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WQU - MFE > Financial Markets - Leverage and Nonlinearity: C1M4 > Flashcards

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.

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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).

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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).

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4
Q

What are the two components of an option’s premium?

A

Intrinsic value and time value.

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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.

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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.

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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.

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8
Q

What happens to a call option’s value if the risk-free interest rate increases?

A

The call option’s value increases.

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9
Q

What is the role of the Options Clearing Corporation (OCC)?

A

It manages the exercise and assignment of options contracts.

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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.

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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

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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.

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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

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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).

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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.

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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.

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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.

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25
Q

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?

A

ROI= Premium Payoff−Premium ×100= 2 (70−50)−2 ×100=900%.

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26
Q

If volatility increases by 10%, and the option premium rises from $5 to $7, what is the percentage increase in the premium?

A

Percentageincrease= (7−5)/5 *100=40%.

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27
Q

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?

A

Payoff=S−K=140−100=40.

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28
Q

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?

A

Profit=(S−K)−Premium=(85−70)−10=5.

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29
Q

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?

A

Profit=(K−S)−Premium=(90−75)−8=7.

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30
Q

What are the two main features of options

A

Leverage and nonlinearity.

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31
Q

Define leverage in the context of investments.

A

Leverage is borrowing capital to amplify potential returns, aiming for returns that exceed the borrowing cost.

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32
Q

How is leverage inherent in options without borrowing?

A

Leverage in options comes from the conversion factor (e.g., 1 option controls 100 shares), allowing for higher exposure with less capital.

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33
Q

What is the conversion factor for stock options?

A

100 shares per option.

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34
Q

What is the main risk associated with leverage?

A

Leverage can amplify losses, potentially wiping out the entire investment or more.

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35
Q

What is the nonlinear payoff of options?

A

A payoff resembling a hockey stick, with no payoff below the strike level and increasing payoff above it.

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36
Q

What happens to an option that expires out of the money?

A

It becomes worthless, resulting in a 100% loss of the premium paid.

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37
Q

What three factors must an options trader predict correctly to make a profit?

A

Direction, timing, and strike level.

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38
Q

How does a straddle position work?

A

By buying a call and a put at the same strike, profiting from significant volatility in either direction.

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39
Q

What does it mean to be “long volatility”?

A

Expecting a large price movement in either direction and profiting from increased volatility.

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40
Q

Calculate the leveraged return for a $100,000 stock purchase with $50,000 borrowed, assuming a 10% return.

A

$10,000 gain on $50,000 original investment = 20% return.

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41
Q

If you invest $25,000 and borrow $25,000, earning a 10% return on $50,000, what is the leveraged return?

A

$5,000 gain on $25,000 investment = 20% return.

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42
Q

For a 10% price drop on a 2:1 leveraged $50,000 investment, what is the loss?

A

50,000 × -10% = -$5,000, resulting in a -20% return.

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43
Q

What is the leveraged return if you invest $5,000 and borrow $95,000, achieving a 10% return?

A

$100,000 × 10% = $10,000 gain. Total return: ($10,000 gain + $5,000 initial) / $5,000 = 300%.

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44
Q

If a stock increases $1 and an option controls 100 shares, how much does the option’s value increase?

A

$1 × 100 = $100.

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45
Q

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?

A

$55 - $50 - $2 = $3 per share.

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46
Q

You sell a call and a put at the same $50 strike, collecting $5 premium each. What is the maximum profit?

A

$5 (call) + $5 (put) = $10 total premium.

47
Q

Calculate the breakeven points for a straddle where the call and put premiums are $5 each, and the strike is $50.

A

Breakeven: $50 ± $10 = $40 and $60.

48
Q

You buy an option for $3 with a strike price of $50. If the stock price ends at $48, what is the return?

A

The option expires worthless. Return: -100%.

49
Q

A stock price moves from $200 to $210. You own a $205 strike call costing $3. What is your profit?

A

$210 - $205 - $3 = $2 per share.

50
Q

A stock drops from $200 to $180. You own a $190 strike put costing $4. What is your profit?

A

$190 - $180 - $4 = $6 per share.

51
Q

You buy a $50 strike call and put for $5 each. The stock ends at $70. What is the net profit?

A

Call: $70 - $50 - $5 = $15; Put expires worthless. Net: $15 - $5 = $10.

52
Q

If volatility drops after selling a straddle for $10 total premium, what is the likely outcome?

