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
Intermediate maturity
Five to twelve years in length
Long-Term Maturity
Twelve years or more in length
Par value
Par value is the dollar amount the holder will receive at the bond’s maturity. It can be any amount
but is typically $1,000 per bond. Par value is also known as principle, face, maturity or redemption
value. Bond prices are quoted as a percentage of par.
coupon rate
A coupon rate states the interest rate the bond will pay the holders each year. To find the coupon’s
dollar value, simply multiply the coupon rate by the par value. The rate is for one year and
payments are usually made on a semi-annual basis. Some asset-backed securities pay monthly,
while many international securities pay only annually. The coupon rate also affects a bond’s price.
Typically, the higher the rate, the less price sensitivity for the bond price because of interest rate
movements.
Zero-Coupon bonds
These instruments pay no interest to the holder and are issued at a
deep discount. As the bond nears maturity, its price increases to reach par value. At maturity,
the bondholder will receive the par price. The interest earned is the difference between the
purchase price of the bond and what the holders receives at maturity.
vlookup function
VLOOKUP(lookup_value,table_array,col_index_num,range_lookup)
[Lookup_value] The value to search in the first column of the table array. Lookup_value can be a value or a reference. If lookup_value is smaller than the smallest value in the first column of table_array, VLOOKUP returns the #N/A error value.
[Table_array] Two or more columns of data. Use a reference to a range or a range name. The values in the first column of table_array are the values searched by lookup_value. These values can be text, numbers, or logical values. Uppercase and lowercase text are equivalent.
[Col_index_num] The column number in table_array from which the matching value must be returned. A col_index_num of 1 returns the value in the first column in table_array; a col_index_num of 2 returns the value in the second column in table_array, and so on.
vlookup with “if” function
Example =IF(ISNA(VLOOKUP(5,A2:E7,2,FALSE)) = TRUE, “Employee not found”, VLOOKUP(5,A2:E7,2,FALSE)) If there is an employee with an ID of 5, displays the employee’s last name; otherwise, displays the message “Employee not found”. (Buchanan)
The ISNA function returns a TRUE value when the VLOOKUP function returns the #NA error value.
step-up notes
Step-up Notes - The interest rate of these bonds increases or “steps-ups” at a stated date(s).
The rate may remain at this level until maturity and in this case would be considered a “single
step-up note”. Step-up notes can also have a series of rate increases and are then referred to
as “multiple step-up notes”.
Deferred Coupon Bonds
A structure that essentially incorporates features of both a zero
coupon bond and a coupon paying bond. These bonds typical do not pay interest for the first
couple of years. After this period the cash interest accrues at a stated rate and is usually paid
semi-annually to the bondholders. The coupon rate is typically higher than other issues in
order to entice investors to purchase these issues. Companies in the high yield arena typically
issue these bonds to conserve their cash flows in the earlier years of their business life.
CUSIP
An identification number assigned to all stocks and registered bonds. The Committee on Uniform Securities Identification Procedures (CUSIP) oversees the entire CUSIP system.
Floating-Rate Bonds
These bonds have coupon rates that reset at predetermined times. The rate is usually based on an index or benchmark with some sort of spread added or subtracted to the benchmark.
Assume the coupon rate of a floating-rate bond is based on the Federal Funds rate plus 25 basis points at three-month intervals. If the Federal Funds are at 3%, what would the coupon rate for this
bond be?
Coupon rate = 3% (Fed Funds) + 25 basis points.
Coupon rate = 3.25%
The coupon rate for this bond would be 3.25% until the next reset date.
What is the formula for the coupon rate of floating-rate bonds?
Coupon rate = Reference Rate + influencing variable.
Floating-Rate caps
state how high the coupon rate can go. Once it hits that level, there can be no further
increase in the rate. Caps are less advantageous for investors because the rate can only keep
pace with market rates up to a point. On the other hand, they protect the issuer by keeping
the cost of borrowing below a certain level.
accrued interest
the amount of interest that builds up in between coupon payments that will be received by the buyer of the bond when a sale occurs between these coupon payments, even though the seller of the bonds earned it.
Full Price
is sometimes referred to as a bond’s dirty price, which is the amount the buyer
will pay the seller. It equals the negotiated price of the bond plus the accrued interest.
Clean Price
is simply the price of the bond without the accrued interest.
Bullet maturity
Most corporate and government bonds use this structure, which requires the borrower to pay the investor one lump sum of the principal on the stated maturity date.
Amortizing securities
Asset-Backed Securities (ABSs) along with Mortgage Backed Securities (MBSs) have structures that pay the principal back at certain intervals during the bond’s life. For example, a mortgage payment includes part principle and part interest. They are called amortizing securities because the principal amount shrinks as the security matures, so that the last payment made to the investors closes out the issuer’s responsibility concerning this bond.
callable bond
A callable bond gives the issuer the right to redeem the bonds on a stated date or a schedule of dates before the stated maturity date for the bonds arrives.
call price
This is the price that the issuer will pay the bondholder; also know as the redemption price.
Call Date
This is the date or dates that the issuer can call the bond from the holders.
Deferred Call
When a callable bond is originally issued, it is said to have a deferred call of so many years up to the first call date, which is the first day the bond can be called by the issuer.
Regular or General Redemption Prices
These price tend to be above par until the first par call date. The price is typically known before the redemption occurs.
special prices
These occur because of certain events such as sinking funds, repossessions, forced
sales, and eminent domain. These usually occur at par value but could be less, depending on the
collateral backing the bonds.
