BKM Chapter 6 Flashcards Preview

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Flashcards in BKM Chapter 6 Deck (26)
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(BKM - 6)

assumption of considerable investment risk to obtain commensurate gain


Risk premium (aka excess return)

(BKM - 6)

excess returns = expected return - risk-free rate



(BKM - 6)

bet or wager on an uncertain outcome

(aka a fair game)


Key difference between a speculation and a gamble

(BKM - 6)

a gamble is undertaken for the enjoyment of risk

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


Utility score

(BKM - 6)

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

A = risk aversion index


Risk aversion index

(BKM - 6)

quantification of an investor's risk preferences

high A = more risk-averse


Variance of risk-free portfolios

(BKM - 6)

variance = 0

(utility = expected return)


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

(BKM - 6)

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


Indifference curves

(BKM - 6)

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)


Mean-variance criterion

(BKM - 6)

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)


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

(BKM - 6)

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)


Capital allocation decision

(BKM - 6)

split of investments between risky and risk-free portfolios


Expected return of the complete portfolio
E[r-sub C]

(BKM - 6)

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

y = % invested in the risky portfolio

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


Standard deviation of the complete portfolio

(BKM - 6)

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


Simplest way to reduce risk

(BKM - 6)

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


Capital allocation line (CAL)

(BKM - 6)

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)


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

(BKM - 6)

S = expected excess return / standard deviation

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


A borrowing or levered position

(BKM - 6)

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


CAL with borrowing

(BKM - 6)

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)


Optimal risky position (y*)

(BKM - 6)

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


Factors that determine the optimal risky position (2)

(BKM - 6)

1. risk aversion (A) - impacts the slope of the indifference curve

2. Sharpe ratio (S) - impacts the slope of the CAL (opportunity set)


Reasonability of standard deviation as a measure of risk

(BKM - 6)

only appropriate with normality

use VaR or expected shortfall with non-normality


Capital market line (CML)

(BKM - 6)

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


Passive strategy

(BKM - 6)

a portfolio decision avoiding direct or indirect security analysis


Reasons to pursue a passive strategy (2)

(BKM - 6)

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)


Certainty equivalent rate of return

(BKM - 6)

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)