6. Foundations of Financial Economics Flashcards

Practice questions

1
Q
  1. Jane studies past prices and volume of trading in major public equities and establishes equity market neutral positions based on her forecasts of prices. Jane consistently outperforms market indices of comparable risk. Does Jane’s investment strategy and performance indicate:

• The underlying equity market is informationally inefficient at the weak level?
• The underlying equity market is informationally inefficient at the semi-strong level, both, or
neither?

A

➢ The underlying equity market is informationally inefficient at both the weak level and the semi-
strong level since any inefficiency at a “lower” level indicates inefficiency at a “higher” level because the underlying information sets are cumulative moving from weak to strong.

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2
Q
  1. List two major factors that drive informational market efficiency through facilitating better investment analysis.
A
  • Assets will also tend to trade at prices closer to their informationally efficient values when there is easier access to better information.
  • Assets will also tend to trade at prices closer to their informationally- efficient values when there is less uncertainty about their valuation. In other words, when there are better valuation methods.
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3
Q
  1. What is the term used to describe a framework for specifying the return or price of an asset based on its risk, as well as future cash flows and payoffs.
A

• Asset pricing model

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4
Q
  1. What is the market portfolio and what is a market-weight?
A

• The market portfolio is a hypothetical portfolio containing all tradable assets in the world.
• The market weight of an asset is the proportion of the total value of that asset to the total value of
all assets in the market portfolio.

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5
Q
  1. What is an ex post excess return?
A

A realized return (an observed historical return) expressed as an excess return by subtracting the
riskless return from the asset’s total return.

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6
Q
  1. What factor is contained in the Fama-French-Carhart model that is not contained in the Fama-French model?
A

• Momentum

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7
Q
  1. Is the Black-Scholes option pricing model a relative pricing model or an absolute pricing model?
A

• Relative pricing model since it describes an option price relative to the given underlying asset price.

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8
Q
  1. What are the two components to the carrying costs of a financial asset?
A

• Opportunity costs of capital (financing cost) and storage or custody costs

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9
Q
  1. What is the name of a model that projects possible outcomes in a variable by modeling uncertainty as two movements: an upward movement and a downward movement?
A

• Binomial tree model

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10
Q
  1. What is the condition that would cause the term structure of forward prices for a financial security to
    be a flat line?
A

• When the interest rate and the dividend rate are equal (i.e. r=d)

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11
Q

Using the CAPM equation, when the risk-free
rate is 2%, the expected return of the market is 10%, and the beta of asset i is
1.25, what is the expected return of asset i?

A

E(R(i)) = R(f) + Beta(t) (E(Rm) - R(f))

Apply equation 6.1 to solve the CAPM equation for the expected return of asset i.
Subtract 10% (expected return of the market) by 2% for a difference of 8%.
Multiply 8% by 1.25 (beta of the asset) for a product of 10%. Lastly, add the riskfree
rate of 2% to 10% for a sum of 12%, which is the expected return of asset i.

Step One: Press 0.1 → - → 0.02
Step Two: Press x → 1.25
Step Three: Press + → 0.02
Step Four: Press =
Answer: 0.12
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12
Q

Returning to the previous example in which the
risk-free rate is 2% and the beta of asset i is 1.25, if the actual return of the
market is 22%, the ex post CAPM model would generate a return due to nonidiosyncratic
effects of? If the asset’s
actual return is 30%, making the idiosyncratic return?

A

27% for the asset: 2% + [1.25(22% – 2%)]. If the asset’s
actual return is 30%, then the extra 3% would be attributable to idiosyncratic return.

Step One: Press 0.22 → - → 0.02
Step Two: Press x → 1.25
Step Three: Press + → 0.02
Step Four: Press =
Answer: 0.27
To find the idiosyncratic return
Step One: Press 0.3 → - → 0.27
Step Two: Press =
Answer: 0.03
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13
Q

A researcher wishes to test for statistically
significant factors in explaining asset returns. Using a confidence level of 90%,
how many statistically significant factors would the researcher expect to identify
by testing 50 variables, independent from one another, that had no true
relationship to the returns?

