# 6. Foundations of Financial Economics Flashcards

## Practice questions

- 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?

➢ 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.

- List two major factors that drive informational market efficiency through facilitating better investment analysis.

- 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.

- 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.

• Asset pricing model

- What is the market portfolio and what is a market-weight?

• 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.

- What is an ex post excess return?

A realized return (an observed historical return) expressed as an excess return by subtracting the

riskless return from the asset’s total return.

- What factor is contained in the Fama-French-Carhart model that is not contained in the Fama-French model?

• Momentum

- Is the Black-Scholes option pricing model a relative pricing model or an absolute pricing model?

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

- What are the two components to the carrying costs of a financial asset?

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

- 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?

• Binomial tree model

- What is the condition that would cause the term structure of forward prices for a financial security to

be a flat line?

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

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?

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

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?

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

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?

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

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?

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

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)?

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

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?

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

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?

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

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 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

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?

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

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?

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(0.030.25), 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

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?

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 $500e0.010.25,

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

absolute pricing model

attempts to describe a price level

based on its underlying economic factors.

arbitrage-free model

is a financial model with

relationships derived by the assumption that arbitrage

opportunities do not exist, or at least do not persist.

asset pricing model

is a framework for specifying the

return or price of an asset based on its risk, as well as future

cash flows and payoffs.

bear spread

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.

binomial tree model

projects possible outcomes in a

variable by modeling uncertainty as two movements: an

upward movement and a downward movement.