Flashcards in BKM Chapter 6 Deck (26)

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1

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Speculation

(BKM - 6)

### assumption of considerable investment risk to obtain commensurate gain

2

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Risk premium (aka excess return)

(BKM - 6)

### excess returns = expected return - risk-free rate

3

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Gamble

(BKM - 6)

###
bet or wager on an uncertain outcome

(aka a fair game)

4

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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

5

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Utility score

(BKM - 6)

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

A = risk aversion index

6

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Risk aversion index

(BKM - 6)

###
quantification of an investor's risk preferences

high A = more risk-averse

7

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Variance of risk-free portfolios

(BKM - 6)

###
variance = 0

(utility = expected return)

8

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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)

9

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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)

10

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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)

11

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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)

12

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Capital allocation decision

(BKM - 6)

### split of investments between risky and risk-free portfolios

13

##
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

Alternative:

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

14

##
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

15

##
Simplest way to reduce risk

(BKM - 6)

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

16

##
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)

17

##
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

18

##
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

19

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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)

20

##
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

21

##
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)

22

##
Reasonability of standard deviation as a measure of risk

(BKM - 6)

###
only appropriate with normality

use VaR or expected shortfall with non-normality

23

##
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

24

##
Passive strategy

(BKM - 6)

### a portfolio decision avoiding direct or indirect security analysis

25

##
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)

26