In: Finance

# Are the profit and payoff of buying an index and buying a put the same as investing in zero-coupon bonds and buying a call?

Given that a 950-strike call has a premium of $120.405 and a 950-strike put has a premium of$51.777 and the 6-month interest rate is 2%. Suppose you buy the S&R index for $1000 and buy a 950-strike put. What are the profit and payoff for this position. Is this the same profit and payoff as investing$931.37 in a zero-coupon bonds and buying a 950-strike call.

## Solutions

##### Expert Solution

Option 1: Buy S&R index for 1000 and buy 950-strike put

The payoff at anytime for buying an S&R index is its spot price, denoted $$S_T$$. Think of it like buying a stock. Once you've bought the stock, your payoff at anytime is the amount you can sell the stock for which is usually it's current price in the stock market which is also called it's spot price. So payoff = $$S_T$$

The payoff for buying a 950-strike put can be found using the put payoff formula: $$\text{put payoff} = \max(0, \text{strike price - spot price})$$ because remember that a put contract gives you the right to sell but not the obligation to sell some amount of the underlying security. So you can choose when to use or exercise the contract meaning if it looks like you will lose money you can simply choose not to exercise the contract. If you think you can make money, the amount of money you can make is the strike price which you've used to buy the put contract minus the current price of the underlying asset. So the payoff = $$\max(0,950-S_T)$$.

Then your total payoff is the combined value of the above two payoffs: total payoff = $$S_T + \max(0,950-S_T)$$

\begin{align*} \text{total payoff} &= S_T + \max(0,950-S_T) \\ &= \max(0+S_T,950-S_T+S_T) \\ &= \max(S_T,950) \end{align*}

Your profit is payoff minus what you paid to get into this position at this current point in time. You paid $1000 to buy the index at $$t=0$$ and a premium of$51.777 to enter the put contract at $$t=0$$. So altogether you paid 1000 + 51.777 = 1051.777 at $$t=0$$ to enter this position. Now we pull that value forward to this current time when the interest rate is 2% is:  1051.777(1 + 0.02) = 1072.81. So then your profit is

\begin{align*} \text{total profit} &= \max(S_T,950) - 1072.81\\ &= \max(S_T - 1072.81,-122.81) \end{align*}

Option 2: Invest 931.37 in zero-coupon bonds and buy a 950-strike call

##### Accounting For Not For Profit Organisation
State the meaning of ‘Not - for - Profit’ Organisations.
##### Functions of Profit in Economy.
What are the Functions of Profit in Economy? Describe in detail.
##### Its gross profit(loss) equals
A company has sales of $7,22,200 and cost of goods sold of$2,89,200.Its gross profit (loss) equals (a) $1,011,240 (b)$2,89,200 (c) $7,22,200 (d)$4,33,000
##### Various important theories of Profit in Economics.
What are the theories of Profit in Economics? Name them.  What is meant by Dynamic Theory, Risk-bearing Theory, Uncertainty Bearing Theory and Schumpeter's Innovation Theory? Illustrate these theoris one by one.
##### Computing profit Margin, Turnovers, and Return on investments
Munoz Corporation’s balance sheet indicates that the company has $600,000 invested in operating assets. During Year 2, Munoz earned operating income of$72,000 on \$1,200,000 of sales.   Required Compute Munoz’s profit margin for Year 2. Compute Munoz’s turnover for Year 2. Compute Munoz’s return on investment for Year 2.
##### Can water stay liquid below zero degrees Celsius?
Please elaborate more and make it in a paragraph form. Do not just copy and paste from the internet.
##### They hydrogen atom is not actually electronegative enough to form bonds to xenon.
They hydrogen atom is not actually electronegative enough to form bonds to xenon. Were the xenon-hydrogen bond to exist, what would be the structure of XeH4?Double-click any atom and type Xe to change the label.Draw the molecule by placing atoms on the grid and connecting them with bonds. Show all lone pairs of electrons.
##### What magnitude and sign of charge Q will make the force on charge q zero?
(Figure 1) shows four charges at the corners of a square of side L. What magnitude and sign of charge Q will make the force on charge q zero? Q =