Chapter 8 part 2 my notes Flashcards
Risk is typically defined as
the possibility of incurring harm
what is ex poste
past or historical returns
what is ex ante
future or expected returns
what does a return on investment consist of
two components 1. income yield 2. capital gain
what is income yield
is the return earned in the form of a periodic cash flow received by the investors - the interest payments from bonds and - the dividends from equities
what is the formula to calculate the income yield
Expected cash flows to be received / the purchase price CF/P
What is the yield to maturity
is the return earned by buying a bond and holding it to maturity - it is also an expected return over that very long investment horizon
What is the dividend yield
the cash that investors can expect to earn if the dividend payments over the next year are the same as they were over the previous period
what is the formula for the dividend yield
current dividend payments / the current value of the index - it is not a forecast of future dividends
what is a capital gain
the appreciation in price of an asset form some starting price, usually the purchase price or the price at the start of the year
what is a capital loss
the depreciation in the price of an asset from some starting price, usually the purchase price or the price at the start of the year
what is the formula for the capital gain (Loss) return or Yield
P1 - P0 / P0 (p I s the selling price or market price)
true of false common shares should gain with inflation (capital gain_ over the long run as their prices and cash flows are not fixed
true
the yield gap will increase or decrease with inflation
increase
how do you get the complete picture of the return form investing in bonds versus common shares
use the total return equation
what is the total return equation
income yield + capital gain (loss) yield
Estimate the income yield, capital gain (or loss0 yield, and total return for the following securities of over the past year a. a $1,000 par value, 6% bond that was purchased one year ago for $990 and is currently selling for $995 b. A stock that was purchased for $20, provided 4 quarterly dividends of $0.25 each, is currently worth $19.50
CF = 0.6 x $1,000 = $60 P0 = $990 P1 = 995 Income yield = 60/990 =6.06% Capital gain return = (995 -990)/990 = .51% total return = 6.06% + .51% = 6.57% or total return = (60 + 995-990) / 990 = 6.57% b. CF = 0.25x 4 = $1.00 P0 = $20 P1 = 19.50 Income yield = 1/20 = 5% Capital gain (loss) return = (19.50 -20)/20 = -2.5% Total return = 5% - 2.5% = 2.5% or (1+19.50 -20) / 20 = 2.5%
what are paper losses
capital losses that people do not accept as losses until they actually sell and realize them
what is a day trader
someone who buys and sells based on intraday price movements
what is mark to market
carrying securities at the current market value regardless of whether they are sold
how do you measure ex post or historical returns
use arithmetic mean or geometric mean
how do you calculate the arithmetic mean
add them all up and divide by how many (regular average)
how do you calculate the geometric mean
add 1 to each number, multiply all the numbers together, then to the exponent of 1/n, -1
which mean will be less the geometric mean or the arithmetic mean
geometric mean will always be less unless all the values are identical
the more the returns vary, the (bigger or lesser) the difference between the Am and GM will be
bigger the difference b/w the Am and GM
what is standard deviation definition
a measure of risk over all the observations; the square root of the variance
what is standard deviation in other terms
movement away from the mean (avg)
the larger the standard deviation the__________ _________ the return
more variable the return
when the standard deviation is squared, we get a measure called
the variance
the difference b/w Am and GM returns is approximately
half the variance
which average (GM or AM) is more accurate
GM or compound rate of return provides the correct annual return amount
The AM simply averages the annual rates of return without taking into account
simply averages the annual rates of return without taking into account the amount invested varies across time
when should you use AM
when we are trying to estiamte the typical return for a given period such as a year
when is it better to use GM
when we are interested in determining the “true” average rate of return over multiple periods - for instance, if we wanted to know our investment (and wealth) will grow over time
- it measures the compounded rate of growth in our investmetn value over multiple periods
what are expected returns - defnition
estimated future returns
expected returns are often estimated based on what
historical averages
what is an alternative to estiamting expected returns other than historical averages
use weighted average
how do you calclaute the weighted average
ex. suppose youa re given the following for two stocks, A and B where the return on each vires with the state of the economy
Prob of Exp return on
occurence Stock A stock B
High growth 0.1 60% 5%
Moderate growth 0.2 20% 25%
No growth 0.5 10% 5%
Recession 0.2 -25% 0%
estiamte the expected return for each stock
ERa = 0.1(60)+ 0.2(20)+ 0.5(10) + 0.2(-25) = 10%
ERb = 0.1(5) + 0.2 (25) + 0.5(5)+ 0.2(0) = 8%
* note it is similar to AM but how it is done is different (calclauting the probability)
- we calclaute the probability of each event directly
how is weighted average and AM different
weighted average we estiamte the probabilities for each event directly
AM - assumes that each observation is equally likely,so the probability of each event is refelected in the number of times we observe it in the data
for expected rates of return, short-term forecasts would use what and long run forecasts use
