Financial Markets - Leverage and Nonlinearity: C1M4 Flashcards
Leverage and Nonlinearity
1
Q
What does the intrinsic value of an option represent?
A
The payoff of the option at any given time if exercised immediately.
2
Q
When is a call option considered in the money (ITM)?
A
When S>K (Stock price S is greater than the strike price K).
3
Q
When is a put option considered out of the money (OTM)?
A
When S>K (Stock price S is greater than the strike price K).
4
Q
What are the two components of an option’s premium?
A
Intrinsic value and time value.
5
Q
Why must an option’s premium always be positive?
A
To prevent arbitrage opportunities, as a premium of zero would imply a free option.
6
Q
How does the strike price affect a call option’s value?
A
Higher strike prices make call options less valuable because they are harder to be in the money.
7
Q
How does time until expiration generally affect an option’s value?
A
Longer expiration times increase an option’s value due to greater optionality.
8
Q
What happens to a call option’s value if the risk-free interest rate increases?
A
The call option’s value increases.
9
Q
What is the role of the Options Clearing Corporation (OCC)?
A
It manages the exercise and assignment of options contracts.
10
Q
A stock is trading at $120, and a call option with a strike price of $110 costs $15. What is the intrinsic value of the option?
A
S−K=120−110=10.
11
Q
A stock is trading at $90, and a put option with a strike price of $100 costs $12. What is the intrinsic value of the option?
A
K−S=100−90=10
12
Q
A call option has a premium of $20. If its intrinsic value is $12, what is the time value of the option?
A
Timevalue=Premium−Intrinsicvalue=20−12=8.
13
Q
A put option costs $8. The stock price is $75, and the strike price is $80. What is the time value of the option?
A
Timevalue = Premium − Intrinsicvalue = 8 − (80 − 75 ) = 3
14
Q
If a stock price increases from $100 to $120, how much does the value of a call option with a strike of $95 increase?
A
ΔPayoff=ΔS=120−100=20.
15
Q
Calculate the payoff for a put option with a strike price of $85 if the stock price at expiration is $78
A
Payoff=K−S=85−78=7.
16
Q
A call option on a stock has a strike price of $100 and is currently trading at $8. If the stock price rises to $110, what is the intrinsic value of the option?
A
S−K=110−100=10.
17
Q
A put option is ITM with a strike price of $50 and a stock price of $40. What is the payoff of the put?
A
K−S=50−40=10.
18
Q
You buy a call option for $5 on a stock with a strike price of $120. The stock price rises to $130 at expiration. What is your net profit?
A
Netprofit=(S−K)−Premium=(130−120)−5=5.
19
Q
A stock is trading at $150, and a call option with a strike price of $140 is worth $20. What is the time value of the option?
A
Timevalue=Premium−Intrinsicvalue=20−(150−140)=10.
20
Q
If the risk-free rate is 5% and you deposit $9,000 in a savings account, how much interest do you earn in a year?
A
Interest=9000×0.05=450.
21
Q
A stock is trading at $200, and the premium of a call option with a strike price of $210 is $12. What is the time value of the option?
A
Timevalue=Premium−Intrinsicvalue=12−0=12 (OTM, so intrinsic value is 0).
22
Q
A stock price is $50, and a call option with a strike price of $55 costs $3. What is the breakeven stock price for the buyer?
A
Breakevenprice=K+Premium=55+3=58.
23
Q
A put option is trading at $10. The stock price is $70, and the strike price is $80. What is the time value of the option?
A
Timevalue=Premium−Intrinsicvalue=10−(80−70)=0.
24
Q
Calculate the profit or loss for a put option buyer with a strike price of $60, a stock price of $55, and a premium of $4
A
Profit/Loss=(K−S)−Premium=(60−55)−4=1.
25
A call option costs $2. The strike price is $50, and the stock price is $60. What is the ROI if the stock price rises to $70?
ROI= Premium Payoff−Premium ×100= 2 (70−50)−2 ×100=900%.
26
If volatility increases by 10%, and the option premium rises from $5 to $7, what is the percentage increase in the premium?
Percentage increase= (7−5)/5 *100=40%.
27
A stock price is $120, and a call option with a strike price of $100 costs $30. If the stock price rises to $140, what is the new payoff?
Payoff=S−K=140−100=40.
