Interest rates and inflation rates

Question 1

What are the fundamental factors determining interest rates?

Answer 1

1) supply of funds from savers (primarily households)
2) demand for funds from businesses to be used to finance investment in plant, equipment and inventories
3) Govt’s net demand for funds as modified by actions of the Federal Bank
4) Expected rate of inflation

Question 2

Define the nominal interest rate

Answer 2

The growth rate of your money

Question 3

What is the real interest rate?

Answer 3

the growth rate of your purchasing power

Question 4

What is the equation relating the real and nominal interest rate?

Answer 4

r real = r nom - i / 1 + i

Question 5

Are assets with a risk free nominal interest rate risky?

Answer 5

yes, in real terms

• because future inflation is uncertain

Question 6

What are real interest rates determined by?

Answer 6

1) propensity of households to save (supply)
2) expected profitability of real investment (demand)
3) government actions including monetary and fiscal policy

Question 7

What is the Fisher hypothesis?

Answer 7

r nom = r real + E(i)

• E(i) = current expectations of inflation

Question 8

What happens when real rates are stable?

Answer 8

changes in nominal interest rates predict changes in inflation rates

Question 9

What do we expect when inflation is higher?

Answer 9

We expect higher nominal interest rates

• leaving the real rate somewhat stable

Question 10

What does the validity of the Fisher hypothesis depend on?

Answer 10

The ability of investors to predict expected inflation

Question 11

What are tax liabilities based on?

Answer 11

1) nominal income

2) tax rate (t) determined by the investor’s tax bracket

Question 12

What does your after tax real return fall by?

Answer 12

= tax rate * inflation rate

–> because you pay taxes even on the portion of interest earnings

Question 13

What is the equation for the real after-tax rate?

Answer 13

r nom(1 - t) - i = (r real + i)(1 - t ) - i = r real (1 - t) - it

Question 14

What are 3 sources of investment risk?

Answer 14

1 ) macroeconomic fluctuations

2) changing fortunes of different industries
3) firm specific unexpected developments

Question 15

What is the equation for holding period returns / realized rate of return?

Answer 15

HPR = (ending price - beginning price + cash dividend) / beginning price

= capital gains + dividend yield

Question 16

What is the expected mean rate of return?

Question 17

What is uncertainty surrounding investment a function of?

Answer 17

• the magnitude of possible ‘surprises’

- the probabilities of possible ‘surprises’

Question 18

Define possible ‘surprises’

Answer 18

deviations of actual returns from the mean returns

Question 19

How do we characterise uncertainty with a single number?

Answer 19

use variance

The variance of the rate of return r -𝑉𝑎𝑟 𝑟 - is:
𝜎^2 = Σ/ 𝑝( s) [𝑟 (𝑠) − 𝐸 (𝑟) ]^2

The higher the dispersion of outcomes from mean, the higher the average value of
the term [𝑟 (𝑠) − 𝐸 (𝑟) ]^2, and thus the higher the uncertainty

Question 20

What does the standard deviation NOT do?

Answer 20

distinguish between good and bad surprises

it treats both only as deviations from the mean

Question 21

What does it mean if the probability distribution is more or less symmetrically distributed about the mean?

Answer 21

standard deviation is a reasonable/ suitable measure of risk

Question 22

What does it mean if the probability distribution is norma?

Answer 22

E(r) and standard deviation can completely characterize the distribution of returns

Question 23

Define the risk premium

Answer 23

the reward offered for the risk involved in investing in stocks

Question 24

What is compensation for the risk of an investment?

Answer 24

the diff. between the expected HPR on the stocks and the risk free rate

Question 25

define the excess return

Answer 25

the diff. between the actual rate of return on a risky asset and the risk free rate

Question 26

Is the risk premium the expected excess return?

Answer 26

YES

Question 27

What does risk aversion dictate?

Answer 27

to which degree investors are willing to commit funds to stocks

Question 28

Define the risk free rate

Answer 28

the rate of interest that can be earned with certainty

e.g. rate on short term T-bills

Question 29

If historical returns fairly represent
the true underlying distribution, then what does the arithmetic average of historical
rates of return provide?

Answer 29

a reasonable forecast of the investment’s expected HPR

Question 30

What does the arithmetic average provide?

Answer 30

an unbiased estimate of the expected future return

Question 31

What is the geometric rate of return (g)?

Answer 31

Intuitive measure of performance over the sample period is the (fixed) annual HPR that would compound over the period to the same terminal value obtained from the sequence of actual returns in the time series

(1 + 𝑔)^n= 𝑇𝑒𝑟𝑚𝑖𝑛𝑎𝑙 𝑉𝑎𝑙𝑢𝑒 ⇒
𝑔 = 𝑇𝑒𝑟𝑚𝑖𝑛𝑎𝑙 𝑉𝑎𝑙𝑢𝑒^1/n − 1

Question 32

What does a greater diff. between arithmetic and geometric means mean?

Answer 32

The greater the volatility in rates of return

Question 33

How do you calculate the Sharpe ratio?

Answer 33

risk premium / std. dev. of excess return

Question 34

Why do we use the Sharpe ratio?

Answer 34

Use it to compare historical and prospective success of alternative portfolios (the
performance of investment managers).

Question 35

What does the Sharpre ratio describe?

Answer 35

the trade-off between the risk premium (reward) and risk

Question 36

Characteristics of normal distribution

Answer 36

✓Symmetric
✓Stable
✓Only mean and standard deviation are needed to estimate future scenarios
✓Statistical relation between returns can be summarized with a single
correlation coefficient

Question 37

When is investment management more manageable?

Answer 37

when returns can be well approximated by normal distribution

Question 38

define the skew of distribution

Answer 38

Standard measure of asymmetry in the probability distribution of returns

Question 39

What does a negative skew mean?

Answer 39

1) extreme bad outcomes are more frequently than extreme good outcomes
2) skewed to the left
3) standard deviation underestimates risk

Question 40

What does a positive skew mean?

Answer 40

1) extreme good outcomes are more frequent than extreme bad outcomes
2) skewed to the right
3) standard deviation overestimates risk

Question 41

What does kurtosis concern?

Answer 41

the likelihood of extreme values on either side of the mean at the expense of a smaller likelihood of moderate deviations

Question 42

What do high values of kurtosis mean ?

Answer 42

there is more probability mass in the tails of

the distribution than predicted by the normal distribution

Question 43

What is kurtosis > 0 a sign of?

Answer 43

fat tails

Question 44

What is value at risk (VaR)?

Answer 44

Loss that will be incurred in the event of an extreme adverse price change with some given, usually low, probability.

e.g., how much would I lose if my return were in the 1st percentile of the distribution?

Question 45

Define the quantile (q) of a distribution?

Answer 45

the value below which lie q% of the possible values

Question 46

What is a 1% VaR?

Answer 46

1% VaR: cut-off point separating the 1% worst-case future scenarios from the rest of the distribution (99%).

To obtain a sample estimate of 1% VaR, we sort observations from high to low and we pick the return at the 1st percentile of the sample distribution.

Question 47

Define expected shortfall (ES)

Answer 47

Expected loss on a security conditional on returns being in the left tail of the probability distribution

Question 48

What is lower partial standard deviation (LPSD)?

Answer 48

SD computed using only the portion of the return distribution below a threshold such as the risk-free rate of the sample average