- Agreement to buy something in the future at a certain price at a certain time.
- Eliminate ambiguities by spelling out all the contingencies
- Lock-in of a forward price
- Eliminate price risk and price opportunity.
- Example – farmers don't plant crops before selling it on contract.
What will be the price of asset X in amount of time Y
What will it cost to keep X for period of Y
Loan (cost of $)
+ Loaning out (income)
+ Transaction Cost
= Cost of Carry
Spot + Cost of Cary = Forward Price
Can't deviate from "Spot + Cost of Cary = Forward Price."
Observed opportunity will drive prices back to equilibrium.
Change of Spot + Change of Cost of Carry = Change in Forward Price
Expectation is built into the spot price.
Forwards reflect cost of carry only.
May not have the money upfront / nor tie up line of credit
The seller of the forward may have lower cost of carry
IBM at $100 today.
+ Cost of money: 5%
- Dividend from IBM: $3
Quote on IBM in a year: $102
Can be done with a basket of stocks as well.
+ Coupon: 8%
- Borrowing cost: 4%
$960 <- Since carrying the bond generates revenue.
Can't be any other price since we could make arbitrage.
Need to over-buy to account for 'slippage'
Slippage – buying more now to account for loss prior to delivery.
Increases the cost of carry.
Securing a rate on a loan ahead of time
Seller (e.g. bank) borrows today and locks in a rate.
Invests until the loan
Calendar conventions (for different rates)
PV = FV / (1 + r *t)
PV = $1mm / ( 1 + [.10 x 366/365])
10% is the interest rate
366 / 365 because the convention is A/365 and it's a leap year
FV = PVe^(rt)
FV = $908m * e^(.12(731/360))
12% is the interest rate
731/360 because the convention is A/360
Use natural log (ln) to get down from e^(X)
FV = PV(1+i)^n
i = the annual rate divided by 2 due to semiannual compounding.
Formula can only be used with 30/360
(Year 1 Loan Compounded) * (Year 2 Loan Compounded)
= (2 Year Loan Compounded)
No third party guarantees at all.
Private contracts – not made public.
No way to guarantee the best price since can only get quotes by request.
Traded in pits on the exchange
Just a security deposit (not a loan) similar to deposit on an apartment.
Daily Mark to Market to reflect the gains and losses
Eliminates credit risk
Prices in the forward and futures markets must be the same to avoid arbitrage.
Gold – monex.com
What happens on the last day of a futures contract?
The forward price is the same as the spot
Both parties pay or get paid the spot price: the gain/loss is already in the margin
Physical delivery not necessary
Short Term Interest Rate Contract
Locking in a forward rata
Priced off of the LIBOR
Combinations of other securities to create a payoff structure or risk/reward tradeoff that’s atypical.
Creating synthetic notes
Functionally the same as a derivative
Credit Linked Note rather than selling a CDS
Avoiding foreign withholding tax – for example if there’s a tax on foreign owners of a security, a local company can buy it and then they send the returns to the foreign owner.
Equity Linked Notes - Instead of owning stocks, you can invest in debt whose return is tied to return on some stocks. This can be important for insurance companies which have to balance out their risk with safe securities and stocks are riskier than bonds.
Religious Restrictions such as Islamic bonds (where interest is prohibited) – structure something so that it pays interest in effect but do not call it interest.
Outperform the S&P without making any stock decision by swapping multiple cash flows.
Convenient packaging of multiple long and short positions
Simpler for investors to execute
Create securities based on investor’s economic outlook
Creating securities that don’t exist or are sold out
Convertible Notes - a bond that includes an option to convert the bond into a given number of shares of common stock. The value of the note can float up along with the stock into which it is convertible.
A = ( # shares that the bond converts to * share price ) + (present value of the interest payments – dividends of the stock)[until expected conversion date]
B = Present Value of all the principal payments and interest + the conversion option
Max of A AND B is the value of the Convertible Bond – we will value the security at its best price since we can treat it as either a bond or a stock.
When is conversion activated
- Sometimes the option is “always on”
- Can convert after some initial period.
- Conditional (e.g. if there’s change in control)
If the price drops
Credit events on the bond
Similarly, the conversion option can deactivate
What stock does the bond convert into?
Usually same as the bond issuer
Banks can issue bonds convertible into other firms’ stocks.
Convertible into some other security (senior debt)
More than one of the above
Does the issuer have to really deliver the shares or just cash equivalence?
Does the bond include any other options (i.e. calls/puts?)
- Almost always callable.
- Hard options – no conditions attached
- Soft options – conditional on something (e.g. price, credit rating change)
Does the bond pay in cash or “pay in kind”
Convertible stock note – adds more bonds instead of paying interest.
Does the bond have anti-dilution clause
Matches the conversion to stock splits
Protects from stock dividends.
Do you get paid accrued interest at the time of conversion?
Sometimes forgo the interest when make big profit on conversion.
Convertible Bond Workout Period
Price of Bond – Conversion Value
------------------------------------------ = Number of years to ‘break even’
Bond Income – Stock Income
The shorter the workout period, the more attractive the bond is. Aggressive investors like WP < 1 year. Medium < 1.5 years. Conservative < 2.0 years. Otherwise, you might as well buy the stock.
Refine Workout Period
Projected dividend changes
Allows patience while waiting for the stock to go up
Better chances of finding a mis-priced bond due to illiquidity
Automatic Asset Allocation
You don’t have to guess whether stocks or bonds are going up.
Better risk/reward ratio
Interest rates (lowers low end as rates rise)
Coupon on bond (raises low end)
Stock Volatility – raises middle
The ‘option to convert is valuable at times of volatility.
Call option – lowers middle
Put option – raises low end
Stock dividends – lowers high end since bond owners miss out on the extra stock.
Acquire Inexpensive Options
Convertible = Bond + Option
Hedge away the bond
Get the value of option
Given the price of option we can get the implied volatility
The option can be held as investment or sold OTC at higher cost.
Set up a delta-neutral hedge by shorting the stock