28
A European-style call option with a strike price of $70 is ITM with a stock price of $85. What is the minimum profit for the holder if the premium was $10?
Profit=(S−K)−Premium=(85−70)−10=5.
29
A put option has a strike price of $90, and the stock price falls to $75. The premium paid was $8. What is the holder’s profit?
Profit=(K−S)−Premium=(90−75)−8=7.
30
What are the two main features of options
Leverage and nonlinearity.
31
Define leverage in the context of investments.
Leverage is borrowing capital to amplify potential returns, aiming for returns that exceed the borrowing cost.
32
How is leverage inherent in options without borrowing?
Leverage in options comes from the conversion factor (e.g., 1 option controls 100 shares), allowing for higher exposure with less capital.
33
What is the conversion factor for stock options?
100 shares per option.
34
What is the main risk associated with leverage?
Leverage can amplify losses, potentially wiping out the entire investment or more.
35
What is the nonlinear payoff of options?
A payoff resembling a hockey stick, with no payoff below the strike level and increasing payoff above it.
36
What happens to an option that expires out of the money?
It becomes worthless, resulting in a 100% loss of the premium paid.
37
What three factors must an options trader predict correctly to make a profit?
Direction, timing, and strike level.
38
How does a straddle position work?
By buying a call and a put at the same strike, profiting from significant volatility in either direction.
39
What does it mean to be "long volatility"?
Expecting a large price movement in either direction and profiting from increased volatility.
40
Calculate the leveraged return for a $100,000 stock purchase with $50,000 borrowed, assuming a 10% return.
$10,000 gain on $50,000 original investment = 20% return.
41
If you invest $25,000 and borrow $25,000, earning a 10% return on $50,000, what is the leveraged return?
$5,000 gain on $25,000 investment = 20% return.
42
For a 10% price drop on a 2:1 leveraged $50,000 investment, what is the loss?
50,000 × -10% = -$5,000, resulting in a -20% return.
43
What is the leveraged return if you invest $5,000 and borrow $95,000, achieving a 10% return?
$100,000 × 10% = $10,000 gain. Total return: ($10,000 gain + $5,000 initial) / $5,000 = 300%.
44
If a stock increases $1 and an option controls 100 shares, how much does the option's value increase?
$1 × 100 = $100.
45
A call option costs $2 per share for a strike price of $50. If the stock rises to $55, what is the profit per share?
$55 - $50 - $2 = $3 per share.
46
You sell a call and a put at the same $50 strike, collecting $5 premium each. What is the maximum profit?
$5 (call) + $5 (put) = $10 total premium.
47
Calculate the breakeven points for a straddle where the call and put premiums are $5 each, and the strike is $50.
Breakeven: $50 ± $10 = $40 and $60.
48
You buy an option for $3 with a strike price of $50. If the stock price ends at $48, what is the return?
The option expires worthless. Return: -100%.
49
A stock price moves from $200 to $210. You own a $205 strike call costing $3. What is your profit?
$210 - $205 - $3 = $2 per share.
50
A stock drops from $200 to $180. You own a $190 strike put costing $4. What is your profit?
$190 - $180 - $4 = $6 per share.
51
You buy a $50 strike call and put for $5 each. The stock ends at $70. What is the net profit?
Call: $70 - $50 - $5 = $15; Put expires worthless. Net: $15 - $5 = $10.
52
If volatility drops after selling a straddle for $10 total premium, what is the likely outcome?
The stock price remains near the strike, and the trader keeps the $10 premium.
53
You invest $10,000 in an option with a 5x leverage effect. The stock price rises 10%. What is the return?
$10,000 × 10% × 5 = $5,000 (50% return).
54
A $50 strike call costs $4. The stock rises to $53. What is the ROI if 1 option controls 100 shares?
Gain: ($53 - $50 - $4) × 100 = $300. ROI: $300 / $400 = 75%.
55
A $200 stock has a $205 strike call priced at $3. The stock rises to $210. What is the percentage return?
($210 - $205 - $3) / $3 = 166.7%.
56
A $50 strike put costs $2, and the stock falls to $45. What is the profit per share?
$50 - $45 - $2 = $3.
57
You purchase a $5,000 option portfolio with a 2x leverage factor. If the portfolio value increases by 15%, what is the gain?
$5,000 × 15% × 2 = $1,500.
58
What is a "non-recourse loan"?
