Studied by 0 people
Looks like no one added any tags here yet for you.
What is the fair price of an asset equal to?
Present value of its future cash flows.
What two things cause the price of an asset to change?
- Change in amount of future CFs
- Change in discount rate r
What is a fixed income security?
An instrument that pays regular interest and repayment of the principal upon maturity.
What is the difference between fixed income securities and equity?
Fixed income securities do not entail ownership.
What are the two characteristics of government bonds?
- Timing of CFs is known
- Risk free
What is another name for a zero-coupon bond?
A strip
What is a bond's yield to maturity?
The bond's internal rate of return if held to maturity.
What is a bond's yield to maturity equal to?
Average rate of return.
What is a spot rate?
The discount rate for a particular period.
What two things does r compensate investors for?
- Inflation
- Opportunity cost
What is the difference between a nominal and real (index) bond?
- Nominal: promise nominal money
- Real: promise real money (i.e. adjust for inflation)
What is the break-even inflation rate?
What investors require as compensation for future inflation.
What is the break-even inflation rate equal to?
Nominal bond yield - real bond yield
What two things are true if a bond is trading at par?
- Price = face value
- Yield = coupon
What two things are true of a bond is trading at a premium?
- Price > face value
- Yield < coupon
What two things are true of a bond is trading at a discount?
- Price < face value
- Yield > coupon
What is a forward rate?
The rate - as expected today - for a future period. It is the rate you can lock-in today for investing in the future.
What do forward rates capture?
Market expectations for future short-term rates.
What is term structure?
Relation between time to maturity and spot rates.
What two theories explain the shape of yield curves?
- Expectation hypothesis
- Liquidity preference theory
What does the expectation hypothesis explain?
Forward rates are unbiased estimates of expected future spot rates.
What does the liquidity preference theory explain?
Investors prefer securities that pay off sooner rather than later. They will be unwilling to hold long-term bonds unless the forward rate exceeds the expected spot rate.
What does a regular upward sloping yield curve indicate?
Investors expect the economy to continue growing.
What does a downward sloping yield curve indicate?
Investors expect a recession.
What does a flat yield curve indicate?
Investors are unsure about the future of the economy.
When is there an arbitrage opportunity?
When the PV of future CFs is not equal to price (law of one price).
What is bootstrapping?
Obtaining spot rates from coupon bonds.
What is the formula for accrued interest?
A = (days since last coupon / days between last and next coupon) * next coupon
What is the dirty price?
The price the buyer actually pays.
What is the clean price?
The quoted price - accrued interest
What is the bid price?
How much you get for selling a security.
What is the ask price?
Cost to buy a security.
What happens to bond prices when interest rates increase?
Bond prices decrease.
What happens to yield when bond prices increase?
Yields decrease.
What does modified duration measure?
The percentage change in the value of a bond for a given change in the yield.
What is the formula for modified duration?
D = T 1 / (1+y)
Does T or y typically have a larger impact on duration?
T
Does duration increase or decrease with maturity?
Increase
Does duration increase or decrease with yield?
Decrease
Does duration increase or decrease with coupon rate?
Decrease
What must be done to the duration formula when discussing coupon bonds?
Must calculate the effective maturity by using Macaulay duration.
Does duration work for large changes in yield?
No since it is an approximation.
What is true about bonds with the same duration?
They have the same interest rate sensitivity.
What do bonds with higher duration have?
Higher interest rate sensitivity.
What is the duration of a bond portfolio equal to?
The weighted average of the durations of the individual assets.
Will the actual price after the yield change be higher or lower than predicted by duration?
Higher
How can you hedge against interest rate risk using duration?
Equate the duration of your liabilities to the duration of your assets (increases in liabilities due to changes in yield is compensated by increases in assets).
What interest rate do banks quote for mortgages?
The semi-annual rate multiplied by two by it is compounded monthly.
How do corporate bonds differ from government bonds?
They have default risk.
If a corporation defaults on its bonds, what two things can investors do to recover their investments?
- Negotiate a new payment schedule
- Liquidate firm assets
What four things does the price of a corporate bond depend on?
- Promised cash flows
- Spot rates
- Default risk
- Recovery in default
What are the highest bond rating and what does it mean?
A = practically no default risk
How does the calculation of the price of a bond change when there is default risk?
