TOPIC 4 - CAPITAL ALLOCATION Flashcards
Speculation is:
undertaking of a risky investment for its risk premium.
Risk premium has to be large enough to compensate a
risk-averse investor for the risk of the investment.
a fair game is a risky prospect that has:
a zero risk premium.
an investment without a higher return for more risk accepted. Thus, an investor may take on higher risk without the possibility of higher return. Risk-averse investors tend to avoid these investments.
will a fair game be undertaken by a risk averse investor?
NO
investors’ preferences toward the expected return and volatility of a portfolio may be expressed by:
a utility function that’s higher for expected returns and lower for higher portfolio variances.
More risk-averse investors will apply
greater penalties for risk.
how to describe investors’ preferences for risk graphically?
indifference curves
certainty equivalent value of a portfolio summarises what?
the desirability of a a risky portfolio to a risk-averse investor
certainty equivalent rate of return is a value that,
if received with certainty would yield the same utility as the risky portfolio
The certainty equivalent is a guaranteed return that someone would accept now, rather than taking a chance on a higher, but uncertain, return in the future. … The certainty equivalent represents the amount of guaranteed money an investor would accept now instead of taking a risk of getting more money at a future date.
shifting funds from the risky portfolio to the risk-free asset is the simplest way to
reduce risk (other methods involve diversification of the risky portfolio and hedging)
T-bills provide
a perfectly risk-free asset in nominal terms only
why are t-bills considered the rf rate and not bonds?
bc the t-bills have pretty low SD of real returns vs other assets like long-term bonds and common stocks
why do we refer to the assets traded in the money market as risk free generally?
bc these are all short term and pretty safe relative to most other risky assets
an investor’s risky portfolio can be characterised by its reward to volatility which is:
Sharpe Ratio:
S = [E(rn) - rf] / SDp
the Sharpe ratio is the slope of what
the Capital Allocation Line (CAL)
what does the CAL show?
when graphed it goes from the rf asset through to the risky asset.
Shows all combos of the risk free asset on this line.
ceterus paribus, an investor would prefer what in terms of the CAL:
a steeper sloping CAL bc that means higher expected return for any level of risk.
If borrowing rate is greater than the lending rate, CAL then,
the CAL will be ‘kinked’ at the point of the risky asset.
investor’s degree of risk aversion characterised by what
slope of his/her indifference curve.
Indifference curve shows at any level of expected return and risk, teh required risk premium for taking on one additional % of SD.
more risk-averse investors have what type of indifference curve?
steeper –> they require a greater risk premium for taking on more risk
a passive investment strategy disregards what?
security analysis, instead targets the rf asset and a broad portfolio of risky assets like the S&P 500 portfolio.
Speculation=
assuming considerable investment risk to obtain commensurate gain
- occurs in spite of the risk involved bc 1 perceives a favourable risk-return trade-off
gambling =
to be or wager on an uncertain outcome
risk is assuumed for enjoyment of the risk itself
what’s the key dif btw speculation and gambling?
gambler doesn’t have commensurate gain
to turn from gambling to speculation, you need
an adequate risk premium to compensate risk-averse investors for the risks they bear.
Risk aversion and speculation are consistent.
risk-averse investors consider only:
risk-free or speculative prospects w. +ve risk premiums (reject fair games –> risk premium of 0 or worse)
Utility function:
U= E(r) - 1/2A * Variance
A = index of investor’s risk aversion
Variance of returns
1/2 –> the scaling factor
for low risk portfolios the higher the level of risk aversion, the
lower the measured utility score
the higher the level of risk aversion for any given level ofSD
the lower the overall utility score
certainty equivalent rate of return =
rate a risk-free investment would need to offer to provide the same utility as the risky portfolio
(aka the rate that if earned w certainty would provide a utility score = that of the portfolio in Q)
a portfolio is only desirable where:
certainty equiv return > rf alternative
risk averse investors consider risky portfolios only if
they provide compensation for risk via a risk premium.
A (index of risk aversion) >0
risk in the form of variance reduces utility
risk neutral investors find level of risk
irrelevant and only consider expected return of risk prospects
A = 0
judge risk prospects solely by their expected rates of return.
risk lovers <3 willing to accept
lower expected returns on prospects with higher amounts of risk
A <0
more variance equates to higher utility (not v conventional)
will risk lovers always take a fair game?
YES!!
their upward adjustment of utility for risk gives the fair game a certainty equivalent that exceeds the alternative of the risk-free investment
mean-variance criterion
portfolio A dominates portfolio B If:
E(ra) >/ E(Rb)
SDa < SDb
Passive strategy avoids
any direct or indirect security analysis
Capital Market Line (CML) results when
using the market index as the risky portfolio
The capital market line (CML) represents
portfolios that optimally combine risk and return.
CML is a special case of the CAL where
the risk portfolio is the market portfolio. Thus, the slope of the CML is the sharpe ratio of the market portfolio.
The intercept point of CML and efficient frontier would result
in the most efficient portfolio called the tangency portfolio.
An indifference curve shows a combination of
two goods that give a consumer equal satisfaction and utility thereby making the consumer indifferent.
Along the indifference curve, the consumer has what sort of preference
an equal preference for the combinations of goods shown—i.e. is indifferent about any combination of goods on the curve.
Typically, indifference curves are shown convex to the origin, and no two indifference curves ever intersect.
As income increases, what happens to an individual’s indifference curve ?
an individual will typically shift their consumption level because they can afford more commodities, with the result that they will end up on an indifference curve that is farther from the origin—hence better off.
does a less risk averse investor have a shallower or steeper indifference curve?
shallower
