IFM

Bear Spread

(opposite of bull spread) Call Bear: Short call (K1) + Long call (K2), K1< K2 Put Bear: Short put (K1) + Long put (K2), K1< K2

Hedging Strategies Using Exotic Options

- Forward start options are useful for hedging guarantees that will come into effect during the payout period of a GMWB while the variable annuity is still in the accumulation period. Chooser options are useful hedging tools for variable annuities with two-sided guarantees, e.g, a GMDB with a return-of- premium guarantee and an earnings- enhanced death benefit equal 35% of any account value gains. Lookback options are useful for hedging variable annuity guarantees where the guarantee value is periodically recalculated as the greater of the account value and the existing guarantee value. Shout options are useful for hedging variable annuity guarantees in situations where the guarantee value is recalculated at the discretion of the policyholder. Rainbow options are useful hedging tools when policyholders can hold multiple assets in their accounts and the guarantee applies to the account as a whole rather than individual assets in the account.

Alternatives to bankruptcy

-Workout. The company negotiates directly with creditors and works out an agreement -Prepackaged bankruptcy (or "prepack"). The company will first create a reorganization plan with the agreement of its primary creditors, and then file Chapter 11 reorganization to implement the plan.

Market Risk Premium

-the historical risk premium: uses the historical average excess return of the market over the risk free interest rate -a fundamental approach: uses the constant expected growth model to estimate the market portfolios expected return

costs of financial distress and bankruptcy,

1. The costs of financial distress and bankruptcy, in the event they occur. o Direct costs - fees to outside professionals like legal and accounting experts, consultants, appraisers, auctioneers, and investment bankers. -Higher for firms with more complicated business operations - Typically higher, in percentage terms, for smaller firms o Indirect costs - loss of customers, loss f suppliers, loss of employees, loss of receivables, fire sale of assets, inefficient liquidation, cost to creditors. - Are difficult to measure and are often much larger than direct costs -May occur even prior to bankruptcy the potential perceived threat of future bankruptcy is high o Companies with marketable tangible assets (e.g, airlines, steel nanufacturers) have lower costs of financial distress than companies without these assets (eg, information technology companies, companies in the service industry) because tangible assets can be sold relatively easily.

Standard steps to launching a typical IPO:

1. Underwriters typically manage an IPO and they are important because they: Market the IPO. o Assist in required filings. o Ensure the stock's liquidity after the IPO. 2. Companies must file a registration statement, Stutement. which contains two main parts: o Preliminary prospectus/red herring. o Final prospectus. 3. A fair valuation of the company is performed by the underwriter through road show and book building. 4. The company will pay the IPO underwriters an underwriting spread. After the IPO, underwriters can protect themselves more against losses by using the over-allotment allocation or greenshoe provision.

probability of financial distress and bankruptcy occurring

2. The probability of financial distress and bankruptcy occurring o Companies with a higher debt-to- equity ratio have a higher probability of bankruptcy. o This probability increases when the volatility of a firm's cash flows and asset values increases. o Firms with steady cash flows (e.g. utility companies) can use high levels of debt t and and still have low probability of default. o Firms with volatile cash flows (e.g. semiconductor firms) must have low levels of debt in order to have low probability of default

appropriate discount rate for the distress costs

3. The appropriate discount rate for the distress costs o The higher the firm's beta: -The more likely it will be in distress -The more negative the beta of the distress costs -The lower the discount rate for the distress costs -The higher the PV of distress costs

Abnormal Return

= Actual Return - Expected Return where: Expected Return = α+β*Actual Market Return

Value of real option

= NPV(with option) - NPV(without option)

Annualized forward premium rate

=(1/T) ln[F0,T/So]

Compound Option

A compound call allows the owner to buy another option at the strike price. A compound put allows the owner to sell another option at the strike price.

Financial Distress Costs

A firm that fails to make its required payments to debt holders is said to default on its debt. After the firm defaults, the debt holders have claims to the firm's assets through a legal process called bankruptcy. Two forms of bankruptcies: • Chapter 7 liquidation. A trustee supervises the liquidation of the firm's assets through an auction. The proceeds from the liquidation are used to pay the firm's creditors, and the firm ceases to exist. • Chapter 11 reorganization. The firm's existing management is given the opportunity to propose a reorganization plan. While developing the plan, management continues to operate the business.

Expected Returns and the Efficient Portfolio

A portfolio is efficient if and only if the expected return of every available asset equals it's required return

Adverse selection:

A seller with private information is likely to sell you worse-than- average goods.

Arbitrage

A transaction which generates a positive cash flow either today or in the future by simultaneous buying and selling of related assets, with no net investment or risk. Arbitrage strategy: "Buy Low, Sell High."

Required Return on New Portfolio

Adding the new investment will increase the Sharpe ratio of portfolio P if its expected return exceeds its required return

Asset-Backed Securities

An asset-backed security (ABS) is a security whose cash flows are backed by the cash flows of its underlying securities. The biggest sector of the ABS market is the mortgage-backed security (MBS) sector. An MBS has its cash flows backed by home mortgages. Because mortgages can be repaid early, the holders of an MBS face prepayment risk Banks also issue ABS using consumer loans, such as credit card receivables and automobile loans. A private ABS can be backed by another ABS. This new ABS is known as a collateralized debt obligation (CD0).

