L2 Risk Premiums, Risk Aversion and Real Rate of Return Flashcards
What are risk premiums?
Expected return in excess of that on risk-free securities.
What is excess return?
Rate of return in excess of the risk-free rate.
What is risk aversion?
Reluctance to accept risk.
What is an example of a risk- free asset?
Treasury bills- As the government guarantees paying their face value upon maturing.
What is the relationship between risk and returns?
Returns (over longer periods of time) should be consistent with risk.
This is generally supported by evidence from historical risks and rewards.
What is the calculation for risk premiums?
Expected HPR - Risk free return
= E(r) - rf
What must occur before risk averse investors commit funds to risky assets?
Positive risk premium is necessary.
What is investor utility?
It is used to map investor preferences to their optimal portfolio.
What is the optimal portfolio?
The combination of expected returns and standard deviation {E(r), s}
What is the utility function formula?
u= E(r) -0.5A * σ^2
E(r)= Expected return
σ^2= variance of returns
A= The degree of risk aversion
What does the indifference curve represent?
It represents an investors willingness to trade-off return and risk.
How is risk aversion calculated?
E(rp) −rf = 1/2 * A * σ^2
We suppose that investors choose portfolios based on both expected return E(rp) and the validity of returns as measured by the variance σ^2
rf= treasury bills
A= Risk aversion
What does the sharpe ratio measure?
The incremental reward for each increase of 1% in the SD of that portfolio.
What is the calculation for the sharpe ratio?
E(rp)-rf / σ(p)
- A higher sharpe measure indicates a better reward per unit of volatility/ a more efficient portfolio.
What is mean-variance analysis?
Portfolio analysis in terms of mean and SD in excess return.
How do you calculate market portfolio price of risk?
Market price of risk=
E(rm) - rf / σm
E(rm) = average expected return with the market portfolio
σm= SD of market returns
The numerator represents the market risk premiums.
Explain the influence of inflation on purchasing power and potential returns on investment.
It is possible that in the course of the year prices of goods increase and your purchasing power will not equal the increase your money wealth.
This measure of prices is measured by examining changes in the consumer price index (CPI)
What is the formula for real interest rates?
R= nominal rate
r= real rate
i= inflation rate
r approximately equals R-i
The precise relationship is:
r= R=i / 1+i
What is a complete portfolio?
The entire portfolio including risky and risk-free assets.
What is capital allocation to risk assets?
The choice between risky and risk-free assets.
What are the money market mutual funds?
Treasury bills
Short term treasury and U.S. agency securities
Repurchase agreements
These are the mos accessible risk-free asset for most investors.
What is the expected return of a complete portfolio formula?
E(rc) = (1-y) * rf + y*E(rp)
rp= Actual risky rate of return
E(rp) expected rate of return
rf= risk free rate pf return
y= investment budget
The standard deviation of the complete portfolio (σc)depends only on the risky portfolios SD (σp), as the risk-free asset has zero SD.
What is the SD of complete portfolio calculation?
σc= y * σp
What are some effects of asset allocation?
When you reduce the fraction of the complete portfolio allocated to the risky asset by half, you reduce both the risk and risk premium by half.
Thus, the risk premium of the complete portfolio will equal the risk premium of the risky asset * the fraction of the portfolio invested in the risky asset.
The SD of the complete portfolio will equal the SD of the risky asset * the fraction of the portfolio invested in the risky asset.
What does the Capital allocation line (CAL) show?
It shows all feasible risk-return combinations available from allocating the complete portfolio between a risky portfolio and a risk-free asset.
What is the calculation for the slope of the CAL?
The same as the sharpe ratio:
s= E(rp) - rf / σP
A higher sharpe ratio (steeper CAL slope) indicates a better risk-return trade-off.
