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%

1. 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