4. Nominal and Real Interest Rates

Question 1

Equilibrium real rate of interest

Answer 1

Determined by supply, demand, government actions, central bank actions, expected rate of inflation

Question 2

Nominal interest rates

Answer 2

R, what you get on bank account

Question 3

Real interest rates

Answer 3

r, inflation corrected interest rate

Question 4

Fisher effect

Answer 4

Inflation and (short) interest rate move closely together

Formula

Question 5

Taxes and inflation

Answer 5

Taxes are paid on nominal income

Question 6

Holding period return

Answer 6

Volatility in returns determines risk

Question 7

Historical returns: empirical distribution and probability distribution

Answer 7

o Empirical distribution: probability distribution plotted using historical data

o Probability distribution: summarized information (probability for each possible
return), risky investments have different returns with own likelihood of occurring

Question 8

Expected return

Answer 8

Conceptual difference between average returns (using historical data that represent one possible path) and expected returns (take probability function into account), weighted average of possible returns, where weights correspond to probabilities

Formula

Question 9

Risk premium

Answer 9

Expected excess return, difference between expected holding period return and risk-free rate

Question 10

Distribution

Answer 10

mean, variance/standard deviation, skewness (left or right), kurtosis (fat tails)

Question 11

Speculation

Answer 11

Speculation: considerable investment risk to obtain commensurate gain.

o Considerable risk: risk is sufficient to affect decision.

o Commensurate gain: positive risk premium, expected profit > risk-free alternative.

Question 12

Gambling

Answer 12

Gambling: risk (uncertain outcome) for no purpose but enjoyment of risk itself, whereas speculation is undertaken in spite of risk involved, because favorable risk-return trade-off.

o Hot hand: gamblers fallacy -> good in history ≠ good in future.

Question 13

Mean-variance utility function

Answer 13

𝑈 = 𝐸(𝑟) − 1/2 𝐴 × 𝜎^2(𝑟)

A: coefficient of risk aversion, lower = more risk taking. If there is little risk, utility drops lot for risk averse people.

Portfolio A dominates portfolio B if 𝐸(𝑟𝐴) ≥ 𝐸(𝑟𝐵) and 𝜎𝐴 ≤ 𝜎𝐵

Question 14

Advantage normality assumption

Answer 14

Full distribution can be characterized by mean(s) and (co)variances of returns only, no need for kurtosis and skewness

Question 15

Risk profile

Answer 15

• Cumulative distribution of future wealth: 𝑃𝑟(𝑊𝑡+1 < 𝑋)
• Current wealth is current wealth that grows with return in investment period:
  𝑊 = 𝑃𝑡+1𝑊𝑡 = 𝑊 (1 + 𝑟 )
• Assumptions: returns are normally distributed

Question 16

Value at risk

Answer 16

• Combination of expected return and risk, 5% probability that portfolio will fall in value by more than VaR over one year period

𝑃𝑟(𝑧 < −1.64) = 5% -> 𝑉𝑎𝑅 = 𝑊 (1.64𝜎 − 𝜇), only true if normal distribution.

Question 17

Two effects of investment horizon

Answer 17

• Time-diversification (stddev. effect): if this is only effect, Annual VaR would simply
  be √12 * monthly VaR – but it is not
• Expected return effect: the longer the horizon, the more dominant the impact of the expected return will be

Question 18

Expected shortfall

Answer 18

(conditional tail expectation): focuses on expected loss in worst-case scenario (left tail of distribution) instead of one quintile. More conservative measure of downside risk than VaR.