Interest rates and inflation rates Flashcards
What are the fundamental factors determining interest rates?
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) Govtβs net demand for funds as modified by actions of the Federal Bank
4) Expected rate of inflation
Define the nominal interest rate
The growth rate of your money
What is the real interest rate?
the growth rate of your purchasing power
What is the equation relating the real and nominal interest rate?
r real = r nom - i / 1 + i
Are assets with a risk free nominal interest rate risky?
yes, in real terms
- because future inflation is uncertain
What are real interest rates determined by?
1) propensity of households to save (supply)
2) expected profitability of real investment (demand)
3) government actions including monetary and fiscal policy
What is the Fisher hypothesis?
r nom = r real + E(i)
- E(i) = current expectations of inflation
What happens when real rates are stable?
changes in nominal interest rates predict changes in inflation rates
What do we expect when inflation is higher?
We expect higher nominal interest rates
- leaving the real rate somewhat stable
What does the validity of the Fisher hypothesis depend on?
The ability of investors to predict expected inflation
What are tax liabilities based on?
1) nominal income
2) tax rate (t) determined by the investorβs tax bracket
What does your after tax real return fall by?
= tax rate * inflation rate
β> because you pay taxes even on the portion of interest earnings
What is the equation for the real after-tax rate?
r nom(1 - t) - i = (r real + i)(1 - t ) - i = r real (1 - t) - it
What are 3 sources of investment risk?
1 ) macroeconomic fluctuations
2) changing fortunes of different industries
3) firm specific unexpected developments
What is the equation for holding period returns / realized rate of return?
HPR = (ending price - beginning price + cash dividend) / beginning price
= capital gains + dividend yield
What is the expected mean rate of return?
What is uncertainty surrounding investment a function of?
- the magnitude of possible βsurprisesβ
- the probabilities of possible βsurprisesβ
Define possible βsurprisesβ
deviations of actual returns from the mean returns
How do we characterise uncertainty with a single number?
use variance
The variance of the rate of return r -πππ π - is:
π^2 = Ξ£/ π( s) [π (π ) β πΈ (π) ]^2
The higher the dispersion of outcomes from mean, the higher the average value of
the term [π (π ) β πΈ (π) ]^2, and thus the higher the uncertainty
What does the standard deviation NOT do?
distinguish between good and bad surprises
it treats both only as deviations from the mean
What does it mean if the probability distribution is more or less symmetrically distributed about the mean?
standard deviation is a reasonable/ suitable measure of risk
What does it mean if the probability distribution is norma?
E(r) and standard deviation can completely characterize the distribution of returns
Define the risk premium
the reward offered for the risk involved in investing in stocks
What is compensation for the risk of an investment?
the diff. between the expected HPR on the stocks and the risk free rate
define the excess return
the diff. between the actual rate of return on a risky asset and the risk free rate
Is the risk premium the expected excess return?
YES
What does risk aversion dictate?
to which degree investors are willing to commit funds to stocks
Define the risk free rate
the rate of interest that can be earned with certainty
e.g. rate on short term T-bills
If historical returns fairly represent
the true underlying distribution, then what does the arithmetic average of historical
rates of return provide?
a reasonable forecast of the investmentβs expected HPR
What does the arithmetic average provide?
an unbiased estimate of the expected future return
What is the geometric rate of return (g)?
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 + π)^n= ππππππππ ππππ’π β
π = ππππππππ ππππ’π^1/n β 1
What does a greater diff. between arithmetic and geometric means mean?
The greater the volatility in rates of return
How do you calculate the Sharpe ratio?
risk premium / std. dev. of excess return
Why do we use the Sharpe ratio?
Use it to compare historical and prospective success of alternative portfolios (the
performance of investment managers).
What does the Sharpre ratio describe?
the trade-off between the risk premium (reward) and risk
Characteristics of normal distribution
βSymmetric
βStable
βOnly mean and standard deviation are needed to estimate future scenarios
βStatistical relation between returns can be summarized with a single
correlation coefficient
When is investment management more manageable?
when returns can be well approximated by normal distribution
define the skew of distribution
Standard measure of asymmetry in the probability distribution of returns
What does a negative skew mean?
1) extreme bad outcomes are more frequently than extreme good outcomes
2) skewed to the left
3) standard deviation underestimates risk
What does a positive skew mean?
1) extreme good outcomes are more frequent than extreme bad outcomes
2) skewed to the right
3) standard deviation overestimates risk
What does kurtosis concern?
the likelihood of extreme values on either side of the mean at the expense of a smaller likelihood of moderate deviations
What do high values of kurtosis mean ?
there is more probability mass in the tails of
the distribution than predicted by the normal distribution
What is kurtosis > 0 a sign of?
fat tails
What is value at risk (VaR)?
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?
Define the quantile (q) of a distribution?
the value below which lie q% of the possible values
What is a 1% VaR?
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.
Define expected shortfall (ES)
Expected loss on a security conditional on returns being in the left tail of the probability distribution
What is lower partial standard deviation (LPSD)?
SD computed using only the portion of the return distribution below a threshold such as the risk-free rate of the sample average