Initial Public Offering

An initial public offering (IPO) is the first time a company sells its stock to the public Advantages of IPO: • Greater liquidity • Better access to capital Disadvantages of IPO: • Dispersed equity holdings • Compliance is costly and time-consuming There are two major types of offerings: • Primary offerings: New shares sold to raise new capital. • Secondary offerings: Existing shares sold by current shareholders.

Lookback Option

An option whose payoff at expiration depends on the maximum or minimum of the stock price over the life of the option. Standard lookback options are known as lookback options with a floating strike price. Extrema lookback options are known as lookback options with a fixed strike price.

Rainbow Option

An option whose payoff depends on two or more risky assets.

No arbitrage condition

Arbitrage is possible of the following inequality is not satisfied: 0<p*<1

Risk neutral pricing

Assume α = γ = r Vo = exp(-rT)E*[payoff]

Capital Asset Pricing Model (CAPM)

Assumptions: -investors can buy and sell all securities at competitive market prices. There are no taxes or transaction costs. Investors can borrow and lend at the risk free rate -investors hold only efficient portfolios of traded securities -investors have homogeneous expectations regarding the volatilities, correlations, and expected returns of securities Consequence: the market portfolio is the efficient portfolio SML is a graphical representation of CAPM

Trade-Off Theory

Balance the value-enhancing effects of debt on a firm's capital structure with the value- reducing effects. VL= Vụ + PV(Interest tax shield) - PV(Financial distress costs) - PV(Agency costs of debt) + PV(Agency benefits of debt)

Butterfly Spread (Symmetric/Asymmetric)

Buy high- and low-strike options. Sell middle-strike option. Quantity sold = Quantity bought. Example - For 3 strike prices 30, 43, 46: • Buy 46 - 43 = 3 options with strike 30 • Buy 43 - 30 = 13 options with strike 46 • Sell 46 - 30 = 16 options with strike 43 Any multiple of (buy 3, sell 16, buy 13) would work

Zero-coupon Bond (ZCB)

Buying a risk-free ZCB = Lending at risk-free rate Selling a risk-free ZCB = Borrowing at risk-free rate that the Payoff on a risk-free ZCB = ZCB's decline. maturity value money Profit on a risk-free ZCB = 0 corporation. risk

PCP for Bonds

C(B, K) - P(B, K)= FT(B) - Kexp(-r(T-t)) where FT(B) = B - PV(Coupons)

PCP for Futures

C(F, K) - P(F, K) = Fexp(-r(T-t))- Kexp(-r(T-t))

PCP for Stocks

C(S, K) - P(S, K) = F0T(pre)(S) - Kexp(-r(T-t))

Bull Spread

Call Bull: Long call (K:) + Short call (K:), K, < K2 Put Bull: Long put (Ki) + Short put (K2), Ki < K2

Hedging of Catastrophic Risk

Catastrophe bond: A bond issued to investors where repayments and principal payments are contingent on there not being a catastrophe which causes large losses for the insurer. Thus, investors who buy these bonds face the risk of not receiving coupon payments or repayment of their principal. In general, cat bondholders typically receive higher interest rates for taking on this risk.

Credibility principle:

Claims in one's self- interest are credible only if they are supported by actions that would be too costly to take if the claims were untrue. Managers consider how their actions will be perceived by investors in selecting financing methods for new investments: -Issuing equity is typically viewed as a negative signal as managers tend to issue equity when they believe that the firm's stock is overvalued. • Issuing more debt is typically viewed as a positive signal as the company is taking on commitment to make timely interest and principal payments.

Proxy Error:

Due to the lack of competitive price data, the market proxy cannot include most of the tradable assets in the economy. exposed the inherent capital. (Reasons Why the Market Portfolio Might Not Be Efficient)

Estimating the Debt Overhang

Equity holders will benefit from a new investment requiring investment I only if:

Forward Premium

F(0,T)/So

• R&D-Intensive Firms.

Firms with high research and development costs typically maintain low levels of debt.

Political cycle effect:

For a given political administration, its first year and last year yield higher returns than the years in between.

Chooser Option

For an option that allows the owner to choose at time t whether the option will become a European call or put with strike K and expiring at time T:

Mortgage Loan as Put

For an uninsured position, the loss to the mortgage lender is max(B + C - R,0). where: • Bis the outstanding loan balance at default • C'is the lender's total settlement cost • Ris the amount recovered on the sale of property This is a put payoff with K = B + C and S = R.

Relationship between Ft.T(S) and Ft,T(S) (pre)

Ft,T(S) = Accumulated Value of F(S) = Fr(S)(pre)exp(rT)

Monte Carlo Simulation

General steps: 1. Build the model of interest, which is a function of several input variables. Assume a specific probability distribution for each input variable. 2. Simulate random draws from the assumed distribution for each input variable. 3. Given the inputs from Step 2, determine the value of the quantity of interest. 4. Repeat Steps 2 and 3 many times. 5. Using the simulated values of the quantity of interest, calculate the mean, variance, and other measures. Inversion method: Set Fx(x) =u.

