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Fina 385: Theory of Finance 1 > stuff from lesson 1 > Flashcards

stuff from lesson 1 Flashcards

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1
Q

the fundamental factors that determine the level of interest rates

A
  1. The supply of funds from savers, primarily households
  2. The demand for funds from businesses to be used to finance physical investments in plant, equipment, and inventories (real assets or capital formation)
  3. The government’s net supply demand for funds as modified by actions of the monetary authority
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2
Q

An interest rate

A

a promised rate of return denominated in some unit of account over some time period

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3
Q

risk-free rate

A

no default risk

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4
Q

The consumer price index (CPI)

A

measures purchasing power

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5
Q

nominal interest rate

A

the growth rate of your money

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6
Q

real interest rate

A

the growth rate of your purchasing power

r = R - i or r = (R - i)/(1 + i)

R: the nominal rate

r: the real rate
i: the inflation rate

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7
Q

is the future real rate known?

A

nah bro

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8
Q

what determines the real interest rate?

A

supply

demand

government actions

expected inflation

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9
Q

why do economists frequently talk as if there were a single representative rate economy wide?

A

because the many different interest rates economywide move together

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10
Q

the nominal rate equation

The so-called Fisher equation

A

R = r + E(i)

R: the nominal rate

r: the real rate

E(i): expected inflation

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11
Q

what does the Fisher equation imply when real rates are reasonably stable?

A

changes in nominal rates ought to predict changes in inflation rates

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12
Q

Tax liabilities are based on nominal income or real income?

A

nominal income

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13
Q

the after-tax interest rate

A

R(1 - t)

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14
Q

The real after-tax rate

what does this mean?

A

r = (R(1 - t) - i + i · t) / (1 - t)

the after-tax real rate of return falls as inflation rises

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15
Q

Zero-coupon bonds

A

bonds that are sold at a discount from par value

provide their entire return from the difference between the purchase price and the ultimate repayment of par value

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16
Q

effective annual rate (EAR)

A

the percentage increase in funds invested over a 1-year horizon

For a 1-year investment, the EAR equals the total return

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17
Q

how can we find effective annual rate (EAR)?

what is the formula?

A

we compound the periodic interest

EAR = (1 + nominal rate)^(payments per year) - 1

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18
Q

annual percentage rates

formula

A

simple interest

APR = ((1 + EAR)^r - ) / T

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19
Q

what is the formula to find the EAR when we, theoretically, reach the point of continuous compounding?

A

EAR = e^rcc - 1

rcc: The continuously compounded annual percentage rate

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20
Q

for the past 56 years (except since like 2001), what has been the driving force for the nominal rate of interest?

why?

A

inflation

because of the fisher equation

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21
Q

average rate of inflation in Canada his increased or decreased?

A

decreased

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22
Q

a wealth index

A

The progression of the value of a $1 investment

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23
Q

through time, has inflation fucked up our purchasing power even if we include compound interest?

A

ye bruv

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24
Q

when will the correlation between inflation and nominal T-bill rates will be close to perfect (1.0)?

how does it affect the correlation between inflation and the realized real rate

A

When the expected real rate is stable and realized inflation matches initial expectations

the correlation between inflation and the realized real rate will be close to 0

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25
Q

when will the correlation between inflation and nominal T-bill rates will be close to perfectly negative (-1.0)?

why?

A

when investors either ignored or were very poor at predicting inflation

because the real rate would then fall one-for-one with any increase in inflation

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26
Q

dividend yield

A

dividends earned per dollar invested

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27
Q

total holding-period return (HPR)

A

depends on the price at which you check it in the future (at the end of the period)

also depends on the amount of dividend you received

HPR = capital gain (loss) + dividends yield

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28
Q

expected or mean return E(r)

A

probability-weighted average of the rates of return in all scenarios

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29
Q

The standard deviation of the rate of return (σ)

A

a measure of risk

measure the uncertainty of outcomes

the square root of the variance

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30
Q

risk free rate

A

the rate you can earn by leaving money in risk-free assets such as T-bills, money market funds, or the bank

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31
Q

how do we measure the expected reward for the risk involved in investing in an asset?