A loan where the lender can only recover the collateral (e.g., the home) in case of default, not pursue the borrower's other assets.
59
Why might a borrower avoid defaulting on a mortgage despite financial incentives?
Due to moral considerations, social stigma, potential damage to credit scores, and financial barriers to relocation.
60
What role does negative equity play in strategic mortgage defaults?
Borrowers are more likely to default strategically as the size of their negative equity increases.
61
How did the elimination of down payment requirements contribute to the housing crisis?
It reduced borrowers' equity cushion, increased loan-to-value ratios, and heightened the risk of negative equity and default.
62
What is "securitization" in the context of mortgages?
The process of pooling mortgages and selling them as securities to investors, transferring default risks to the capital markets.
63
What are "no-money-down loans"?
Loans that allow borrowers to finance 100% of a home's purchase price without an initial down payment.
64
What was the median combined loan-to-value (LTV) ratio for subprime purchase loans from 2005 to 2007?
100%, meaning many borrowers financed the entire purchase price of their homes.
65
How did lenders' reliance on securitization influence their lending practices?
It encouraged offering high-risk subprime loans, as lenders could transfer the default risks to investors through securitized assets.
66
What are Residential Mortgage-Backed Securities (RMBS)?
Securities backed by residential mortgages that are sold to investors in the secondary market.
67
How does mortgage securitization bypass financial institution mediation?
By transforming non-liquid residential mortgages into tradable securities in the secondary market, where investors trade directly.
68
What is a "piggyback mortgage"?
A second mortgage taken simultaneously with a first mortgage, often used to avoid making a down payment.
69
How did non-recourse mortgages and no-down-payment loans contribute to the housing bubble?
By reducing borrower deterrence against default and encouraging riskier financial behavior, fueling the housing price bubble.
70
What is the impact of a foreclosure on a borrower's credit score?
It can reduce the score by 140-150 points and leave a negative mark on credit records for up to seven years.
71
Why did subprime borrowers often default on no-down-payment loans during the housing crisis?
Because high LTV ratios left them with little to no equity, making default a financially rational choice in the face of declining home values.
72
What was the purpose of introducing "credit enhancements" in securitization?
To mitigate risks for investors by retaining some of the riskiest securities within the lending institution or affiliates.
73
What is leverage in the context of mortgages?
Leverage is financing the purchase of a home using borrowed funds (a mortgage), similar to buying equity with borrowed money.
74
How is homeownership different from stock investments in terms of leverage?
Homeownership is less speculative since people often live in the home, whereas stocks are typically purchased solely for investment purposes.
75
Why are mortgage markets more generous with leverage compared to stock markets?
Mortgage markets often allow up to 80% financing, while the SEC limits stock purchases to 50% financing.
76
What are the carry costs of homeownership?
Carry costs include mortgage payments, real estate taxes, insurance, utilities, maintenance, and energy bills.
77
What is the Merton model's interpretation of equity in a firm?
The Merton model sees equity as a call option on the firm's assets, with the strike price being the firm's debt.
78
How does the Merton model relate to home equity?
Home equity is like a call option on the house’s value, with the mortgage amount acting as the strike price.
79
What happens to home equity when the home’s market price exceeds the mortgage?
The homeowner has positive equity and can sell the house, repay the mortgage, and keep the difference as profit.
80
What does it mean for a house to be "underwater"?
A house is underwater when its market value is less than the remaining mortgage balance.
81
How does a non-recourse loan benefit homeowners?
In a non-recourse loan, the homeowner can walk away from an underwater mortgage without being pursued for additional repayment beyond the home's value.
82
What is the issue with non-recourse loans combined with no-money-down mortgages?
They create a "free option" for homeowners, encouraging speculation and potentially contributing to asset bubbles.
83
Why are free options dangerous in mortgage markets?
Free options invite speculators who can profit from rising prices without risking losses, increasing the likelihood of asset bubbles and defaults.
84
What position does the lender have in the mortgage-as-options framework?
The lender is short a put option on the house’s value, struck at the mortgage amount.
85
What happens to the lender’s position if the house price falls below the mortgage value?
The lender’s short put option is in the money, resulting in a loss because they cannot recover the full mortgage amount.
86
What are the risks of excessive speculation in housing markets?
Excessive speculation can inflate asset bubbles, leading to market crashes and widespread defaults.