A
If there is 1 researcher conducting the test with a 90% confidence level
Step One: Press 1 → - → .9
Step Two: Press x → 50
Step Three: Press =
Answer: 5
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14
Q

The answer is five, which is found by multiplying the number of unrelated
variables (50) by the probability of mistakenly concluding that the variables were
true factors (10%). What if research were performed with a confidence level of
99.9% but with 100 researchers, each testing 50 different variables on different
data sets?

A
If there are 100 researchers conducting the test with a 99.9% confidence level
Step One: Press 1 → - → .999
Step Two: Press x → 50
Step Three: Press x → 100
Step Four: Press =
Answer: 5
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15
Q

Nine-month riskless securities trade for $97,000,
and 12-month riskless securities sell for $P (both with $100,000 face values and
zero coupons). A forward contract on a three-month, riskless, zero-coupon bond,
with a $100,000 face value and a delivery of nine months, trades at $99,000.
What is the arbitrage-free price of the 12-month zero-coupon security (i.e., P)?

A

The 12-month bond offers a ratio of terminal wealth to investment of
($100,000/P). The nine-month bond reinvested for three months using the
forward contract offers ($100,000/$97,000)($100,000/$99,000). Setting the two
returns equal and solving for P generates P = $96,030. The 12-month bond must
sell for $96,030 to prevent arbitrage.

Step One: Press 100000 → ÷ → 97000
Step Two: Press = ”1.030927835”
Step Three: Press 100000 → ÷ → 99000
Step Four: Press x → 1.030927835
Step Five: Press = “1.041341247”
Step Six: Press 100000 → ÷ → 1.041341247
Answer: 96030.00
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16
Q

A three-year riskless security trades at a yield of
3.4%, whereas a forward contract on a two-year riskless security that settles in
three years trades at a forward rate of 2.4%. Assuming that the rates are
continuously compounded, what is the no-arbitrage yield of a five-year riskless
security?

A

Inserting 3.4% as the shorter-term rate in Equation 6.9 and 2.4% as the left side
of equation 6.9, the longer-term rate, RT, can be solved as 3.0%, noting that T =
5 and t = 3. Note that earning 3.0% for five years (15%) is equal to the sum of
earning 3.4% for three years (10.2%) and 2.4% for two years (4.8%). The rates
may be summed due to the assumption of continuous compounding.
FT–t = (T x RT – t x Rt)/(T – t)

Step One: Press 5 → - → 3
Step Two: Press x → 0.024
Step Three: Press = “0.048”
Step Four: Press 3 → x → 0.034
Step Five: Press + → 0.048
Step Six: Press ÷ → 5
Step Seven: Press =
Answer: 0.03
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17
Q

A stock currently selling for $10 will either rise to
$30 or fall to $0 in one year. How much would a one-year call sell for if its strike
price were $20?

A

The payoff of the call ($10) would be one-third the payoff of the
stock. Therefore, the call must sell for $3.33 ($10 stock price x 1/3).

Step One: Press $30 → - → $20
Step Two: Press ÷ → $30
Step Three: Press x → $10
Step Four: Press =
Answer: 3.33
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18
Q

A stock sells for $100 and is certain to make a
cash distribution of $2 just before the end of one year. A forward contract on that
stock trades with a settlement in one year. Assume that the cost to finance a
$100 purchase of the stock is $5 (due at the end of the year). What is the noarbitrage
price of this forward contract?

A

A one-year forward contract on the stock must trade at $103. At settlement, a
long position in the forward contract obligates the holder to pay $103 in exchange
for delivery of the stock. If the investor uses the cash market, after one year the
investor will pay the same amount for the asset ($103). The $103 at the end of
the year includes the cost of buying the stock in the spot market with 100%
financing (which accrues to $105 at settlement) and the benefit of receiving the
$2 dividend.

Step One: Press $100 → + → $5
Step Two: Press - → $2
Step Three: Press =
Answer: $103

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19
Q

If the spot price of an equity index that pays no
dividends is $500 and if the riskless interest rate is zero, what is the one-year
forward price on the equity index?

A

The forward contract of every time to delivery has a forward price of exactly
$500. Market participants would be indifferent between buying and selling the
index in the spot market with instant delivery or in the forward market with
delayed delivery because there are no interest payments and dividends to
consider.