A

the risk premium

the difference between the expected return (expected HPR) and the risk free rate

ER - RF

32
Q

excess return

A

The difference between the actual rate of return on a risky asset and the risk free rate

33
Q

the risk premium

A

the expected excess return

34
Q

risk aversion

A

with no risk premium, no one would invest

only invest if the reward is enough to compensate for the risk undertaken

In theory then, there must always be a positive risk premium on stocks in order to induce risk-averse investors to hold the existing supply of stocks instead of placing all their money in risk-free asset

35
Q

forward-looking scenario analysis

A

we determine a set of relevant scenarios and associated investment outcomes (rates of return)

–> we assign probabilities to each

–> conclude by computing the risk premium (the reward) and standard deviation (the risk) of the proposed investment

36
Q

in which form do asset and portfolio return histories come from?

A

in the form of time series of past realized returns

–> they disregard past assessment of probabilities

–> we only observe dates and associated HPRs

37
Q

arithmetic average for rates of return

A

(E of past returns) / n

n: number of periods

basically, the average of the past rates of return because each past scenarios are equal scenarios

38
Q

geometric mean

A

[(1 + past return 1) · (1 + past return 2) · (1 + past return 3) · … · (1 + past return n)]^(1/n) - 1

39
Q

when does the arithmetic average return form a historical period provide a good forecast of expected HPR?

A

If the time series of historical returns fairly represent the true underlying probability distribution

40
Q

when is the discrepancy between the arithmetic and geometric averages larger?

A

when the swings in rates of return are larger

–> between the compound rate earned over the sample period and the average of the annual returns

41
Q

what are we interested in when thinking about risk?

A

we are interested in the likelihood of deviations from the expected return

42
Q

the two types of standard deviation

A

ex ante (expected standard deviation)

ex post (standard deviation looking at past results)

43
Q

ex ante (expected standard deviation)

A

σ = (E(probi) · (ri - ER)^2)^(1/2)

future or expected

44
Q

ex post (standard deviation looking at past results)

A

past or historical

σ = ((E(ri - r_)^2) / (n - 1))^(1/2)

r_: the average return (using the arithmetic average)

ri: return in year I
n: number of observations

45
Q

do observation frequencies have any impact on the accuracy of mean estimates?

what else could improve the accuracy of mean estimates?

A

nah boy

the duration of sample time series is what improves the accuracy of mean estimates

46
Q

how is the monthly average return (r_M) annualized (r_A)?

A

with compounding

r_A = (1 + r_M)^12 - 1

–> or just do it with financial calculator

47
Q

how can the accuracy of estimates of the standard deviation and higher moments be made more precise?

A

by increasing the number of observations

48
Q

how do we annualize monthly standard deviation (σM) when monthly returns are uncorrelated to one another?

A
  1. we find the monthly variance (σ^2M)
  2. we multiply the monthly variance by 12

–> 12σ^2M = σ^2A

  1. we find the annualized standard deviation

–> σA

49
Q

The Reward-to-Variability (Sharpe) Ratio

A

we measure the attraction of an investment portfolio by the ratio of its risk premium to the Standard Deviation of its excess returns

–> shows the importance of the tradeoff between reward (the risk premium) and risk

Sharpe ratio (for portfolios) = (risk premium) / (SD of excess returns)

widely used to evaluate the perfjoamcne of investment managers

50
Q

how do we annualize the Sharpe ratio from monthly rates?

A

we multiply the risk premium (numerator) by 12

we multiply the SD (denominator) by (12)^(1/2)

51
Q

the four factors of the normal distribution we need to know

A
  1. the normal distribution is symmetric
  2. the normal distribution belongs to a unique family of distributions characterized as “stable,” because of the following property: When assets with normally distributed returns are mixed to construct a portfolio, the portfolio return is also normally distributed
  3. scenario analysis is greatly simplified when only mean and SD need to be estimated to obtain probabilities of future scenarios
  4. when constructing portfolios of securities, we must account for the statistical dependence of returns across securities

–> when securities are normally distributed, the statistical relationships between returns can be summarized with a correlation coefficient

52
Q

what does normality assure?