A

The stock price remains near the strike, and the trader keeps the $10 premium.

53
Q

You invest $10,000 in an option with a 5x leverage effect. The stock price rises 10%. What is the return?

A

$10,000 × 10% × 5 = $5,000 (50% return).

54
Q

A $50 strike call costs $4. The stock rises to $53. What is the ROI if 1 option controls 100 shares?

A

Gain: ($53 - $50 - $4) × 100 = $300. ROI: $300 / $400 = 75%.

55
Q

A $200 stock has a $205 strike call priced at $3. The stock rises to $210. What is the percentage return?

A

($210 - $205 - $3) / $3 = 166.7%.

56
Q

A $50 strike put costs $2, and the stock falls to $45. What is the profit per share?

A

$50 - $45 - $2 = $3.

57
Q

You purchase a $5,000 option portfolio with a 2x leverage factor. If the portfolio value increases by 15%, what is the gain?

A

$5,000 × 15% × 2 = $1,500.

58
Q

What is a “non-recourse loan”?

A

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
Q

Why might a borrower avoid defaulting on a mortgage despite financial incentives?

A

Due to moral considerations, social stigma, potential damage to credit scores, and financial barriers to relocation.

60
Q

What role does negative equity play in strategic mortgage defaults?

A

Borrowers are more likely to default strategically as the size of their negative equity increases.

61
Q

How did the elimination of down payment requirements contribute to the housing crisis?

A

It reduced borrowers’ equity cushion, increased loan-to-value ratios, and heightened the risk of negative equity and default.

62
Q

What is “securitization” in the context of mortgages?

A

The process of pooling mortgages and selling them as securities to investors, transferring default risks to the capital markets.

63
Q

What are “no-money-down loans”?

A

Loans that allow borrowers to finance 100% of a home’s purchase price without an initial down payment.

64
Q

What was the median combined loan-to-value (LTV) ratio for subprime purchase loans from 2005 to 2007?

A

100%, meaning many borrowers financed the entire purchase price of their homes.

65
Q

How did lenders’ reliance on securitization influence their lending practices?

A

It encouraged offering high-risk subprime loans, as lenders could transfer the default risks to investors through securitized assets.

66
Q

What are Residential Mortgage-Backed Securities (RMBS)?

A

Securities backed by residential mortgages that are sold to investors in the secondary market.

67
Q

How does mortgage securitization bypass financial institution mediation?

A

By transforming non-liquid residential mortgages into tradable securities in the secondary market, where investors trade directly.

68
Q

What is a “piggyback mortgage”?

A

A second mortgage taken simultaneously with a first mortgage, often used to avoid making a down payment.

69
Q

How did non-recourse mortgages and no-down-payment loans contribute to the housing bubble?

A

By reducing borrower deterrence against default and encouraging riskier financial behavior, fueling the housing price bubble.

70
Q

What is the impact of a foreclosure on a borrower’s credit score?

A

It can reduce the score by 140-150 points and leave a negative mark on credit records for up to seven years.

71
Q

Why did subprime borrowers often default on no-down-payment loans during the housing crisis?

A

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
Q

What was the purpose of introducing “credit enhancements” in securitization?

A

To mitigate risks for investors by retaining some of the riskiest securities within the lending institution or affiliates.

73
Q

What is leverage in the context of mortgages?

A

Leverage is financing the purchase of a home using borrowed funds (a mortgage), similar to buying equity with borrowed money.

74
Q

How is homeownership different from stock investments in terms of leverage?

A

Homeownership is less speculative since people often live in the home, whereas stocks are typically purchased solely for investment purposes.

75
Q

Why are mortgage markets more generous with leverage compared to stock markets?

A

Mortgage markets often allow up to 80% financing, while the SEC limits stock purchases to 50% financing.

76
Q

What are the carry costs of homeownership?

A

Carry costs include mortgage payments, real estate taxes, insurance, utilities, maintenance, and energy bills.

77
Q

What is the Merton model’s interpretation of equity in a firm?

A

The Merton model sees equity as a call option on the firm’s assets, with the strike price being the firm’s debt.

78
Q

How does the Merton model relate to home equity?

A

Home equity is like a call option on the house’s value, with the mortgage amount acting as the strike price.

79
Q

What happens to home equity when the home’s market price exceeds the mortgage?

A

The homeowner has positive equity and can sell the house, repay the mortgage, and keep the difference as profit.

80
Q

What does it mean for a house to be “underwater”?