Step One: Press 0 → - → 0
Step Two: Press x → 1
Step Three: Press 2nd → e(^x)
Step Four: Press x → 500
Step Five: Press =
Answer: $500
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20
Q

Assuming a continuously compounded annual
interest rate of 5%, if the spot price of an equity index with 2% dividends is $500,
what would be the forward price on the equity index with settlement in three
months?

A

The price of every forward contract on that index for every time to
settlement would be $500e(0.05–0.02)T. The three-month forward price would be
$500e(0.030.25), or $503.76. Six-month and 12-month forward prices would be
$507.56 and $515.28, respectively (found by inserting 0.50 and 1.00 for T, and
0.03 for r – d).

Three-Months
Step One: Press 0.05 → - → 0.02
Step Two: Press x → 0.25
Step Three: Press 2nd → ex
Step Four: Press x → 500
Step Five: Press =
Answer: $503.76
Six-Months
Step One: Press 0.05 → - → 0.02
Step Two: Press x → 0.50
Step Three: Press 2nd → ex
Step Four: Press x → 500
Step Five: Press =
Answer: $507.56
Twelve-Months
Step One: Press 0.05 → - → 0.02
Step Two: Press x → 1
Step Three: Press 2nd → ex
Step Four: Press x → 500
Step Five: Press =
Answer: $515.23
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21
Q

Assuming a continuously compounded annual
interest rate of 2%, if the spot price of an equity index with 3% dividends is $500,
what would be the forward price of a contract with settlement in three months?

A

The price of every forward contract of every time to delivery would be $500e(–
0.01)T, with (r – d) = –1%. The three-month forward price would be $500e0.010.25,
or $498.75. Six-month and 12-month forward prices would be $497.51 and
$495.01, respectively (found by inserting 0.50 and 1.00 for T).
F(T) = S x e(^r–d)T

Three-Months
Step One: Press 0.02 → - → 0.03
Step Two: Press x → 0.25
Step Three: Press 2nd → ex
Step Four: Press x → 500
Step Five: Press =
Answer: $498.75
Six-Months
Step One: Press 0.02 → - → 0.03
Step Two: Press x → 0.50
Step Three: Press 2nd → ex
Step Four: Press x → 500
Step Five: Press =
Answer: $497.51
Twelve-Months
Step One: Press 0.02 → - → 0.03
Step Two: Press x → 1
Step Three: Press 2nd → ex
Step Four: Press x → 500
Step Five: Press =
Answer: $495.02
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22
Q

absolute pricing model

A

attempts to describe a price level

based on its underlying economic factors.

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23
Q

arbitrage-free model

A

is a financial model with
relationships derived by the assumption that arbitrage
opportunities do not exist, or at least do not persist.

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24
Q

asset pricing model

A

is a framework for specifying the
return or price of an asset based on its risk, as well as future
cash flows and payoffs.

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25
Q

bear spread

A

An option combination in which the long option position is at
the higher of two strike prices is this, which offers
bearish exposure to the underlying asset that begins at the
higher strike price and ends at the lower strike price.

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26
Q

binomial tree model

A

projects possible outcomes in a
variable by modeling uncertainty as two movements: an
upward movement and a downward movement.

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27
Q

black-scholes call option formula

A

expresses the price of a
call option as a function of five variables: the price of the
underlying asset, the strike price, the return volatility of the
underlying asset, the time to the option’s expiration, and the
riskless rate.

28
Q

bull spread

A

An option combination in which the long option position is at
the lower of two strike prices is this, which offers
bullish exposure to the underlying asset that begins at the lower
strike price and ends at the higher strike price.

29
Q

carrying cost

A

is the cost of maintaining a position
through time and includes direct costs, such as storage or
custody costs, as well as opportunity costs, such as forgone
cash flows.

30
Q

cash market

A

The spot market or this is any market in which
transactions involve immediate payment and delivery: The
buyer immediately pays the price, and the seller immediately
delivers the product.

31
Q

collar

A

generally refers to a long position in an asset
combined with a short call option and a long put option on that
asset, in which the call option has a higher strike price than the
put option.