A

normality of excess returns hugely simplify portfolio selection

assures us that standard deviation is a complete measure of risk

assures us that the sharpe ratio is a complete measure of portfolio performance

53
Q

Moments of a distribution

A

can define a distribution

  1. mean
  2. volatility
  3. skewness
  4. Kurtosis
54
Q

what does the number of moments needed to define a distribution depend on?

A

on how well it behaves

55
Q

the mean (arithmetic Average)

A

he first moment of the normal distribution

the point where we observe the highest number of observations

56
Q

Volatility (standard deviation)

A

Volatility is the square root of the Variance

–> both are the second moment of the distribution

measures dispersion of the distribution

measures the uncertainty of the outcome

57
Q

Skewness

A

the third moment of the distribution

measures asymmetry of the distribution

the ratio of the average cubed deviation from the mean to the cubed standard deviation

58
Q

what happens if If skewness is positive?

A

the Standard Deviation (Volatility) overestimates the risk

59
Q

what happens if skewness is negative?

A

the Standard Deviation underestimates the risk

60
Q

Kurtosis

A

the fourth moment of the distribution

measures the degree of fat tails in the distribution

61
Q

what does a higher kurtosis mean?

A

the fatter the tails of the distribution, the more the standard deviation will underestimate the risk

62
Q

the values of skewness and kurtosis in a normal distribution

A

they are both 0

63
Q

Factors Affecting Stock Prices Fluctuations

A

Expectations about future CFs (the numerator)

Expectation of Discount Rates

–> RF (Changes by Central Bank Rates)

–> RP (Changes in the amount of risk and Changes in the compensation required by investors to bear risk (price of risk))

64
Q

how does inflation affect bonds?

A

Discount Rates may rise

Bonds future CFs are known in advance

–> Based on the PV pricing formula, Bond Price may Fall

–> bond will sell at discount if interest rate goes above coupon rate

65
Q

how does inflation affect stocks?

A

Discount Rates may rise

Stock future CFs are not known in advance

Over the long run, the two effect cancel each other and stock prices remain unchanged

Over the short run, stock prices tend to fall (until the market adjust)

66
Q

when do we use the geometric average?

A

when we want to estimate the average one period return

achieved on our investment

67
Q

when do we use the arithmetic average?

A

when want to predict future expected next period return

68
Q

true or false

Geometric Average is always less than Arithmetic Average

A

true

69
Q

the most important

macroeconomic measure

A

Interest rates

70
Q

Other Measures of Risk

A

Value at Risk (VaR)

Lower Conditional Tale Expectation (LCTE) or Expected Shortfall (ES)

Lower Partial Standard Deviation (LPSD)

Sortino Ratio

71
Q

Value at Risk (VaR)

A

Is the quintile of a distribution 

Usually we define VaR by the 1% or 5% quintile

A 1% VaR means that there is a 1% probability that our loss will be below the VaR value

However we have no idea about the magnitude of our loss

72
Q

Lower Conditional Tale Expectation (LCTE) or Expected Shortfall (ES)

A

LCTE answer the question that VaR does not answer

LCTE adds to VaR

LCTE gives us a rough idea about what should be the expected magnitude of our loss

If VaR tell us that there is a 5% probability that our loss be equal or below the VaR value then LCTE continues and say that the expected (average) loss would be of …

73
Q

Lower Partial Standard Deviation (LPSD)

A

Similar to usual standard deviation

Uses only negative deviations from the risk-free return

Addresses the asymmetry in returns issue

74
Q

Sortino Ratio

A

The ratio of average excess returns to LPSD

75
Q

true or false

discount rate = RF + Risk Premium (or excess returns)?

A

true

RF: compensate investors for the time value for money

Risk Premium (or excess returns): compensate investors for bearing the risk of future CFs

Fina 385: Theory of Finance 1 (12 decks)

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