Timing Option (Call Option)

Gives a company the option to delay making an investment with the hope of having better information in the future.

Haircut:

Haircut: Additional collateral placed with lender by short-seller. It belongs to the short-seller.

Super Bowl effect:

Historical data shows in the year after the Super Bowl, the stock market is more likely to do better if an NFC team won and worse if an AFC team won.

Breakeven DELTA & GAMMA HEDGING

If the price of the underlying stock changes by one standard deviation over a short period of time, then a delta-hedged portfolio does not produce profits or losses.

Underdiversification

Individual investors fail to diversify their portfolios adequately. They invest in stocks of companies that are in the same industry or are geographically close. Explanations: • Investors suffer from familiarity bias, favoring investments in companies they are familiar with. • Investors have relative wealth concerns, caring most about how their portfolio performs relative to their peers. DOES NOT IMPACT EFFICIENCY OF MARKET

Excessive Trading and Overconfidence

Individual investors tend to trade very actively. Explanations: • Overconfidence bias. They often overestimate their knowledge or expertise. Men tend to be more overconfident than women. • Trading activity increases with the number of speeding tickets an individual receives - sensation seeking. DOES NOT IMPACT EFFICIENCY OF MARKET

International bonds

International bonds are classified into four broadly defined categories: • Domestic bonds - issued by local, bought by foreign • Foreign bonds - issued by foreign, bought by local • Eurobonds - issued by local or foreign • Global bonds

Herd Behavior

Investors actively try to follow each other's behavior. Explanations: • Investors believe others have superior information, resulting in information cascade effect. • Investors follow others to avoid the risk of underperforming compared to their peers (relative wealth concerns). • Investment managers may risk damaging their reputations if their actions are far different from their peers. If they feel they are going to fail, then they would rather fail with most of their peers than fail while most succeed. IMPACTS EFFICIENCY OF MARKET

Non-Tradable Wealth:

Investors are exposed to significant risks outside their portfolio. They may choose to invest less in their respective sectors to offset the inherent exposures from their human capital. (Reasons Why the Market Portfolio Might Not Be Efficient)

Behavioral Biases:

Investors may be subject to systematic behavioral biases and therefore hold inefficient portfolios. (Reasons Why the Market Portfolio Might Not Be Efficient)

Disposition Effect

Investors tend to hold on to investments that have lost value and sell investments that have increased in value. • People tend to prefer avoiding losses more than achieving gains. They refuse to "admit a mistake" by taking the loss. • Investors are more willing to take on risk in the face of possible losses. • The disposition effect has negative tax consequences. IMPACTS EFFICIENCY OF MARKET

Earnings announcement puzzle:

Investors underreacted to the earnings announcement.

Neglected firm effect:

Lesser-known firms yield abnormally high returns.

Ratio Spread

Long and short an unequal number of calls/puts with different strike prices

Box Spread

Long call (put) bull spread + Long put (call) bear spread

Collared Stock

Long collar + Long stock

Straddle

Long put (K) + Long call (K)

Strangle

Long put (K1) + Long call (K2), K1 < K2

Collar

Long put (K1) + Short call (K2), K1 < K2

The Agency Benefits of Leverage

Managers have interests that may differ from shareholders' and debt holders' interests: Empire building. Managers tend to take on investments that increase the size, rather than the profitability, of the firm Managerial entrenchment. Because managers face little threat of being replaced, managers can run the firm to suit their interests. Leverage can provide incentives for managers to run a firm more efficiently and effectively due to: • Increased ownership concentration. - Reduced wasteful investment. • Reduced managerial entrenchment and increased commitment. Free cash flow hypothesis: Wasteful spending is more likely to happen when firms have high levels of cash flow in excess of what is needed.

Pecking order hypothesis:

Managers prefer to make financing choices that send positive rather than negative signals to outside investors. The pecking order (from most favored to least favored financing option): Internally generated equity (ie., retained earnings) > Debt > External equity (i.e., newly issued shares)

• Low-Growth, Mature Firms.

Mature, low-growth firms with stable cash flows and tangible assets benefit from high debt.

Monotonicity:

Monotonicity: If X<= Y, then g(X) <= g(Y)

Naked Writing vs. Covered Writing

Naked Writing vs. Covered Writing • If an option writer does not have an offsetting position in the underlying asset, then the option position is said to be naked. • If an option writer has an offsetting position in the underlying asset, then the option position is said to be covered.

Features of Futures Contract

Notional Value =# Contracts x Multipler x Futures price Bal(t)= Bal(t-1)exp(rh) + Gain where • Gain, =# Contracts x Multipler x Price Change, (for long position) • Gain, = - # Contracts x Multipler x Price Change, (for short position)

Portfolio Volatility

Observations: • The diversification effect is most significant initially. Even with a very large portfolio, we cannot eliminate all risk. The remaining risk is systematic risk that cannot be avoided through diversification.

Shout Option

Option An option that gives the owner the right to lock in a minimum payoff exactly once during the life of the option, at a time that the owner chooses. When the owner exercises the right to lock in a minimum payoff, the owner is said to shout to the writer. S' is the value of the stock at the time when the option owner shouts to the option writer.