A

A house is underwater when its market value is less than the remaining mortgage balance.

81
Q

How does a non-recourse loan benefit homeowners?

A

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
Q

What is the issue with non-recourse loans combined with no-money-down mortgages?

A

They create a “free option” for homeowners, encouraging speculation and potentially contributing to asset bubbles.

83
Q

Why are free options dangerous in mortgage markets?

A

Free options invite speculators who can profit from rising prices without risking losses, increasing the likelihood of asset bubbles and defaults.

84
Q

What position does the lender have in the mortgage-as-options framework?

A

The lender is short a put option on the house’s value, struck at the mortgage amount.

85
Q

What happens to the lender’s position if the house price falls below the mortgage value?

A

The lender’s short put option is in the money, resulting in a loss because they cannot recover the full mortgage amount.

86
Q

What are the risks of excessive speculation in housing markets?

A

Excessive speculation can inflate asset bubbles, leading to market crashes and widespread defaults.

87
Q

What is the primary lesson from viewing home equity as an option?

A

It demonstrates the financial risks and incentives in housing markets, particularly with the structure of mortgages and their impact on homeowners and lenders.

88
Q

What is corporate undercapitalization?

A

It occurs when a company has insufficient equity capital to cover its risks, leading to potential issues for creditors and other stakeholders.

89
Q

Why are governmental or municipal authorities not considered voluntary creditors?

A

Because they do not choose to deal with specific entities or assess their financial details, unlike contractual parties.

90
Q

Who are “non-adjustable” creditors?

A

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
Q

Why might even informed contractual creditors face risks with undercapitalized companies?

A

Because a company’s financial situation can change after the contract is formed, impacting the creditor’s expected outcomes.

92
Q

What are the two main remedies for corporate undercapitalization?

A
  1. Piercing the corporate veil.
  2. Addressing shareholder investments made as loans instead of equity.
93
Q

What does piercing the corporate veil entail?

A

Removing the legal separation between a corporation and its shareholders, making shareholders personally liable for the corporation’s debts.

94
Q

Why is piercing the corporate veil considered an extreme remedy?

A

Why is piercing the corporate veil considered an extreme remedy?

95
Q

In what situation is piercing the corporate veil more likely to be applied?

A

In cases of severe undercapitalization, especially when a holding company undercapitalizes its subsidiary.

96
Q

What are some characteristics of non-adjustable creditors?

A

General creditors with small claims who find it too costly to verify financial information.

Sophisticated creditors bound by fixed contractual terms.

97
Q

How does undercapitalization affect tort creditors differently than contractual creditors?

A

Tort creditors often have no choice in becoming creditors, making them more vulnerable to the company’s financial inadequacies.

98
Q

What empirical finding connects undercapitalization with veil-piercing cases?

A

Undercapitalization is present in over 18% of contract cases involving piercing the corporate veil.

99
Q

What is the main difference between European and American options?

A

European options can only be exercised at expiration, while American options can be exercised anytime before expiration.

100
Q

What are Bermudan options?

A

Bermudan options can be exercised on specific dates before expiration, similar to American options, but with more limited flexibility.

101
Q

Why might early exercise of a put option be valuable for American-style options?

A

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
Q

What are the factors to consider when trading options?

A

Strike price, direction (call or put), timing (expiration date), and size.

103
Q

What are the three types of options based on their strike prices?

A

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
Q

How do the costs of options vary based on their strike prices?

A

ITM options are more expensive than ATM options, and ATM options are more expensive than OTM options due to intrinsic value.

105
Q

What is the difference between hedging with options and speculating with options?

A

Hedging involves using options to minimize risk, while speculating involves using options to bet on price movements for profit.

106
Q

How might a farmer use options to hedge the cost of buying seed?

A

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
Q

What is the difference between using options and futures for risk management?

A

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
Q

What is a bull spread strategy in options?

A

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
Q

How does a speculator use options to profit?

A

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
Q

What is the primary risk for a speculator using options?

A

The primary risk is that the option can expire worthless, leading to a 100% loss of the premium paid.

111
Q

What is arbitrage in options trading?

A

Arbitrage involves exploiting price differences for equivalent payoffs across different markets, allowing a trader to lock in riskless profits.

112
Q

How could an arbitrageur exploit an opportunity between two portfolios?

A

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
Q

What is the risk of options for hedgers compared to speculators?

A

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

WQU - MFE (6 decks)

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