BKM Chapter 6

Question 1

Speculation

BKM - 6

Answer 1

assumption of considerable investment risk to obtain commensurate gain

Question 2

Risk premium (aka excess return)

BKM - 6

Answer 2

excess returns = expected return - risk-free rate

Question 3

Gamble

BKM - 6

Answer 3

bet or wager on an uncertain outcome

aka a fair game

Question 4

Key difference between a speculation and a gamble

BKM - 6

Answer 4

a gamble is undertaken for the enjoyment of risk

speculation is undertaken in spite of risk because of a perceived favorable risk-return tradeoff

Question 5

Utility score

BKM - 6

Answer 5

U = E[r] - .5 * A * sigma^2

Question 6

Risk aversion index

BKM - 6

Answer 6

quantification of an investor’s risk preferences

high A = more risk-averse

Question 7

Variance of risk-free portfolios

BKM - 6

Answer 7

variance = 0

utility = expected return

Question 8

Risk aversion index for risk-averse, risk-lovers, and risk-neutral investors

(BKM - 6)

Answer 8

risk-averse: A > 0
risk-neutral: A = 0
risk-lover: A < 0 (does not reject fair games/gambles)

Question 9

Indifference curves

BKM - 6

Answer 9

plot expected returns against risk (x-axis)

all points on the curve represent portfolios with the same utility score (e.g. investor is indifferent between them)

Question 10

Mean-variance criterion

BKM - 6

Answer 10

one portfolio dominates another if:
- it has the same/better expected return AND
- it has the same/lower risk/volatility
(with one inequality being strict)

Question 11

Relationship between the risk aversion index (A) and indifference curves and explanation

(BKM - 6)

Answer 11

more risk-averse investors (higher A) will have a steeper indifference curve (b/c they require a greater increase in return for an increase in risk)

Question 12

Capital allocation decision

BKM - 6

Answer 12

split of investments between risky and risk-free portfolios

Question 13

Expected return of the complete portfolio (risky & risk-free portfolio) + alternative formula
E[r-sub C]

(BKM - 6)

Answer 13

E[r-sub C] = y * expected return for the risky portfolio + (1 - y) * risk-free rate

y = % invested in the risky portfolio

Alternative:
E[r-sub C] = risk-free rate + sharpe ratio * std. deviation of the complete portfolio

Question 14

Standard deviation of the complete portfolio
sigma-C

(BKM - 6)

Answer 14

sigma-C = y * sigma-P

b/c the std. dev. of the risk-free portfolio is 0
sigma-P = std. dev. of the risky portfolio

Question 15

Simplest way to reduce risk

BKM - 6

Answer 15

shift funds away from the risky asset to the risk-free asset

Question 16

Capital allocation line (CAL)

BKM - 6

Answer 16

linear combination of all risk-return combinations available to investors with varying proportions y invested in the risky asset

plots expected return against risk (x-axis)

Question 17

Sharpe ratio (S, aka reward-to-volatility ratio) & interpretation

(BKM - 6)

Answer 17

S = expected excess return / standard deviation

interpretation: average % excess return for every 1% increase in standard deviation

Question 18

A borrowing or levered position, calculation of y, and relative risk

(BKM - 6)

Answer 18

a short position where y > 1

in this case, y = total funds available / initial investment budget and the amount invested in the risk-free portfolio is still = 1 - y

generally will have higher risk

Question 19

CAL with borrowing

BKM - 6

Answer 19

line will be “kinked” at point p (y = 1) because investors usually cannot borrow at the risk-free rate

(to determine the slope, replace the risk-free rate with the borrowing rate)

Question 20

Optimal risky position (y*) definition and graphical representation

(BKM - 6)

Answer 20

the proportion invested in the risky asset that maximizes utility (U)

graphically: point on the highest possible indifference curve that is tangential to the CAL

Question 21

Factors that determine the optimal risky position (2)

BKM - 6

Answer 21

1. risk aversion (A) - impacts the slope of the indifference curve
2. Sharpe ratio (S) - impacts the slope of the CAL (opportunity set)

Question 22

Reasonability of standard deviation as a measure of risk and alternative

(BKM - 6)

Answer 22

only appropriate with normality

use VaR or expected shortfall with non-normality

Question 23

Capital market line (CML)

BKM - 6

Answer 23

a CAL using 1-month T-bills as the risk-free portfolio and a well-diversified portfolio of common stocks that represents the risky portfolio

also = the opportunity set represented by a passive strategy

Question 24

Passive strategy

BKM - 6

Answer 24

a portfolio decision avoiding direct or indirect security analysis

Question 25

Reasons to pursue a passive strategy (2)

BKM - 6

Answer 25

1. passive strategies are less expensive than active strategies (both time & cost of information/market knowledge)
2. free-rider benefit: with many active knowledgeable investors most assets in the market will be fairly priced (because investors buy and drive up the price of underpriced stocks and sell/drive down the price of overpriced stocks)

Question 26

Certainty equivalent rate of return

BKM - 6

Answer 26

expected return with std. dev = 0 and same utility as the risky portfolio

(return received with certainty that the risk-free investment would need to provide to achieve the same utility as the risky portfolio)

Question 27

When to borrow funds to invest in the risky asset

BKM - 6

Answer 27

borrow funds when expected return of risky portfolio > risk-free borrowing rate