4 Ways to Buy a Share of Stock

Outright purchase Fully leveraged purchase Prepaid forward contract Forward contract

DELTA & GAMMA HEDGING Overnight Profit

Overnight Profit A delta-hedged portfolio has 3 components: • Buy/sell options • Buy/sell stocks • Borrow/lend money (sell/buy bond) Overnight profit is the sum of: • Profit on options bought/sold • Profit on stocks bought/sold • Profit on bond Alternatively, overnight profit is the sum of: • Gain on options, ignoring interest • Gain on stocks, ignoring interest • Interest on borrowed/lent money

New-Issue/IPO puzzle:

Overreaction to new issues pushes up stock prices initially.

Corporate Debt: Private Debt

Private debt is negotiated directly with a bank or a small group of investors. It is cheaper to issue due to the absence of the cost of registration. 2 main types of private debt: • Term loan • Private placement

Short-Selling

Process of short-selling: • Borrow an asset from a lender • Immediately sell the borrowed asset and receive the proceeds (usually kept by lender or a designated 3ed party) • Buy the asset at a later date in the open market to repay the lender (close/cover the short position)

Corporate Debt: Public Debt

Public debt trades on public exchanges. The bond agreement takes the form of an indenture, which is a legal agreement between the bond issuer and a trust company.

Real Options

Real options are capital budgeting options that give managers the right, but not the obligation, to make a particular business decision in the future after new information becomes available.

B

Represents amount to lend at risk free rate

Δ

Represents how many shares to buy

Stock split effect:

Returns are higher before and after the company announces the stock split.

Size effect:

Small-cap companies have outperformed large-cap companies on a risk-adjusted basis.

Alternative Risk Preferences:

Some investors focus on risk characteristics other than the volatility of their portfolio, and they may choose inefficient portfolios as a result. (Reasons Why the Market Portfolio Might Not Be Efficient)

Static vs. Dynamic Hedging

Static/hedge-and-forget: Buy options and hold to expiration Dynamic: Frequently buy/sell assets and/or derivatives with the goal of matching changes in the value of guarantee

Adding a New Investment

Suppose we have a portfolio, P, with an expected return of E[Rp] and a volatility of σp

Synthetic Forward

Synthetic long forward is created by: • buying a stock and borrowing money (Le. selling a bond), or • buying a call and selling a put at the same strike.

Synthetic short forward

Synthetic short forward is the opposite of long, created by: • selling a stock and lending money (ie, buying a bond), or • selling a call and buying a put at the same strike.

Cash-and-Carry

The actual forward is overpriced. Short actual forward + Long synthetic forward

Reverse Cash-and-Carry

The actual forward is underpriced. Long actual forward + Short synthetic forward

Alpha

The difference between a security's expected return and the required return

Risk premium

The excess of the expected return of the asset over the risk free return Option: γ-r Stock: α -r γ -r = Ω(α-r) σ(option) = |Ω|σ(stock)

WACC with Taxes

The firm's effective after-tax WACC measures the required return to the firm's investors after taking into account the benefit of the interest tax shield: Note: • As debt increases, the reduction due to interest tax shield increases, WACC falls, and thus the value of the firm increases.

leverage ratchet effect

The leverage ratchet effect explains that once existing debt is in place: • Equity holders may have an incentive to take on more debt even if it reduces the firm value. • Equity holders will not have an incentive to decrease leverage by buying back debt even if it will increase the firm value.

Project Risk Analysis

The net present value (NPV) of a project equals the present value of all expected net cash flows from the project. The discount rate for a project is its cost of capital.

optimal level of debt,

The optimal level of debt, D", occurs at the point where the firm's value is maximized. It balances the benefits and costs of leverage.

Asian Option

The value of an average price Asian option is less than or equal to the value of an otherwise equivalent ordinary option. As N increases: • Value of average price option decreases • Value of average strike option increases

value of compound option

The value of the underlying option at time t1 V(St, K,T-t1) The value of the compound call at time t1 max[0, V(S1, K, T- t1) - x] The value of the compound put at time t1 = max[0, x - V(S1, K, T-t1)) where • K is the strike of the underlying option • x is the strike of the compound option • Tis the maturity of the underlying option • t1 is the maturity of the compound option

Reversal effect:

There is a negative serial correlation in stock prices as investors overreact to new information.

Momentum effect:

There is a positive serial correlation in stock prices as investors underreact to new information.

Fama-French-Carhart (FFC)

This model consists of 4 self-financing factor portfolios: • Market portfolio. Accounts for equity risk. Take a long position in the market portfolio and finance itself with a short position in the risk-free asset. -Small-minus-big (SMB) portfolio. Accounts for differences in company size based on market capitalization. Buy small firms and finance itself by short selling big firms. -High-minus-low (HML) portfolio. Accounts for differences in returns on value stocks and growth stocks. Buy high book-to-market stocks (i.e., value stocks) and finance itself by short selling low book-to-market stocks (Le, growth stocks). -Momentum. Accounts for the tendency of an asset return to be positively correlated with the asset return from the previous year. Buy the top 30% stocks and finance itself by short selling the bottom 30% stocks.

