Wk 8 - Risk and Real Rate of Return

Question 1

What is reward

Answer 1

The difference between the expected HPR E(r) and the risk-free rate rf

Reward is known as the RISK PREMIUM

Question 2

What are risk premiums

Answer 2

Expected return in excess of that on risk-free securities

Question 3

What is Excess Return

Answer 3

Rate of return in excess of Risk-free rate

Question 4

What is the calculation for Risk Premium

Answer 4

Risk Premium = E(r) - rf

Risk Premium = Expected HPR - Risk Free Return

Question 5

What is risk aversion

Answer 5

Reluctance to accept risk

Question 6

What is a risk premium of 0 called

Answer 6

Fair Game

Question 7

What is Risk Averse

Answer 7

Require risk premium
Willing to take risk only when the risk premium is +ve

Implies investors will accept a lower reward (measured by E(r)) in exchange for a sufficient reduction in risk (measured by the SD of their portfolio retrun)

Question 8

What is Risk Neutral

Answer 8

Does not react to risks
Expected return is the only decision role

Question 9

What is Risk Seeking

Answer 9

Does not require +ve risk premium
Satisfied by taking risks rather than E(r)
Will participate fair game / gambling

Question 10

What is Utility Function

Answer 10

u = E(r) - 0.5A * σ^2

E(r) = Expected return on asset
σ^2 = Risk (Variance of Returns)
A = The degree (coefficient) of risk aversion

Question 11

How do you quantify an investor’s degree of risk aversion

Answer 11

Assume investors choose portfolios based on both expected return E(rp), and the volatility of returns as measured by the variance σp^2

Risk Averse investors will demand higher risk premiums to place their wealth in portfolios with higher volatility

Question 12

What is the formula for measuring Risk Aversion

Answer 12

E(rp) - rf = 1/2 * A * σp^2

Assume that the risk premium is proportional to the product of their risk aversion, A, and the variance of the risky portfolio’s rate of return, σp^2.

Question 13

What is the Risk premium and Standard Deviation of a Risk free asset

Answer 13

Risk premium = 0
SD = 0

Question 14

What is the Sharpe Measure

Answer 14

S measures the incremental rewad for each increase of 1% in the SD of that portfolio

A higher Sharpe measure indicates a better reward per unit of volatility (more efficient portfolio)

Question 15

What is the Sharpe measure formula

Answer 15

S = [E(rp) - rf] / σp

= portfolio risk premium / standard deviation of the portfolio

Question 16

What is market risk

Answer 16

-Risk from factors that affect the entire market
-Cannot be eliminated through diversification
- Causes inc: Δ interest rates, exchange rates, geopolitical events, or recessions.

Question 17

What is the formula for market risk

Answer 17

[ E(rm) - rf ] / σm

Numerator represents the market risk premium (extra reward above risk free rate)

Question 18

How is the general trend in prices measured

Answer 18

CPI

Measures the cost of purchasing a bundle of goods

Question 19

at 10% annual rate of return, could you have bought 10% more goods with the extra money

Answer 19

suppose rate of inflation (i) or ( %Δ CPI), amounted to i = 6%
with a 10% rate of return, - 6% reduction in purchasing power = net ^ purchasing power = 4%

Question 20

how do you distinguish between nominal and real interest rate

Answer 20

If R = nominal rate, r = real rate, and i = inflation rate
r ≈ R - i
The real rate is approx. the nominal rate - loss of purchasing power

Question 21

What is the precise relationship between Real and Nominal interest rate

Answer 21

1 + r = (1+R) / (1+i)
Rearranged:
r = (R-1) / (1+i)

r = real
R = nominal
i = Inflation rate

Question 22

If interest rate on a 1 year investment is 8% and inflation is 5%, Calculate the approximate and exact real rate provided by the investment

Answer 22

Approx:
r = 8% - 5% = 3%

Exact:
r = (0.08-0.05) / (1+0.05) = 0.0286 = 2.86%

Question 23

If you invest all funds into risky assets, what does y =

Answer 23

y=1

Question 24

If you invest all funds into risk-free assets, what does (1-y) =

Answer 24

(1-y) = 1

Question 25

If you invest all funds into risk-free assets, what does y =

Answer 25

y = 0

Question 26

If you invest all funds into risky assets, what does (1-y) =

Answer 26

(1-y) = 0

Question 27

What is the risk and return for a combined portfolio where 50% of the funds are invested into both Risky and Risk-free assets

Answer 27

E(rc) = yE(rp) + (1-y)rf
σc = yσp + (1-y)σf

Question 28

How do you calculate the risk premium of the complete portfolio

Answer 28

The risk premium of the complete portfolio = risk premium of the risky asset * the portion invested into the risky asset

Question 29

How do you calculate the Standard Deviation of the complete portfolio

Answer 29

The Standard Deviation of the complete portfolio = SD of the risky asset * the portion invested into the risky asset

Question 30

What is CAL

Answer 30

Capital Allocation Line

Available risk-return combinations by changing the value of y

Question 31

What is the formula for the Slope of CAL

Answer 31

S= [ E(rp) - rf ] / σp

Question 32

What does the slope of CAL represent

Answer 32

The slope = the ^ in E(r) per unit of additional SD.
Extra return per Extra Risk -> Sharpe measure

It is the same for the risky portfolio and the complete portfolio (inc risk-free)