L2 Risk Premiums, Risk Aversion and Real Rate of Return

Question 1

What are risk premiums?

Answer 1

Expected return in excess of that on risk-free securities.

Question 2

What is excess return?

Answer 2

Rate of return in excess of the risk-free rate.

Question 3

What is risk aversion?

Answer 3

Reluctance to accept risk.

Question 4

What is an example of a risk- free asset?

Answer 4

Treasury bills- As the government guarantees paying their face value upon maturing.

Question 5

What is the relationship between risk and returns?

Answer 5

Returns (over longer periods of time) should be consistent with risk.

This is generally supported by evidence from historical risks and rewards.

Question 6

What is the calculation for risk premiums?

Answer 6

Expected HPR - Risk free return

= E(r) - rf

Question 7

What must occur before risk averse investors commit funds to risky assets?

Answer 7

Positive risk premium is necessary.

Question 8

What is investor utility?

Answer 8

It is used to map investor preferences to their optimal portfolio.

Question 9

What is the optimal portfolio?

Answer 9

The combination of expected returns and standard deviation {E(r), s}

Question 10

What is the utility function formula?

Answer 10

u= E(r) -0.5A * σ^2

E(r)= Expected return
σ^2= variance of returns
A= The degree of risk aversion

Question 11

What does the indifference curve represent?

Answer 11

It represents an investors willingness to trade-off return and risk.

Question 12

How is risk aversion calculated?

Answer 12

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

Question 13

What does the sharpe ratio measure?

Answer 13

The incremental reward for each increase of 1% in the SD of that portfolio.

Question 14

What is the calculation for the sharpe ratio?

Answer 14

E(rp)-rf / σ(p)

• A higher sharpe measure indicates a better reward per unit of volatility/ a more efficient portfolio.

Question 15

What is mean-variance analysis?

Answer 15

Portfolio analysis in terms of mean and SD in excess return.

Question 16

How do you calculate market portfolio price of risk?

Answer 16

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.

Question 17

Explain the influence of inflation on purchasing power and potential returns on investment.

Answer 17

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)

Question 18

What is the formula for real interest rates?

Answer 18

R= nominal rate
r= real rate
i= inflation rate
r approximately equals R-i

The precise relationship is:

r= R=i / 1+i

Question 19

What is a complete portfolio?

Answer 19

The entire portfolio including risky and risk-free assets.

Question 20

What is capital allocation to risk assets?

Answer 20

The choice between risky and risk-free assets.

Question 21

What are the money market mutual funds?

Answer 21

Treasury bills

Short term treasury and U.S. agency securities

Repurchase agreements

These are the mos accessible risk-free asset for most investors.

Question 22

What is the expected return of a complete portfolio formula?

Answer 22

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.

Question 23

What is the SD of complete portfolio calculation?

Answer 23

σc= y * σp

Question 24

What are some effects of asset allocation?

Answer 24

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.

Question 25

What does the Capital allocation line (CAL) show?

Answer 25

It shows all feasible risk-return combinations available from allocating the complete portfolio between a risky portfolio and a risk-free asset.

Question 26

What is the calculation for the slope of the CAL?

Answer 26

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.