Barrier Option

Three types: • Knock-in: Goes into existence barrier is reached. • Knock-out: Goes out of existence if barrier is reached. • Rebate: Pays fixed amount if barrier is reached.

True Pricing

To calculate option price, discount the true expected option payoff at the expected rate of return on the option: Vo = exp(-γT)E[payoff]

Reducing Agency Costs

To mitigate the agency costs of debt, firms and debt holders can: • Issue short-term debt • Include debt covenants in bonds that place restrictions on the actions a firm can take

Supporting Strong Form of EMH

Top performing fund managers in one year only have a 50% chance to beat their reference index the following year. • The performance of actively managed mutual funds from 1971 to 2013 only beat the Wilshire 5000 index 40% of the time.

Diversification

Total risk = Systematic risk + Unsystematic risk Diversification reduces a portfolio's total risk by averaging out nonsystematic fluctuations: • Investors can eliminate nonsystematic risk for free by diversifying their portfolios. Thus, the risk premium for nonsystematic risk is zero. • The risk premium of a security is determined by its systematic risk and does not depend on its nonsystematic risk.

Siamese twins:

Two stocks with claims to a common cash flow should be exposed to identical risks but perform differently.

Option price (based on Δ and B)

V = ΔS + B

Value effect:

Value stocks have consistently outperformed growth stocks.

Venture Capital Financing Terms

Venture capitalists typically hold convertible preferred stock, which differs from common stock due to: • Liquidity preference Liquidity preference Multiplier x Initial inv • Participation rights • Seniority • Anti-dilution protection • Board membership There are two ways to exit from a private company: • Acquisition • Public offering

Interest Tax Shield with a Target Debt- Equity Ratio

When a firm adjusts its debt over time so that its debt-equity ratio is expected to re main constant, we can value the interest tax shield by: 1. Calculating the value of the unlevered firm, Vu, by discounting cash flows at the unlevered cost of capital (ie, pre-tax WACC). 2. Calculating the value of the levered firm, VL. by discounting cash flows at the WACC (L.e., after-tax WACC). 3. PV(Interest tax shield) = VL- Vụ

Costs of Asymmetric Information

When managers have more information about a firm than investors, there is asymmetric information.

Lemons principle:

When managers have private information about the value of a firm, investors will discount the price they are willing to pay for new equity issue due to adverse selection.

Decision tree

a graphical approach that illustrates alternative decisions and potential outcomes in an uncertain economy. 2 kinds of nodes in the decision tree: • The square node is the decision node where you have control over the decision. • The circular node is the information node where you have no control over the outcome.

Capital Allocation Line (CAL)

a line representing possible combinations from combining a risky portfolio and a risk-free asset: • At the intercept, the portfolio only consists of the risk-free asset. • At point P, the portfolio only consists of risky assets. • The line extending to the right of op represents portfolios that invest more than 100% in the risky portfolio P. This is done by using leverage (borrow money to invest). A portfolio that consists of a short position in the risk-free asset is known as a levered portfolio.

Interest rate on haircut

belongs is called: • short rebate in the stock market • repo rate in the bond market

Floor • Write a covered put

covered put = - Floor = - Stock - Put

Subadditivity:

g(X + Y) <= g(X) + g(Y)

Translation invariance:

g(X + c) = g(X) +c

Positive homogeneity:

g(cX) = c*g(X)

• A guaranteed minimum death benefit (GMDB)

guarantees a minimum amount will be paid to a beneficiary when the policyholder dies

• guaranteed minimum accumulation benefit (GMAB)

guarantees a minimum value for the underlying account after some period of time, even if the account value is less

• A guaranteed minimum withdrawal benefit (GMWB)

guarantees that upon the policyholder reaching a certain age, a minimum withdrawal amount over a specified period will be provided.

A guaranteed minimum income benefit (GMIB)

guarantees the purchase price of a traditional annuity at a future time.

Sovereign debt

issued by the national government. In the US, sovereign debt is issued as bonds called "Treasury securities."

Municipal bond

issued by the state and local governments. There are also several types of municipal bonds based on the source of funds that back them: • Revenue bonds • General obligation bonds

subordinated debenture.

new debt that has lower seniority than existing debenture issues

funding round

occurs when a private company raises money. An initial funding round might start with a "seed round," and then in later funding rounds the securities are named "Series A," "Series B," etc.

Debt cost of capital / cost of debt / required return on debt:

the rate of return that the debt holders require in order for them to contribute their capital to the firm.

Equity cost of capital / cost of equity / required return on equity:

the rate of return that the equity holders require in order for them to contribute their capital to the firm.

Cost of capital

the rate of return that the providers of capital require in order for them to contribute their capital to the firm.

Multiple Greeks Hedging

Δstock = 1; all other Greeks of the stock = 0 To hedge multiple Greeks, set the sum of the Greeks you are hedging to zero.

Elasticity

Ω = (% change in option price)/(% change in stock price) = ΔS/V Ω > 1 ; Ω < 0

Sharpe Ratio

φ(option) = Options risk premium/options volatility = (γ-r)/σ(option) φ(stock) = Stocks risk premium/options volatility = (α-r)/σ(stock) Φc = φstock; Φp = -φstock

Supporting Semi-Strong Form of EMH

• 3 months prior to a takeover announcement, the stock price gradually increased. At the time of announcement, stock price instantaneously jumped. After the announcement, the abnormal returns dropped to zero.

