Level 1 CFA® Exam:
Replication & Cost of Carry
We can replicate certain assets or derivatives by taking long or short positions in different financial instruments, for example:
- long underlying asset + short risk-free asset = long forward contract
- long underlying asset + short forward contract = long risk-free asset
- short forward contract + short risk-free asset = short underlying asset
Where:
- A long position in a risk-free asset is an equivalent of lending money.
- A short position in a risk-free asset is an equivalent of borrowing money.
The concept of replication is important because it helps us price derivatives and do arbitrage.
The basic formula for a forward price if we assume there are no benefits and costs related to holding the underlying asset apart from opportunity cost represented by the risk-free interest rate:
(...)
We enter into a forward contract on stock of Mist, Inc. expiring in 189 days. The current stock price amounts to USD 15.22. What is the value of the forward price if we are expecting that the stock will pay dividends in the amount of USD 0.55 per one share 72 days from now. Assume that one year has 365 days and the risk-free interest rate is 7.2%.
To compute the forward price, we have to compute the present value of the dividend first, and then subtract it from the current stock price and multiply it all by \((1+r)^T\).
The PV of the dividend is equal to:
\(i=\frac{0.55}{(1+7.2\%)^{\frac{72}{365}}}=0.5425\)
Now we can compute the forward price:
\(F=(S_0-i)\times(1+r)^T=(15.22-0.5425)\times1.072^{\frac{189}{365}}=15.2155\)
- We can replicate certain assets or derivatives by taking long or short positions in different financial instruments.
- Dividends, risk-free rate earned on a foreign currency, and bond coupons are monetary (usually) benefits of holding an underlying asset (aka. benefits of ownership).
- Convenience yield is a non-monetary benefit of holding an asset. The convenience yield can be observed in the case of commodities derivatives.
- The (net) cost of carry is defined as the difference between the benefits of holding the underlying asset and the costs related to holding the underlying asset.