BKM Chapter 6 Flashcards
(27 cards)
Speculation
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
Gamble
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
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 and explanation
(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 (risky & risk-free portfolio) + alternative formula
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
Alternative:
E[r-sub C] = risk-free rate + sharpe ratio * std. deviation of the complete portfolio
Standard deviation of the complete portfolio
sigma-C
(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, calculation of y, and relative risk
(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*) definition and graphical representation
(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
- risk aversion (A) - impacts the slope of the indifference curve
- Sharpe ratio (S) - impacts the slope of the CAL (opportunity set)
Reasonability of standard deviation as a measure of risk and alternative
(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
