LM 1: Portfolio Risk & Return: Part 1

Question 1

Whats the difference between historical mean return and expected return?

Answer 1

historical mean return is return based on past prices whereas expected return is what some expects the investment will return

Question 2

What is the expected return formula and use?

Answer 2

reflects anticipated future performance

1 + (expected return) = (1 + risk free return) [1 + expected inflation rate] [1 + expected risk premium]

aka nominal return

Question 3

What is normal distribution?

Answer 3

distribution symmetric around its mean, showing data closer to mean than away from mean

Question 4

What are the 2 characteristics of a normal distribution?

Answer 4

1. Its mean, median, and mode are equal.
2. It is symmetric around its mean.

Question 5

How many observations fall within 1 SD, 2 SD, & 3 SD?

Answer 5

1 SD = 68%
2 SD = 95%
3 SD = 99%

Question 6

What does positively skewed vs negatively skewed mean?

Answer 6

positively skewed = more extreme positive returns

negatively skewed returns = more extreme negative returns

Question 7

What does the graph look like for positively skewed vs negatively skewed?

Answer 7

positively skewed = big hump then flattens out

negatively skewed = flattens out then big hump

Question 8

What is kurtosis?

Answer 8

measure of how often outliers occur in a distribution.

distributions with fatter tails which means extreme returns are more likely. tail goes out further than normal distribution.

Question 9

What does a fat tails distribution mean in terms of returns for stocks?

Answer 9

fat tails distribution means higher probability of both extreme positive & negative returns

Question 10

What are 2 limits to markets being operationally efficient?

Answer 10

1. trading costs (brokerage commissions, bid-ask spread)
2. liquidity

Question 11

What is risk aversion?

Answer 11

the tendency to avoid risk and have a low risk tolerance.

Question 12

What are the 3 types of risk aversion investors, describe them?

Answer 12

1. risk seeking: enjoy thrill of gambling
2. risk neutral: only care about the expected return
3. risk averse: choose investment that offers highest return for their desired level of risk

Question 13

What is the utility formula and what does it tell us?

Answer 13

Utility Formula = E(R) - (0.5 *A *O^2)

E(R)= expected return of portfolio

A= Risk Aversion Coefficient

O^2= Volatility of Security Returns (SD)

measures satisfaction gain from a particular portfolio, based on the degree of risk aversion

Question 14

What are 3 conclusions you can draw from the utility function? UHH

Answer 14

1. utility has no maximum or minimum
2. higher expected returns lead to greater utility
3. high variance reduces utility

Question 15

What is the indifference curve tell us?

Answer 15

it tells us the investor is indifferent between any points on the curve, they all generate the same utility

Question 16

Would an investor rather be on the high utility curve or low utility curve?

Answer 16

high utility, same returns with less risk measured by standard deviation

Question 17

For risk averse investors would A (risk aversion coefficient) be greater or less than 0, what about for risk seekers?

Answer 17

risk aversion investors = A>0
risk seeker investor = A<0

Question 18

What is the formula for a portfolio’s expected return consisting of a risk-free asset and 1 risky asset?

Answer 18

E (Rp) = w1Rf + (1-w1)E (Ri)

E (Rp) = expected return of portfolio

w1 = weight or amount invested in risk free asset

RF = return of risk free asset risk of 0

E (Ri) = expected return of risky asset

Question 19

What is the capital allocation line (CAL)?

Answer 19

different investment options of a portfolio by changing the weights of a risky asset and a risk-free asset.

Question 20

What is CAL equation?

Answer 20

E (Rp) = Rf + [ (E(Ri) - Rf)/ Oi)] * Op

E (Rp) = expected return of portfolio

E (Ri) = expected return of risky asset

Rf = return of risk free asset

Oi = SD of risky asset

Op = SD of portfolio

Question 21

Which part of the CAL equation is the slope and what ratio does the slope represent?

Answer 21

CAL = E (Rp) = Rf + [(E(Ri) - Rf)/ Oi)] * Op

Slope = [(E(Ri) - Rf)/ Oi)]

Slope = Sharpe Ratio

Question 22

The dominant capital allocation line has higher rates of return for levels of risk greater than the optimal risky portfolio because of the investors ability to:

a. lend at the risk free rate

b. borrow at the risk free rate

c. purchase the risk free asset

Answer 22

b. borrow at the risk free asset.

Question 23

Where will the optimal risky portfolio be in regards to CAL and efficient frontier?

Answer 23

optimal risky portfolio will be on the CAL & efficient frontier.

Question 24

What is the formula for portfolio standard deviation given correlation?

Answer 24

SQRT w^2 SD^2 + w^2 SD^2 + 2 w w correlation SD *SD

Question 25

What is the formula for portfolio standard deviation given covariance?

Answer 25

SQRT w^2 SD^2 + w^2 SD^2 + 2 w w * covariance

Question 26

In a 2 asset portfolio what makes up covariance?

Answer 26

correlation * sd1 * sd2

Question 27

Which way do 2 assets move when its perfectly positively correlated, perfectly negatively correlated, and uncorrelated?

Answer 27

perfectly positively correlated = move up and down together = +1

perfectly negatively correlated = move in opposite direction = -1

uncorrelated = no relationship = 0

Question 28

Do portfolios with negative correlation have lower or high expected standard deviation?