32
Q

cost-of-carry model

A

specifies a relationship between two
positions that must exist if the only difference between the
positions involves the expense of maintaining the positions.

33
Q

covered call

A

combines being long an asset with being short

a call option on the same asset.

34
Q

elasticity

A

is the percentage change in a value with respect

to a percentage change in another value.

35
Q

empirical model

A

is derived from observation. An example
would be a model that recognizes that the returns of some
traditional assets are correlated with their market-to-book
ratios.

36
Q

excess return

A

of an asset refers to the excess or deficiency

of the asset’s return relative to the periodic risk-free rate.

37
Q

fama-french model

A

links the returns of assets to three
factors: (1) the market portfolio, (2) a factor representing a
value versus growth effect, and (3) a factor representing a
small-cap versus large-cap effect.

38
Q

fama-french-carhart model

A

adds a fourth factor to the

Fama-French model: momentum.

39
Q

financed positions

A

enable economic ownership of an asset

without the posting of the purchase price.

40
Q

forward contract

A

is simply an agreement calling for

deferred delivery of an asset or a payoff.

41
Q

idiosyncratic return

A

is the portion of an asset’s return that is
unique to an investment and not driven by a common
association.

42
Q

idiosyncratic risk

A

is the dispersion in economic outcomes
caused by investment-specific effects. This section focuses on
realized returns and the modeling of risk.

43
Q

informational market efficiency

A

refers to the extent to which

asset prices reflect available information.

44
Q

lambda or omega

A

for a call option is the elasticity of an
option price with respect to the price of the underlying asset
and is equal to delta multiplied times the quantity (S/c).

45
Q

multifactor models

A

of asset pricing express systematic risk
using multiple factors and are extremely popular throughout
traditional and alternative investing.

46
Q

naked option

A

A short option position that is unhedged is often referred as this.

47
Q

omicron

A

is the partial derivative of an option or a position
containing an option to a change in the credit spread and is
useful for analyzing option positions on credit-risky assets.

48
Q

option collar

A

generally refers only to the long position in a

put and a short position in a call.

49
Q

option combination

A

contains both calls and puts on the

same underlying asset.

50
Q

Option spread

A

1) contains either call options or put
options (not both), and (2) contains both long and short
positions in options with the same underlying asset.

51
Q

option straddle

A

is a position in a call and put with the
same sign (i.e., long or short), the same underlying asset, the
same expiration date, and the same strike price.

52
Q

option strangle

A

is a position in a call and put with the same
sign, the same underlying asset, the same expiration date, but
different strike prices.

53
Q

protective put

A

combines being long an asset with a long

position in a put option on the same asset.

54
Q

put-call parity

A

is an arbitrage-free relationship among the
values of an asset, a riskless bond, a call option, and a put
option.

55
Q

relative pricing model

A

prescribes the relationship between

two prices.

56
Q

rho

A

is the sensitivity of an option price with respect to

changes in the riskless interest rate.

57
Q

risk reversal

A

A long out-of-the-money call combined with a short out-ofthe-
money put on the same asset and with the same
expiration date is termed as this.

58
Q

semistrong form informational market efficiency

A

(or semistrong level) refers to market prices
reflecting all publicly available information (including not only
past prices and volumes but also any publicly available
information such as financial statements and other underlying
economic data).

59
Q

single-factor asset pricing model.

A

explains returns and

systematic risk using a single risk factor.

60
Q

strong form informational market efficiency

A

(or strong level) refers to market prices reflecting all publicly
and privately available information.

61
Q

systematic return

A

is the portion of an asset’s return driven

by a common association.

62
Q

systematic risk

A

is the dispersion in economic outcomes

caused by variation in systematic return.

63
Q

term structure of forward contracts

A

is the relationship
between forward prices (or forward rates) and the time to
delivery of the forward contract.

64
Q

theoretical model

A

the factors are derived from reasoning

based on known facts and relationships.

65
Q

tradable asset

A

is a position that can be readily established
and liquidated in the financial market, such as a stock position,
a bond position, or a portfolio of liquid positions.

66
Q

weak form informational market efficiency

A

(or weak level)
refers to market prices reflecting available data on past prices
and volumes.