Chapter 5 - Risk, return, and the historical record Flashcards
holding period return
- Rate of return over a given investment period
- Dollars earned (price appreciation + dividend) per dollar invested
HPR =
= (endP - begP + div) / begP
or
= div yield + capital gains yield
dividend yield
- dividend / share price
- the percentage return from dividends
div yield =
= (cash dividends / beginning price)
capital gains yield
the percentage price increase
arithmetic average
The sum of returns in each period divided by the number of periods
geometric average
- The single per-period return that gives the same cumulative performance as the sequence of actual returns
- e.x. r = [(1 +.10) x (1 + .25) x (1 - .20) x (1 + .20)]^¼ - 1 = 7.19%
Dollar-weighted average return
The internal rate of return on an investment
IRR
the interest rate that sets the present value of the cash flows equal to the initial cost of establishing the portfolio
APR =
= per-period rate x periods per year
EAR =
= ((1 + rate per period)^n) - 1
= ((1 + APR / n)^n) - 1
nominal interest rate
The interest rate in terms of nominal (not adjusted for purchasing power) dollars
real interest rate
The growth rate of purchasing power derived from an investment
Rreal =
= (Rnom - i) / (1 + i)
fisher equation
Rreal ≈ Rnom - E(i)
consumer price index
measures purchasing power by averaging the prices of goods and services in the consumption basket of an average urban family of four
inflation rate
The rate at which prices are rising, measured as the rate of increase of the CPI
equilibrium nominal rate of interest
Rnom = Rreal + E(i)
scenario analysis
A list of possible economic scenarios, the likelihood of each, and the HPR that will be realized in each case
probability distribution
List of possible outcomes with associated probabilities
expected return of scenario analysis
The mean value of the distribution of HPR
Variance(Var)
The expected value of the squared deviation from the mean
standard deviation
The square root of the variance
Value at risk(VaR)
- Measure of downside risk
- The worst loss that will be suffered with a given probability, often 1% or 5%
- =NORMSINV(.05) in excel
kurtosis
- Measure of the fatness of the tails of a probability distribution relative to that of a normal distribution
- Indicates likelihood of extreme outcomes
skew
Measure of the asymmetry of a probability distribution
risk free rate
The rate of return that can be earned with certainty, often measured by the rate on Treasury bills
risk premium
An expected return in excess of that on risk-free securities
excess returns
Rate of return in excess of the risk-free rate
risk aversion
Reluctance to accept the risk
individual risk =
risk premium of portfolio (E(rC) - rf) / variance of portfolio return(σ^2C)
price of risk
The ratio of portfolio risk premium to variance
sharpe ratio
- Ratio of portfolio risk premium to standard deviation
- Quantifies the incremental reward(increase in risk premium) for each 1% increase in the portfolio stdev
- Only for ranking portfolios, not individual assets
sharpe ratio =
= portfolio risk premium / stdev of portfolio excess return
mean-variance analysis
Evaluating portfolios according to their expected returns and standard deviations (or variances)
A high book-to-market (B/M) ratio is interpreted as…
- value stock
- an indication that the value of the firm is driven primarily by assets already in place, rather than the prospect of high future growth
asset allocation
Portfolio choice among broad investment 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
Risk premium of the complete portfolio =
= risk premium of the risky asset x the fraction of the portfolio invested in the risky asset
The stdev of the complete portfolio =
stdev of the risky asset times the fraction of the portfolio invested in the risky asset
capital allocation line (CAL)
- Plot of risk-return combinations available by varying portfolio allocation between a risk-free asset and a risky portfolio
- The slope, S, equals the increase in expected return that an investor can obtain per unit of additional stdev
Investors preferred capital allocation =
= available risk premium to variance ratio / required risk premium to variance ratio
passive strategy
Investment policy that avoids security analysis, often entails indexing
capital market line (CML)
The capital allocation line using the market index portfolio as the risky asset