Answer 28

lower, negative correlation moves in opposite directions. giving more diversified risk.

Question 29

When should an asset be added to a portfolio in terms of its sharpe ratio and what is sharpe ratio?

Answer 29

it should only be added to portfolio if sharpe ratio of individual asset is greater than sharpe ratio of the portfolio

sharpe ratio measure of risk adjusted returns. how much excess return you receive for the extra volatility you endure for holding a riskier asset.

Question 30

The portfolio on the minimum-variance frontier with the lowest standard deviation is:

a. unattainable.

b. the optimal risky portfolio.

c. the global minimum-variance portfolio.

Answer 30

c. global minimum variance portfolio.

Question 31

What is the Markowitz efficient frontier?

Answer 31

set of optimal portfolios that offer the highest expected return for a defined level of risk or the lowest risk for an expected return.

Question 32

What is two fund separation theorem?

Answer 32

The two-fund separation theorem states that all investors regardless of risk preferences will aim at having a portfolio located on the capital allocation line that is tangent to the efficient frontier.

The only thing differing between investors with different levels of risk appetite is how much or the weight they have of the the risk free asset

Question 33

How is the optimal portfolio determined by individual investors?

Answer 33

determined by each individuals investors risk preference

Question 34

What 2 things does total variance consist of?

Answer 34

systematic variance and nonsystematic variance

Question 35

What is the difference in the shape of the curve for risk averse investors vs risk seeking investors?

Answer 35

risk averse investor will have much steeper indifference curve

risk seeker investor will have much less steeper indifference curve

Question 36

What kind of risk premiums do risk averse, risk neutral, and risk seeking investors expect?

Answer 36

risk averse: premiums for anything more than risk free rate as compensation for accepting various risks

risk neutral: no premium

risk seeking: negative premiums, they’ll accept any return even if negative

Question 37

What is the difference between a lending portfolio and a borrowing portfolio in terms of CML?

Answer 37

lending portfolio is less than market portfolio (has some risky assets)

borrowing portfolio is more than the market portfolio (leveraged portfolio)

Question 38

What is the difference between Capital Market Line (CML) & the Capital Allocation Line (CAL)?

Answer 38

CAL makes up allocation of risk free assets and risky portfolios for an investor

CML makes up allocation of risk free assets and market portfolios instead of risky portfolios

Question 40

Why do we calculate Holding Period Return (HPR) & what are the 2 formula?

Answer 40

we calculate it to measure financial performance of an asset or investment for a single period

HPR = (ending value - beginning value) + income / beginning value

HPR = (1+ RETURN) (1+RETURN) (1+ RETURN) -1

Question 41

What is the arithmetic or mean return & formula? When is it used?

Answer 41

use when multiple holding periods and assumes that amount invested at beginning of period is the same

arithmetic mean = sum of returns every year / # of observations

Question 42

What is geometric return & formula? When is it used?

Answer 42

used when there is a longer time horizon and when there is compounding, compounds the returns instead of single amount

[(1 +r1) ( 1+r2).(1+r3)]^(1/n) -1

n = number of observation returns

Question 43

What is money-weighted return or internal rate of return use & formula?

Answer 43

takes into account contributions, reinvested distributions, and etc.

CF/ (1+IRR)^0 + CF/ (1+IRR)^1

Question 44

What is time-weighted return use & formula?

Answer 44

used to measure compound rate of growth of $1 initially invested. neutralizes the effect of cash withdrawals, or additions to the portfolio.

(1 + HPR)* (1+HPR) -1

Question 45

What is annualized return use & formula?

Answer 45

used when investment has been held for number of years

((1+ return) ^ (1/time in year/time))-1

Question 46

What is nominal returns formula?

Answer 46

(1 +nominal rate) = (1 + risk free rate) (1 + inflation rate) (1+ risk premium)

Question 47

What is the difference between pre-tax and after tax nominal return?

Answer 47

pre-tax is before capital gains or dividend taxes have been taken into account

after-tax is after capital gains or dividend taxes have been taken into account

Question 48

What is real return use & formula?

Answer 48

earnings on investment after accounting for taxes & inflation

((1 + nominal rate) / (1 + inflation rate)) -1

Question 49

What is leveraged return use and formula?

Answer 49

return on assets using borrowed money

divide the return by the leveraged amount

Question 50

How do you calculate Money-weighted return or Internal rate of return on a BA II PLUS calculator?

Answer 50

hit cash flow, put in the CF information

then hit IRR, then Compute

Question 51

What is the formula for time-weighted return and use?

Answer 51

(1+ return) (1+ return) (1+ return) -1

multiplies the returns for each sub-period then links them together to show how returns are compounded over time. good for comparing since it takes into account inflows and outflows of money

Question 52

What is the real rate of return formula & what does it tell us?

Answer 52

annual percentage of profit earned on an investment, adjusted for inflation

(1+ nominal rate)/(1+ inflation rate) -1

Question 53

What is the risk premium formula and what does it tell us?

Answer 53

the amount an investment will return in excess of the risk free rate of return

(1+ expected rate) / (1+ risk free rate) -1