Finance 2 Flashcards
What’s the purpose of the coefficient of variation?
The coefficient of variation (CV) helps the analyst interpret relative dispersion. In other words, a
calculated standard deviation value is just a number. Does this number indicate high or low
dispersion?
Sharpe ratio
The Sharpe ratio is a measure of the risk-reward tradeoff of an investment security or portfolio. It
starts by defining excess return, or the percentage rate of return of a security above the risk-free
rate. In this view, the risk-free rate is a minimum rate that any security should earn. Higher rates
are available provided one assumes higher risk.
Sharpe ratio formula
Sharpe ratio = [(mean return) - (risk-free return)] /standard deviation of return
kurtosis
The kurtosis formula measures the degree of peak. Kurtosis equals three for a normal distribution;
excess kurtosis calculates and expresses kurtosis above or below 3.
random variable
A random variable refers to any quantity with uncertain expected future values. For example, time is
not a random variable since we know that tomorrow will have 24 hours, the month of January will
have 31 days and so on. However, the expected rate of return on a mutual fund and the expected
standard deviation of those returns are random variables. We attempt to forecast these random
variables based on past history and on our forecast for the economy and interest rates, but we
cannot say for certain what the variables will be in the future - all we have are forecasts or
expectations.
event
When a particular outcome or a series of outcomes are defined, it is referred to
as an event. If our goal for the blue chip mutual fund is to produce a minimum 8% return every
year on average, and we want to assess the chances that our goal will not be met, our event is
defined as average annual returns below 8%. We use probability concepts to ask what the chances
are that our event will take place.
a priori probabilities
A priori probabilities represent probabilities that are objective and based on deduction and reasoning
about a particular case. For example, if we forecast that a company is 70% likely to win a bid on a
contract (based on an either empirical or subjective approach), and we know this firm has just one
business competitor, then we can also make an a priori forecast that there is a 30% probability that
the bid will go to the competitor.
subjective probabilities
Relationships must be stable for empirical probabilities to be accurate and for investments and the
economy, relationships change. Thus, subjective probabilities are calculated; these draw upon
experience and judgment to make forecasts or modify the probabilities indicated from a purely
empirical approach.
empirical probabilities
Empirical probabilities are objectively drawn from historical data. If we assembled a return
distribution based on the past 20 years of data, and then used that same distribution to make
forecasts, we have used an empirical approach.
unconditional probability
Unconditional probability is the straightforward answer to this question: what is the probability of
this one event occurring? In probability notation, the unconditional probability of event A is P(A),
which asks, what is the probability of event A? If we believe that a stock is 70% likely to return 15%
in the next year, then P(A) = 0.7, which is that event’s unconditional probability.
conditional probability
Conditional probability answers this question: what is the probability of this one event occurring,
given that another event has already taken place? A conditional probability has the notation P(A |
B), which represents the probability of event A, given B. If we believe that a stock is 70% likely to
return 15% in the next year, as long as GDP growth is at least 3%, then we have made our
prediction conditional on a second event (GDP growth). In other words, event A is the stock will rise
15% in the next year; event B is GDP growth is at least 3%; and our conditional probability is P(A |
B) = 0.9.
covariance
Covariance is a measure of the relationship between two random variables, designed to show the
degree of co-movement between them. Covariance is calculated based on the probability-weighted
average of the cross-products of each random variable’s deviation from its own expected value. A
value of 0 indicates no relationship
What does a positive covariance indicate?
A positive number indicates co-movement (i.e. the variables tend to move in the same direction)
What does a negative covariance indicate?
a negative covariance shows that the variables move in the
opposite direction.
What does a correlation of 1 indicate?
1 means a perfectly positive linear relationship (unit changes in one always bring the same
unit changes in the other)
What does a correlation of -1 indicate?
(-)1 indicates a perfectly inverse relationship (a unit change in one means that the other will
have a unit change in the opposite direction)
What is the formula for correlation?
Covariance (A, B) = Correlation (A, B)Standard Deviation (A)Standard Deviation (B)
Expected return of a portfolio
Expected return is calculated as the weighted average of the expected returns of the assets in the
portfolio, weighted by the expected return of each asset class. For a simple portfolio of two mutual
funds, one investing in stocks and the other in bonds, if we expect the stock fund to return 10% and
the bond fund to return 6%, and our allocation is 50% to each asset class, we have: Expected return (portfolio) = (0.1)(0.5) + (0.06)(0.5) = 0.08, or 8%
probability distribution
A probability distribution gathers together all possible outcomes of a random variable (i.e. any
quantity for which more than one value is possible), and summarizes these outcomes by indicating
the probability of each of them.
discrete random variables
Discrete random variables can take on a finite or countable number of possible outcomes. The
previous example asking for a day of the week is an example of a discrete variable, since it can only
take seven possible values. Monetary variables expressed in dollars and cents are always discrete,
since money is rounded to the nearest $0.01. In other words, we may have a formula that suggests
a stock worth $15.75 today will be $17.1675 after it grows 9%, but you can’t give or receive threequarters of a penny, so our formula would round the outcome of 9% growth to an amount of
$17.17.
continuous random variables
A continuous random variable has infinite possible outcomes. A rate of return (e.g. growth rate) is
continuous: a stock can grow by 9% next year or by 10%, and in between this range ).
probability density function
A probability density function (or pdf) describes a probability function in the case of a continuous
random variable. Also known as simply the “density”, a probability density function is denoted by “f
(x)”. Since a pdf refers to a continuous random variable, its probabilities would be expressed as
ranges of variables rather than probabilities assigned to individual values as is done for a discrete
variable. For
Maturity
Maturity is the time at which the bond matures and the holder receives the final payment of
principal and interest. The “term to maturity” is the amount of time until the bond actually
matures.
Short-term maturity
One to five years in length
