Chapter 10 Flashcards
(43 cards)
define probability distribution (Pr)
a graph that provides the probability of every possible discrete state
define expected (mean) return
weighted average of the possible returns, where the weights correspond to the probabilities
E[R] = sum of Pr x R
define variance
a method to measure the risk of a probability distribution, it’s the expected squared deviation from the mean
variance is a measure of how “spread out” the distribution of the return is
define standard deviation
a common method used to measure the risk of a probability distribution. it’s the square root of the variance, the expected squared deviation from the mean
SD = volatility of a return
what’s the variance and SD of the return distribution formula
Var(R) = E[9R-E[R])^2] = sum of Pr x (r-E[R])^2
SD(R) = squareroot of Var(R)
define realized return
the return that actually occurs over a particular time period
how to calculate realized annual returns
1 + Rannual = (1 + Rq1)(1 + Rq2) (1 + Rq3) (1 + Rq4)
define empirical distribution of the returns
a plot showing the frequency of outcomes based on historical data
define average annual returns
the arthmetic average of an investment’s realized returns for each year
R = (1/T)* (R1 + R2 ..+… Rt) = (1/T) sum of Rt
what’s unique about the average annual return
it’s the balancing point of the empirical distribution—in this case, the probability of a return occurring in a particular range is measured by the number of times the realized return falls in that range. Therefore, if the probability distribution of the returns is the same over time, the average return provides an estimate of the expected return.
how to calculate the difference in variability
estimate the standard deviation of the distribution of returns using the variance estimate using realized returns
Var R = [1/(T-1)] * sum of (Rt - R(average))^2
what’s the difficulties using past returns to predict the future returns
- We do not know what investors expected in the past; we can only observe the actual returns that were realized.
- he average return is just an estimate of the true expected return. If we assume that investors are neither overly optimistic nor overly pessimistic on average, however, then we can use a security’s historical average return to estimate its actual expected return. As with all statistics, however, an estimation error will occur. Given the volatility of stock returns, this estimation error will be large even when we have many years of data.
define standard error
the standard deviation of the estimated value of the mean of the actual distribution around its true value; that is, it’s the standard deviation of the average return
what’s the formula of the standard error of the estimate of the expected return
SD (average of independent, identical Risks) = SD(individual Risk)/ square root (number of observations)
Because the average return will be within two standard errors of the true expected return approximately 95% of the time,106 the standard error can be used to determine a reasonable range for the true expected value. = historical average return is +- (2 x standard error)
how to calculate the CAGR or the geometric average of the annual returns
[(1+R1)(1+R2)…*(1+Rt)]^(1/T) - 1
what are the limitations of expected return estimates
Individual stocks tend to be even more volatile than large portfolios, and many have been in existence for only a few years, providing little data with which to estimate returns. Because of the relatively large estimation error in such cases, the average return investors earned in the past is not a reliable estimate of a security’s expected return. Instead, we need to derive an alternative method to estimate the expected return—one that relies on more reliable statistical estimates
how are investors are risk averse
The benefit they receive from an increase in income is smaller than the personal cost of an equivalent decrease in income. This idea suggests that investors would not choose to hold a portfolio that is more volatile unless they expected to earn a higher return
define excess return
the difference between the average return for an investment and the average return for a risk-free investment
is there a relationship between investment size and risk?
yes, Larger stocks tend to have lower volatility overall. In addition, even the largest stocks are typically more volatile than a portfolio of large stocks
is there a relationship between volatility and return
While the smallest stocks have a slightly higher average return, many stocks have higher volatility and lower average returns than other stocks. And almost all stocks seem to have higher risk and lower returns than we would have predicted from a simple extrapolation of our data from large portfolios.
define common risk
perfectly correlated risk
define independent risk
risks that bear no relation to each other. if risks are independent, then knowing the outcome of one provides no information about the other. Independent risks are always uncorrelated, but the reverse need not be true
define diversification
the averaging of independent risks in a large portfolio to reduce risk
how do stock prices and dividends fluctuate due to 2 types of news
- Market-wide news is news about the economy as a whole and therefore affects all stocks.
- Firm-specific news is good or bad news about the company itself.