87
What is the primary lesson from viewing home equity as an option?
It demonstrates the financial risks and incentives in housing markets, particularly with the structure of mortgages and their impact on homeowners and lenders.
88
What is corporate undercapitalization?
It occurs when a company has insufficient equity capital to cover its risks, leading to potential issues for creditors and other stakeholders.
89
Why are governmental or municipal authorities not considered voluntary creditors?
Because they do not choose to deal with specific entities or assess their financial details, unlike contractual parties.
90
Who are "non-adjustable" creditors?
Creditors who cannot or do not adjust their terms or assess the company's financial status, including small general creditors and sophisticated creditors with fixed terms.
91
Why might even informed contractual creditors face risks with undercapitalized companies?
Because a company's financial situation can change after the contract is formed, impacting the creditor's expected outcomes.
92
What are the two main remedies for corporate undercapitalization?
1. Piercing the corporate veil.
2. Addressing shareholder investments made as loans instead of equity.
93
What does piercing the corporate veil entail?
Removing the legal separation between a corporation and its shareholders, making shareholders personally liable for the corporation’s debts.
94
Why is piercing the corporate veil considered an extreme remedy?
Why is piercing the corporate veil considered an extreme remedy?
95
In what situation is piercing the corporate veil more likely to be applied?
In cases of severe undercapitalization, especially when a holding company undercapitalizes its subsidiary.
96
What are some characteristics of non-adjustable creditors?
General creditors with small claims who find it too costly to verify financial information.
Sophisticated creditors bound by fixed contractual terms.
97
How does undercapitalization affect tort creditors differently than contractual creditors?
Tort creditors often have no choice in becoming creditors, making them more vulnerable to the company's financial inadequacies.
98
What empirical finding connects undercapitalization with veil-piercing cases?
Undercapitalization is present in over 18% of contract cases involving piercing the corporate veil.
99
What is the main difference between European and American options?
European options can only be exercised at expiration, while American options can be exercised anytime before expiration.
100
What are Bermudan options?
Bermudan options can be exercised on specific dates before expiration, similar to American options, but with more limited flexibility.
101
Why might early exercise of a put option be valuable for American-style options?
If the stock price is very low, the option holder can exercise early to lock in the value of the put and invest the proceeds risk-free.
102
What are the factors to consider when trading options?
Strike price, direction (call or put), timing (expiration date), and size.
103
What are the three types of options based on their strike prices?
In-the-money (ITM): Strike is favorable to the holder.
At-the-money (ATM): Strike is equal or close to the current stock price.
Out-of-the-money (OTM): Strike is unfavorable to the holder.
104
How do the costs of options vary based on their strike prices?
ITM options are more expensive than ATM options, and ATM options are more expensive than OTM options due to intrinsic value.
105
What is the difference between hedging with options and speculating with options?
Hedging involves using options to minimize risk, while speculating involves using options to bet on price movements for profit.
106
How might a farmer use options to hedge the cost of buying seed?
The farmer could buy a call option to lock in a maximum price for seed. If prices rise, they can buy at the lower strike price, ensuring a competitive cost.
107
What is the difference between using options and futures for risk management?
Options provide a fixed cost (the premium), and can expire worthless without further cost, while futures involve a variable cost that could lead to unfavorable terms.
108
What is a bull spread strategy in options?
A bull spread involves buying a call at a lower strike price and selling a call at a higher strike price, limiting the upside potential but reducing the cost.
109
How does a speculator use options to profit?
Speculators use options to leverage their predictions of stock price movements, either by buying calls, selling puts, or using spreads to limit risk while maximizing potential gains.
110
What is the primary risk for a speculator using options?
The primary risk is that the option can expire worthless, leading to a 100% loss of the premium paid.
111
What is arbitrage in options trading?
Arbitrage involves exploiting price differences for equivalent payoffs across different markets, allowing a trader to lock in riskless profits.
112
How could an arbitrageur exploit an opportunity between two portfolios?
If one portfolio is priced higher than another but offers the same payoff, the arbitrageur could sell the more expensive portfolio and buy the cheaper one to pocket the difference.
113
What is the risk of options for hedgers compared to speculators?
For hedgers, the risk is limited to the premium paid, like the cost of insurance. For speculators, the risk is the entire premium, with no guarantee of a favorable outcome
