6. Foundations of Financial Economics

Question 1

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?

Answer 1

➢ 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.

Question 2

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

Answer 2

• 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.

Question 3

3. 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.

Answer 3

• Asset pricing model

Question 4

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

Answer 4

• 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.

Question 5

5. What is an ex post excess return?

Answer 5

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

Question 6

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

Answer 6

• Momentum

Question 7

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

Answer 7

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

Question 8

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

Answer 8

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

Question 9

9. 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?

Answer 9

• Binomial tree model

Question 10

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

Answer 10

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

Question 11

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?

Answer 11

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

Question 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?

Answer 12

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

Question 13

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?

Answer 13

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

Question 14

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?

Answer 14

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

Question 15

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)?

Answer 15

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

Question 16

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?

Answer 16

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

Question 17

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?

Answer 17

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

Question 18

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?

Answer 18

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

Question 19

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?

Answer 19

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

Question 20

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?

Answer 20

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

Question 21

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?

Answer 21

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

Question 22

absolute pricing model

Answer 22

attempts to describe a price level based on its underlying economic factors.

Question 23

arbitrage-free model

Answer 23

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

Question 24

asset pricing model

Answer 24

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

Question 25

bear spread

Answer 25

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.

Question 26

binomial tree model

Answer 26

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

Question 27

black-scholes call option formula

Answer 27

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.

Question 28

bull spread

Answer 28

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.

Question 29

carrying cost

Answer 29

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.

Question 30

cash market

Answer 30

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.

Question 31

collar

Answer 31

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.

Question 32

cost-of-carry model

Answer 32

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

Question 33

covered call

Answer 33

combines being long an asset with being short a call option on the same asset.

Question 34

elasticity

Answer 34

is the percentage change in a value with respect to a percentage change in another value.

Question 35

empirical model

Answer 35

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.

Question 36

excess return

Answer 36

of an asset refers to the excess or deficiency of the asset’s return relative to the periodic risk-free rate.

Question 37

fama-french model

Answer 37

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.

Question 38

fama-french-carhart model

Answer 38

adds a fourth factor to the Fama-French model: momentum.

Question 39

financed positions

Answer 39

enable economic ownership of an asset without the posting of the purchase price.

Question 40

forward contract

Answer 40

is simply an agreement calling for deferred delivery of an asset or a payoff.

Question 41

idiosyncratic return

Answer 41

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

Question 42

idiosyncratic risk

Answer 42

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

Question 43

informational market efficiency

Answer 43

refers to the extent to which asset prices reflect available information.

Question 44

lambda or omega

Answer 44

Delta

Measures Impact of a Change in the Price of Underlying

Gamma

Measures the Rate of Change of Delta

Question 45

multifactor models

Answer 45

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

Question 46

naked option

Answer 46

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

Question 47

omicron

Answer 47

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.

Question 48

option collar

Answer 48

generally refers only to the long position in a put and a short position in a call.

Question 49

option combination

Answer 49

contains both calls and puts on the same underlying asset.

Question 50

Option spread

Answer 50

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.

Question 51

option straddle

Answer 51

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.

Question 52

option strangle

Answer 52

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

Question 53

protective put

Answer 53

combines being long an asset with a long position in a put option on the same asset.

Question 54

put-call parity

Answer 54

is an arbitrage-free relationship among the values of an asset,

a riskless bond,

a call option, and

a put option.

Question 55

relative pricing model

Answer 55

prescribes the relationship between two prices.

Question 56

rho

Answer 56

is the sensitivity of an option price with respect to changes in the riskless interest rate.

Question 57

risk reversal

Answer 57

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

Question 58

semistrong form informational market efficiency

Answer 58

(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).

Question 59

single-factor asset pricing model.

Answer 59

explains returns and systematic risk using a single risk factor.

Question 60

strong form informational market efficiency

Answer 60

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

Question 61

systematic return

Answer 61

is the portion of an asset’s return driven by a common association.

The part of the return dependent on the benchmark return = ß

Question 62

systematic risk

Answer 62

is the dispersion in economic outcomes caused by variation in systematic return.

Question 63

term structure of forward contracts

Answer 63

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

Question 64

theoretical model

Answer 64

the factors are derived from reasoning based on known facts and relationships.

Question 65

tradable asset

Answer 65

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.

Question 66

weak form informational market efficiency

Answer 66

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