Replicating Portfolio - Revision history

Dirkjan at 19:25, 27 August 2020

2020-08-27T19:25:45Z

Dirkjan: Replaced content with "Replicating Portfolio Category:finance Category:M12 Category:Principles of Corporate Finance Category:Term"

2020-08-27T18:39:27Z

Replaced content with "Replicating Portfolio Category:finance Category:M12 Category:Principles of Corporate Finance Category:Term"

Dirkjan: Created page with "In Principles of Corporate Finance a replicating portfolio is defined as the combination of: * Borrowing money * Buying a ratio of stock Su..."

2020-08-25T07:41:21Z

Created page with "In Principles of Corporate Finance a replicating portfolio is defined as the combination of: * Borrowing money * Buying a ratio of stock Su..."

New page

In [[Principles of Corporate Finance|Principles of Corporate Finance]] a replicating portfolio is defined as the combination of:
* Borrowing money
* Buying a ratio of stock
Such that you replicate exactly the payoff from one call option. The number of shares need to replicate one call is called the ''option delta'' or ''hedge ratio''.

Take the example of a stock with has a current stock price of \$80,- with a maximum downside potential of 25% drop and an upside of 33% increase. This means that the stock can move between
* \$60,-
* \$106,67,-

A call option for \$80,- in this case would be moving between:
* \$0,- (in the case there the stock price was below \$80,-)
* Between \$0,- and \$26,67 if the stock price was moving between and \$106,67,-
* \$26,67 (in the case the stock price was exactly \$106,67,-)

How should we value such a call option? There are two methods of calculation:

=Calculate option delta=
The option delta can be calculate as follows:

<math>\text{Option delta}</math> = <math>\frac{\text{Spread of option prices}}{\text{Spread of share prices}}</math>=<math>\frac{26.67 - 0}{106.67 - 60}</math>=<math>\frac{26.67}{46.67}</math>=<math>\frac{4}{7}</math>

<math>\frac{80 - ((4/7) \cdot 80)}{1.025}</math>= <math>33.45</math>

A more intuitive way of calculating the amount of money that needs to be borrowed is to simply subtract

The value of the call is then:

<math>\text{Value of call}</math> = <math>\text{Value of (4/7) shares}</math> - <math>\text{33.45 bank loan}</math> =
= <math>80 \cdot (4/7) - 33.45</math> = <math>12.26</math>

=Risk Neutral Valuation=
{{:Risk-Neutral Valuation}}
[[Category:finance]]

[[Category:M12]]

[[Category:Principles of Corporate Finance]]

[[Category:Term]]

← Older revision		Revision as of 18:39, 27 August 2020
Line 1:		Line 1:
−	~~In [[Principles of Corporate Finance\|Principles of Corporate Finance]] a replicating portfolio is defined as the combination of:~~	+	Replicating Portfolio
−	* Borrowing money
−	* Buying a ratio of stock
−	~~Such that you replicate exactly the payoff from one call option. The number of shares need to replicate one call is called the ''option delta'' or ''hedge ratio''.~~
−
−	~~Take the example of a stock with has a current stock price of \$80,- with a maximum downside potential of 25% drop and an upside of 33% increase. This means that the stock can move between~~
−	* \$60,-
−	* \$106,67,-
−
−	~~A call option for \$80,- in this case would be moving between:~~
−	* \$0,- (in the case there the stock price was below \$80,-)
−	* Between \$0,- and \$26,67 if the stock price was moving between and \$106,67,-
−	* \$26,67 (in the case the stock price was exactly \$106,67,-)
−
−	~~How should we value such a call option? There are two methods of calculation:~~
−
−	~~=Calculate option delta=~~
−	~~The option delta can be calculate as follows:~~
−
−	<math>\text{Option delta}</math> = <math>\frac{\text{Spread of option prices}}{\text{Spread of share prices}}</math>=<math>\frac{26.67 - 0}{106.67 - 60}</math>=<math>\frac{26.67}{46.67}</math>=<math>\frac{4}{7}</math>
−
−	~~<math>\frac{80 - ((4/7) \cdot 80)}{1.025}</math>= <math>33.45</math>~~
−
−	~~A more intuitive way of calculating the amount of money that needs to be borrowed is to simply subtract~~
−
−	~~The value of the call is then:~~
−
−	~~<math>\text{Value of call}</math> = <math>\text{Value of (4/7) shares}</math> - <math>\text{33.45 bank loan}</math> =~~
−	~~= <math>80 \cdot (4/7) - 33.45</math> = <math>12.26</math>~~
−
−	~~=Risk Neutral Valuation=~~
−	~~{{:Risk-Neutral Valuation}}~~
	[[Category:finance]]		[[Category:finance]]

← Older revision		Revision as of 19:25, 27 August 2020
Line 1:		Line 1:
−	~~Replicating Portfolio~~	+	In [[Principles of Corporate Finance\|Principles of Corporate Finance]] a replicating portfolio is defined as the combination of:
		+	* Borrowing money
		+	* Buying a ratio of stock
		+	Such that you replicate exactly the payoff from one call option. The number of shares need to replicate one call is called the ''option delta'' or ''hedge ratio''.
		+
		+	Take the example of a stock with has a current stock price of \$80,- with a maximum downside potential of 25% drop and an upside of 33% increase. This means that the stock can move between
		+	* \$60,-
		+	* \$106,67,-
		+
		+	A call option for \$80,- in this case would be moving between:
		+	* \$0,- (in the case there the stock price was below \$80,-)
		+	* Between \$0,- and \$26,67 if the stock price was moving between and \$106,67,-
		+	* \$26,67 (in the case the stock price was exactly \$106,67,-)
		+
		+	How should we value such a call option? There are two methods of calculation:
		+
		+	=Calculate option delta=
		+	The option delta can be calculate as follows:
		+
		+	<math>\text{Option delta}</math> = <math>\frac{\text{Spread of option prices}}{\text{Spread of share prices}}</math>=<math>\frac{26.67 - 0}{106.67 - 60}</math>=<math>\frac{26.67}{46.67}</math>=<math>\frac{4}{7}</math>
		+
		+	<math>\frac{80 - ((4/7) \cdot 80)}{1.025}</math>= <math>33.45</math>
		+
		+	A more intuitive way of calculating the amount of money that needs to be borrowed is to simply subtract
		+
		+	The value of the call is then:
		+
		+	<math>\text{Value of call}</math> = <math>\text{Value of (4/7) shares}</math> - <math>\text{33.45 bank loan}</math> =
		+	= <math>80 \cdot (4/7) - 33.45</math> = <math>12.26</math>
		+
		+	=Risk Neutral Valuation=
		+	{{:Risk-Neutral Valuation}}
	[[Category:finance]]		[[Category:finance]]