GMDB with a Return of Premium Guarantee

• A guarantee which returns the greater of the account value and the original amount invested: max(ST, K) = St + max( K - ST.0) • The embedded option is a put option.

Long vs. Short

• A long position in an asset benefits from an increase in the price of the asset. • A short position in an asset benefits from a decrease in the price of the asset.

Efficient Frontier

• A portfolio is efficient if the portfolio offers the highest level of expected return for a given level of volatility . • The portfolios that have the greatest expected return for each level of volatility make up the efficient frontier.

Assumptions of Mean-Variance Analysis

• All investors are risk-averse. • The expected returns, variances, and covariances of all assets are known. • To determine optimal portfolios, investors only need to know the expected returns, variances, and covariances of returns. • There are no transactions costs or taxes.

Systematic risk

• Also known as common, market, or non-diversifiable risk. • Fluctuations in a stock's return that are due to market-wide news.

Nonsystematic risk

• Also known as firm-specific, independent, idiosyncratic, unique, or diversifiable risk • Fluctuations in a stock's return that are due to firm-specific news.

Source of funding for private companies:

• Angel Investors • Venture Capital Firms • Private Equity Firms • Institutional Investors • Corporate Investors

• Ask/Offer price:

• Ask/Offer price: The price at which market-makers will sell and end-users will buy.

Capital Market Line (CML)

• Assume investors have homogeneous expectations. o All investors have the same efficient frontier of risky portfolios, and thus the same optimal risky portfolio and CAL. o Every investor will use the same optimal risky portfolio -- the market portfolio. When the market portfolio is used as the risky portfolio, the resulting CAL is CML • The equation for CML is: - r) • Only efficient portfolios plot on CML. Individual securities plot below this line.

issuing an IPO,

• Best-efforts: Shares will be sold at the best possible price. Usually used in smaller IPOS. • Firm commitment: All shares are guaranteed to be sold at the offer price. Most common. • Auction IPOS: Shares sold through an auction system and directly to the public.

• Bid price:

• Bid price: The price at which market- makers will buy and end-users will sell.

Bid-ask Spread •

• Bid-ask spread = Ask price - Bid price

Breakeven Analysis

• Calculate the value of each parameter so that the project has an NPV of zero. • The internal rate of return (IRR) is the rate at which the NPV is zero.

Cap,

• Cap = - Stock + Call (guarantee a maximum purchase price for stock)

Scenario Analysis

• Change several input variables at a time, then calculate the NPV for each scenario. The greater the dispersion in NPV across the given scenarios, the higher the risk of the project. • The underlying variables are interconnected. Simulation

Sensitivity Analysis

• Change the input variables one at a time to see how sensitive NPV is to each variable. Using this analysis, we can identify the most significant variables by their effect on the NPV. • The range is the difference between the best-case NPV and the worst-case NPV.

BS Formula's Assumptions:

• Continuously compounded returns on the stock are normally distributed and independent over time. There are no sudden jumps in the stock price. Volatility is known and constant. • Future dividends are known. • The risk-free rate is known and constant (ie, the yield curve is flat). • There are no taxes or transaction costs. • Short-selling is allowed at no cost. • Investors can borrow and lend at the risk-free rate.

Who Bears the Financial Distress Costs?

• Debt holders recognize that when the firm defaults, they will not be able to obtain the full value of the assets. As a result, they will pay less (or demand higher yields) for the debt initially. • It is the equity holders who most directly bears the financial distress costs.

portfolio with n individual stocks with arbitrary weights:

• Each security contributes to the portfolio volatility according to its total risk scaled by its correlation with the portfolio, which adjusts for the fraction of the total risk that is common to the portfolio. • As long as the correlation is not +1, the volatility of the portfolio is always less than the weighted average volatility of the individual stocks.

Option Exercise Styles

• European-style options can only be exercised at expiration. • American-style options can be exercised at any time during the life of the option. • Bermudan-style options can be exercised during bounded periods (i.e., specified periods during the life of the option).

Agency Costs of Leverage

• Excessive risk-taking and asset substitution. A company replacing its low-risk assets with high-risk investments. Shareholders may benefit from high-risk projects, even those with negative NPV. • Debt overhang or underinvestment. Shareholders may be unwilling to finance new, positive-NPV projects. • Cashing out. When a firm faces financial distress, shareholders have an incentive to liquidate assets at prices below their market values and distribute the proceeds as dividends.

Floor,

• Floor = + Stock + Put (guarantee a minimum selling price for stock)

Shortcut Method for Graphing Payoff of All Calls or All Puts

• For calls, go left-to-right on payoff diagram, and evaluate slope of the payoff diagram at each strike price. Going left-to-right means that a positive slope is one that increases left-to-right, and a negative slope is one that decreases left-to-right. • For puts, go right-to-left on payoff diagram, and evaluate slope of the payoff diagram at each strike price. Going right-to-left means that a positive slope is one that increases right-to-left, and a negative slope is one that decreases right-to-left.