short term forecasts - use scenario based appraoch (because where we are today as huge impact on what is likely to happen over a short period)
Long-run forecasts - historical approach tends to be better because it reflects what actually happens, even if it was not expected
Long term forecasts for expected returns use
historical approaches like weighted average, am and GM
what is the range
the difference between the maximuma and minimum values
what is a more accurate measure of risk the range or standard deviation and why
standard deviaiton
- because the range only uses two observations, the maximum and the minimum , whereas the standard deviation uses all the observations
securities offering igher expected rates of return tend to be what
riskier
what is the formula for standard deviation
you take the returns ie 4.3% . 3.2%, 5.6%, 10.5% and -7.6%
and the arithmatic mean = 3.2%
- take the (return % subtract the mean)+ (the next return - the mean) etc / number of returns - 1
then square root it
what does the SD measure
it estiamtes the variability of the reutrns over the smaple period
it also like the AM esitmate of the annual reutrn reflects the economic circumstances of the period over which it is estiamted
therfore we also calclaute the scenario based SD as a measure of risk
how do you measure (formula) scenario-based Standard deviation? and what else is it called
Ex ante measure
- becasue we are explcility taking into account updated probabilites of the future events happening
What is VAR
another commonly used measure of risk
called Value at Risk
- probability based measure of loss potential to a firm
- represnets the estiamted loss (In money terms) tha tccoudl be exceeded (minimum loss) at a given level of probability
- a lower proability translates into a highe rpotential loss, all else being equal
what is portfolio
a collection of securities, such as stocks and bonds, tha tare combined an dconsidered a single asset
what is modern portfolio theory MPT
the theory that securites should be managed within a portfoli, rather than individually, to create risk-reduction gains; also stipulates that investors should divderisy their investments so as not to be unnecessarily exposed to a single negative event
(dont’ put all your eggs in one basket)
what does MPT do
takes the basic idea of don’t put all your eggs in one basket and operationalizes it to show how to form portfolios with the highest possible expected rate of return for any given level of risk
how do you calclaute the estimating expected portfolio return
add both portfolios up and divide by the total
ie 600 + 1400 = 2,000
weighted avg amout invested in Portfolio a = 600 / 2000 = .3
weighted avg. amount invested in Portfolio b = 1,400 / 2,000 = .7
next
take the estiamted expected return for each ie A = 10% and B = 8%
(0.3)(10%) + (0.7) (8%) = 8.6%
what is covariance
a statistical measure of the correlation of the fluctuaitons of ht eannual rates of return of different investments
how do you calcluate covariance
add
is the portfolio SD less or more than the weighted average of the SD of each individual security
always less than except one special case
what is correlation coefficent
a statistical measure that identifies how security returns move in relation to one another
although covariance provides a sueful measure of the realtionship of the co-movements of returns on individual securities, it is difficult to interpret what
intuitively because as in the case iwth the variance, the unit is perecent squared. fortunatley, covariance is related to another statistical measure, the correlation coeeficient whcih can be interpretted more intuitievely
what does a +1 correlation coefficent mean
perfect or positve correlation
- move together (A increases B increases)
- returns on securities tend to move together,
- doesn’t mean that they are ALWAYS together
correlation coefficient - the clsoer the absolute value of the correlation coefficent is to one,
the stronger the relationship between the returns on the two securities
in fact, +1 that is, perfect positive correlation - and we know thte return on one security, we can predict the return on the other security with certainty.
exteme correlation coefficents do not occur for traditional common shares in practice becuase
returns dispaly positive correlations with one another, but are less than one. because securiteis tend ot follow the movement of the overall marekt
when do correlations tend to be higher amoung securities
whose companies are simialr in nature, if htey are in the same industry, are about the same size, and so on
as you movee negaive with standard deviaiton as the correlation moves negative what happens
standard deviation goes down, less risk
Postive realtionship - standard deviation increase, more risk
as you move postive correclation,
standard deviation increases, more risk
the closer the corecclation coefficent is to 1 the
higher the %
when we have a perfect postive correlation, the variablity changes in what way
a linear or straight line fashion with the portfolio weights
if the realtionsip correlation is less than perfectly positve (negative correlation)it is
bowed
- it becomes more bowed as as the correlation decreases ;until, with a perfect negative correlation we can remove all risk
The perfect negative correlation case is of great importance to finacne because
it is the basis fo hedging (taking an offsetting postgin so as to minimize risk)
although when you have two secuties are perfectly negatively correlated, we
do not create an equally weighted portfolio in wich we invest the same amount of money in each seucity
only if the securities are equally risky, as well as being perfectly negatively correlated, we form
an equally balanced portfolio to remove risk
efficency frontier
please review graph and notes pg 311
