical record

risk and return

• to attract rational investors to take more risk, they must have higher returns

holding period return

• change in value over the period it is held

• includes additional income earned from the investment

arithmetic average

• sum of returns in each period divided by the number of periods

geometric average

• single per period return

• gives the same cumulative performance as a sequence of actual returns

dollar weighted average return

• irr

annual percentage rate

• ignores compounding

• per period date * periods per yr 

effective annual rate

• actual rate an investment grows

• compounding!

fisher equation

• tells us that nominal rates = real rates + expected inflation

inflation history

• since the 1950’s, nominal rates have increased roughly in line w inflation

• volatile inflation effects real rates or return

scenario analysis

• list of possible economic scenarios, the likelihood of each, and the HPR that will be realized

probability distribution

• list of possible outcomes with associated probabilities

expected return

• the mean value of the squared deviation from the mean

standard deviation

• the square root of the variance

normality

• HPR’s up to a month can be treated as normal

  • if they are normally distributed

• long term HPR’s deviate more from normality

value at risk

• statistical measure of downside risk

  • focused only on potential losses

  • worst loss with given probability (usually 1% or 5%)

kurtosis

• measures the fatness of the tails of a probability distribution

  • relative to a normal distribution

• indicates likelihood of extreme outcomes

leptokurtic

• distribution that is more peaked than normal

platykurtic

• a distribution thats less peaked than normal

mesokurtic

• normal curve

• not too peaked or too flat topped

symmetrical distritbution

• mean = median = mode

• skewness = 0

risk aversion

• investors prefer less risk to more risk

• investors do not “minimize risk”

  • it’s a trade off

risk tolerance

• amount of risk an investor can tolerate to achieve an investment goal

  • higher = greater the willingness to task risks

• negatively correlated with risk aversion

risk seeker

• will accept more risk for the potential of higher returns

• maximizes risk and return

risk neutral

• will pursue a portfolio offering higher return 

• maximizes return irrespective of risk

risk averse

• prefer a portfolio with a lower certain return than a higher, less certain return

indifference curve

• plots combinations of risk and return for a given level of utility

• steep slope = risk averse

• flatter = risk seeking

risk free rate

• rate of return that can be earned with certainty

risk premium

• expected return in excess of that on risk free securities

excess return

• rate of return in excess of risk free rate 

price of risk

• ratio of risk premium to variance

  • “For each unit of risk (variance), how much extra return am I earning?”

mean variance analysis

• evaluating portfolios according to their expected returns and standard deviations (or variances)

sharpe ratio

• reward to volatility

• ratio of portfolio risk premium to standard dev

  • “How much extra return (above the risk-free rate) do I get per unit of risk (volatility)?”

time series of return

• scenario analysis derived from sample history of return

asset allocation

• allocation of an investment portfolio across broad asset classes

capital allocation to risky assets

• the choice between risky and risk free assets

complete portfolio

• the entire portfolio including risky and risk free assets

capital allocation line 

• connects the optimal risky portfolio to the risk free asset

two fund separation theorem

• all investors, regardless of risk reference and wealth, will hold a combination of a isk free asset and an optimal portfolio of risky assets

passive strategy

• investment policy that avoids security analysis

• entails indexing 

capital market line

• capital allocation line using a market index portfolio as a risky asset 

cost and benefits of passive investing

• is inexpensive and simple