Must multiply the CFs by the probability that they will be received.
What is yield of a corporate bond (y*)approximately equal to?
y* = r + default
What is credit/yield spread equal to?
Yield of corporate - yield of gov = default risk of firm
Y* - Yg = default
(assuming that the bond holder loses all value in case of default)
What is a derivative?
A financial instrument whose payoffs depend on an underlying asset.
What are three benefits of derivatives?
- Hedging (risk management)
- Speculation
- Arbitrage
What is speculation?
Taking a risky position with the hope of generating high gains.
What do forwards and futures have in common?
Agreements to buy or sell an asset at a certain future time for a certain price.
What are the two differences between forwards and futures?
- Forwards traded over the counter, futures traded on exchanges
- Forwards have counter-party risk (when a party can't keep their promise)
What are the four notations for forwards/futures?
- S: underlying asset price
- F: future agree-upon price
- T: maturity
- rt: spot rate at time t
What is a forward a zero-sum game?
Whatever one side gains, the other side loses.
What is the payoff to the buyer of a forward (long position)?
St - F
What is the payoff to the buyer of a forward (short position)?
F - St
What is no-arbitrage, no storage cost, forward price (F) equal to?
The future value of the asset.
What is no-arbitrage forward price (F) equal to when there is a cost to store?
FV of asset + FV(cost) - FV(benefit)
What is an option?
Contract that gives one party the choice to buy or sell an asset at a specified price at or before a specified time.
What is a call option?
The right to buy the underlying asset.
What is a put option?
The right to sell an underlying asset.
What are the six notations of options?
- S: price of underlying asset
- C: call price
- P: put price
- X: strike price
- T: maturity
- rt: spot rate at time t
What is the difference between a European and American option?
- European: can be exercised at maturity
- American: can be exercised at any time before maturity
What is the value of a call option equal to at maturity?
Ct = max ( 0, St - X )
What is the value of a put option equal to at maturity?
Pt = max ( 0, X - St)
Are options more or less risky than stocks?
More.
What is the difference between spreads and compbinations?
- Spread: portfolio made of all calls or all puts
- Combo: portfolio made of calls and puts
What is a straddle?
Buying a call and a put with the same strike price.
What is a reverse straddle?
Selling a call and a put with the same strike price.
What is a bull spread?
Buying a call and selling a call with a higher strike price.
What is a bear spread?
Buying a call and selling a call with a higher strike price.
What is a long straddle?
Long a call and a put with the same strike prices.
When would you use a long straddle and why?
Right before a company makes an earnings announcement. You will profit whether it is good or bad news.
What is a long butterfly?
Long a call with X1, short two calls with X2, long a call with X3.
What is the put-call parity?
The relation between the price of a call and an otherwise identical put.
What is the put-call parity's formula?
C = P + S - X/(1+r)^t
When does the the put-call parity always hold?
For European options.
What happens when the put-call parity is violated?
Options are mispriced therefore, arbitrage is possible.
What are the two components of an option's value?
- Intrinsic: value if exercised today
- Time value: value arising from time left to maturity
What does the binomial pricing method allow?
The pricing of all derivatives (not as restrictive as put-call parity).
What is the general idea of binomial pricing?
If the portfolio replicates the cash-flows of the option in all future states, then the cost of the replicating portfolio should equal that of the option.
What does the number of stocks in the portfolio represent?
The sensitivity of the derivative to a change in the underlying asset.
Why do we want to minimize the number of stocks in our portfolio?
To reduce its exposure to risk
What five things affect the price of an option?
- Stock price today
- Strike price
- Expected stock price volatility
- Interest rate between now and expiration
- Time to expiration
Is an increase in stock price good or bad for calls and puts?
- Good for calls
- Bad for puts
Is a higher strike price good or bad for calls and puts?
- Bad for calls
- Good for puts
What happens if price movements are more volatile?
Price of calls and puts will be higher.
Is higher r good or bad for calls and puts?
- Good for calls
- Bad for puts
Is more of less time to expiration better for calls and puts?
More (almost always the case).
What is the option formula?
𝑂 = ∆ (𝑆) + B(1/(1+r)^t
What is the Black-Scholes price?
The option price obtained by the binomials model when it converges to infinity.
