Answer :
To understand which portfolio equates to a single convertible bond from the issuer's perspective, we need to break down the components involved.
Convertible Bond: This is a type of bond issued by a company that can be converted into a predetermined number of shares. In this case, the conversion ratio is 40, meaning each bond can be converted into 40 shares of stock.
Equivalence in Options Terms: The equivalence of a convertible bond usually involves both debt and equity components:
- Debt Component: The non-convertible plain bond part.
- Equity Component: Options that reflect the rights to convert the bond into equity.
To replicate this with options and a non-convertible bond:
- By holding the equivalent plain bond, any deviation must relate to the equity conversion.
- You would offset the bond position by shorting a plain bond.
- Then, you add a derivative position that matches the conversion feature.
Breaking Down the Options: Let's analyze each choice:
a. Short a plain bond and write 25 call options with a strike of 40 - This does not match the equity conversion aspect because writing 25 call options at a higher strike price doesn't accurately cover the conversion ratio or its market scenario.
b. Short a plain bond and buy 40 call options with a strike of 25 - Buying calls reflects the control to convert into shares. However, the strike price does not directly align with the conversion ratio.
c. Short a bond and write 40 puts with a strike of 25 - Writing puts does not align well with the equity feature of convertible bonds, as they provide a different payoff scheme.
d. Short a bond and write 40 calls with a strike of 25 - This option mirrors the equity feature of a convertible bond but in reverse because writing a call implies the opposite of holding the conversion right.
e. Buy 40 shares and 40 puts with a strike of 25 - Buying shares somewhat covers the equity position upon conversion, but adding puts alters the payoff structure.
From the issuer's perspective, the most directly matching option is d. Short a bond and write 40 calls with a strike of 25. This mirrors a counter-position where the issuer covers the conversion feature with calls written at the conversion price, aligning the obligation upon conversion.
Chosen Option: d. Short a bond and write 40 calls with a strike of 25.
This way, the combination of shorting the bond (reflecting the removal of principal guarantee) and writing calls (offsetting the conversion feature) represents a close replication to issuing a convertible bond from the issuer's viewpoint.