Sizing Option

• Growth options give the company an option to make additional investments when it is optimistic about the future. • Abandonment options give the company an option to abandon the project when it is pessimistic about the future.

Multi-Factor Model

• If the market portfolio is not efficient, a multi-factor model is an alternative. • It considers more than one factor when estimating the expected return. • An efficient portfolio can be constructed from other well-diversified portfolios. • Also known as the Arbitrage Pricing Theory (APT). • Similar to CAPM, but assumptions are not as restrictive.

Interpreting Beta

• Ifß = 1, then the asset has the same systematic risk as the market. The asset will tend to go up and down the same percentage as the market. • Ifß > 1, then the asset has more systematic risk than the market. The asset will tend to go up and down more than the market, on a percentage basis. • IfB< 1, then the asset has less systematic risk than the market. The asset will tend to go up and down less than the market, on a percentage basis. • If ß = 0, then the asset's return is uncorrelated with the market return.

Option Moneyness

• In-the-money: Produce a positive payoff (not necessarily positive profit) if the option is exercised immediately. • At-the-money: The spot price is approximately equal to the strike price. • Out-of-the-money: Produce a negative payoff if the option is exercised immediately.

Investor Attention. Mood, and Experience

• Individual investors tend to be influenced by attention-grabbing news or events. They buy stocks that have recently been in the news. • Sunshine has a positive effect on mood and stock returns tend to be higher on a sunny day at the stock exchange. • Major sports events have impacts on mood. A loss in the World Cup reduces the next day's stock returns in the losing country. • Investors appear to put inordinate weight on their experience compared to empirical evidence. People who grew up during a time of high stock returns are more likely to invest in stocks. IMPACTS EFFICIENCY OF MARKET

Perfect Capital Markets

• Investors and firms can trade the same set of securities at competitive market prices equal to the present value of their future cash flows. • No taxes, transaction costs, or issuance costs. • The financing and investment decisions are independent of each other.

Homemade leverage:

• Investors can borrow or lend at no cost on their own to achieve a capital structure different from what the firm has chosen. • If an investor adds $x worth of debt to the capital structure, then he must reduce the equity by $x in order for the total firm's value to remain unchanged. To determine x, set the adjusted current debt-equity ratio to equal the target debt-equity ratio:

Weak Form EMH

• It is impossible to consistently attain superior profits by analyzing past returns.

Semi-Strong-Form EMH

• It is impossible to consistently attain superior profits by analyzing public information. • Prices will adjust immediately upon the release of any public announcements (earnings, mergers, etc.). • A semi-strong-form efficient market is also weak-form efficient.

Calendar/Time Anomalies

• January effect: Returns have been higher in January (and lower in December) than in other months. • Monday effect: Returns have been lower on Monday (and higher on Friday) than on other days of the week. • Time-of-day effect: Returns are more volatile close to the opening and closing hours for the market. Also, the trading volumes are higher during these times.

Supporting Weak Form of EMH

• Kendall found that prices followed a random walk model, i.e, past stock prices have no bearing on future prices. • Brealey, Meyers, and Allen created a scatter plot for price changes of four stocks. o No distinct pattern in the points, with the concentration of points around the origin. No bias toward any quadrants. o Autocorrelation coefficients were close to 0. • Poterba and Summers found that variance of multi-period change is approximately proportional to number of periods.

Margin Call

• Maintenance margin: Minimum margin balance that the investor is required to maintain in margin account at all times • Margin call: If the margin balance falls below the maintenance margin, then the investor will get a request for an additional margin deposit. The investor has to add more funds to bring the margin balance back to the initial margin.

Beta Definitions and Key Facts

• Measures the sensitivity of the asset's return to the market return. • Is defined as the expected percent change in an asset's return given a 1% change in the market return. • The beta for a stock, on average, is around 1. • Cyclical industries (tech, luxury goods) tend to have higher betas. • Non-cyclical industries (utility. pharmaceutical) tend to have lower betas.

Factors affecting the timing of investment:

• NPV of the investment o Without the timing option, invest today if NPV of investing today is positive. o With the timing option, invest today only if NPV of investing today exceeds the value of the option of waiting assuming the NPV is positive. • Volatility o When huge uncertainty exists regarding the future value of the investment (ie, high volatility), the option to wait is more valuable. • Dividends o It is better for an investor to wait unless the cost of waiting is greater than the value of waiting.

4 common types of corporate debt:

• Notes (Unsecured) • Debentures (Unsecured) • Mortgage bonds (Secured) • Asset-backed bonds (Secured)

Semi-variance / Downside Semi-variance

• Only cares about downside risk; ignores upside variability. • The average of the squared deviations below the mean: Semi-variance = E[min(0, R - E[R])²1 • The sample semi-variance is: Semi-variance-{ min(0, R, - E[R])^2 • Semi-variance s Variance For a symmetric distribution: Semi-variance = 1/2 Variance

Payoff and Profit

• Payoff: Amount that one party would have if completely cashed out. • Profit: Accumulated value of cash flows at the risk-free rate.

Earnings-Enhanced Death Benefit

• Pays the beneficiary an amount based on the increase in the account value over the original amount invested, e.g., 40%. max( St- K, 0).

Earnings-Enhanced Death Benefit

• Pays the beneficiary an amount based on the increase in the account value over the original amount invested, e.g., 40%. max( St- K, 0). • The embedded option is a call option

• Round-trip transaction cost:

• Round-trip transaction cost: Difference between what you pay and what you receive from a sale using the same set of bid/ask prices.

GMAB with a Return of Premium Guarantee

• Similar to GMDB with ROP guarantee, but the benefit is contingent on the policyholder surviving to the end of the guarantee period. • The embedded option is a put option.

MM Proposition II Notes

• Since debt holders have a priority claim on assets and income above equity holders, debt is less risky than equity, and thus rp < rg. • As companies take on more debt, the risk to equity holders increases, and subsequently the cost of equity increases. • As the amount of debt increases, the chance that the firm will default increases, and subsequently the cost of debt increases. • Although both cost of debt and cost of equity increase as the company takes on more debt, WACC remains unchang because more weight is placed on the lower-cost debt.

Reasons for short-selling assets:

• Speculation - To speculate that the price of a particular asset will decline. • Financing - To borrow money for additional financing of a corporation. • Hedging - To hedge the risk of a long position on the asset.

Tail Value-at-Risk (TVAR)

• TVAR focuses on what happens in the adverse tail of the probability distribution. • Also known as the conditional tail expectation or expected shortfall. If X represents gains, then the risk we are concerned about comes from the low end of the distribution: • IfX represents losses, then the risk we are concerned about comes from the high end of the distribution: - always coherent

4 IPO Puzzles: •

• The average IPO seems to be priced too low. • New issues appear cyclical. -The transaction costs of an IPO are high. • Long-run performance after an IPO is poor on average.

MM Proposition II

• The cost of capital of levered equity increases with the firm's debt-to-equity ratio: • Because there are no taxes in a perfect capital market, the firm's WACC and the unlevered cost of capital coincide:

The Performance of Fund Managers:

• The median mutual fund actually destroys value. • The mutual fund industry still has positive value added because skilled managers manage more money and add value to the whole industry. • On average, an investor does not profit more from investing in an actively managed mutual fund compared to investing in passive index funds. The value added by a fund manager is offset by the mutual fund fees. • Superior past performance of funds was not a good predictor of future ability to outperform the market

Optimal Portfolio Choice

• The optimal risky portfolio to combine with the risk-free asset is the one with the highest Sharpe ratio, where the CAL just touches (i.e, tangent to) the efficient frontier of risky investments. The portfolio that generates this tangent line is known as the tangent portfolio. • The tangent line will always provide the best risk and return tradeoff available to investors. All portfolios on the tangent line (.e, all portfolios that are combinations of the risk-free asset and the tangent portfolio) are efficient portfolios. • The tangent portfolio is the optimal risky portfolio that will be selected by a rational investor regardless of risk preference.

Adverse selection implications for equity issuance:

• The stock price declines on the announcement of an equity issue. • The stock price tends to rise prior to the announcement of an equity issue. • Firms tend to issue equity when information asymmetries are minimized, such as immediately after earnings announcement.

MM Proposition l

• The total value of a firm is equal to the market value of the total cash flows ta generated naR da by su its nasse asset. • The value of a firm is unaffected by its choice of capital structure. • Changing a firm's capital structure merely changes how the value of its assets is divided between debt and equity, but not the firm's total value. • VL= Vu

Interest Tax Shield

• The use of debt results in tax savings for the firm, which adds to the value of the firm. • VL= Vu + PV(Interest tax shield) Interest tax shield = Corp. Tax Rate x Int Pmt For a firm that borrows debt D and keeps the debt permanently, if the firm's marginal tax rate (a.k.a. effective tax advantage of debt) is Tc, then the present value of the interest tax shield is: PV(Interest tax shield) = Tc*D

Pre-Money and Post-Money Valuation

• The value of the firm before a funding round is called the pre-money valuation. • The value of the firm after a funding round is called the post-money valuation.

Strong-Form EMH

• There are only lucky and unlucky investors. No one (not even company insiders) can consistently attain superior profits. • Passive strategy is the best. • Astrong-form efficient market is also semi-strong and weak-form efficient.

Reasons for Using Derivatives

• To manage risk • To speculate • To reduce transaction cost • To minimize taxes / avoid regulatory issues

Futures Compared to Forward

• Traded on an exchange • Standardized (size, expiration, underlying) • More liquid • Marked-to-market and often settled daily • Minimal credit risk • Price limit is applicable

four types of Treasury securities:

• Treasury bills • Treasury notes • Treasury bonds • Treasury inflation-protected securities (TIPS)

Value-at-Risk (VaR)

• VaR of X at the 100a% confidence level is its 100ath percentile, denoted as VaR. (X). - usually doesn't satisfy subadditivity (unless normal)

• Write a covered call

• Write a covered call =- Cap = + Stock - Call

Who Bears the Agency Costs?

• v • When an unlevered firm issues new debt, equity holders will ultimately bear the costs. • Once a firm has debt already in place, some of the bankruptcy or agency costs from taking on additional debt can fall on existing debt holders.