Understanding S&P 500 profit

Question

It is my understanding that opening larger stock positions will, if the stock climbs, produce a larger profit.

For example, if I open a position of $200 on the S&P 500 and that position goes up by 50% then my position will be in profit $100. Obviously, the opposite would be true if the stock goes down.

It then follows that if the position is $1000 and the stock goes up by 50% the position would be in profit by $500.

Is this correct?

The second part to this question is what does 50% mean?

Is the 50% relative to the size of the position (the number of units purchased) or something else? Is the profit incurred relative to the number of units (ie: $ amount) purchased?

I'm trying to understand the following:

Let's say I open a position while the S&P 500 is at 4400 and after a few hours or days I close the position when the S&P 500 is at 4500. This would be in profit. But, would I make twice the $ profit if I open the position with $400 than if I opened it with $200?

I've been looking for a calculator which allows me to enter simply the stock price at open and close and the $ amount at open to calculate the return amount, but have not found one yet.

EDIT

To be more specific, with a real world example...

I open a position with $200 when the SPX500 is at 4377.46 and I close the position when the SPX500 reaches 4486.98. The index has risen by 109.52 points. I'm told that for the $200 investment this would be a % increase of 50% meaning a profit of $100. Is this correct?

According to the sums provided by @flux this would work out this way:

$200 / 4377.46 = 0.0456885956696349
4486.98 * ($200 / 4377.46) = $205.0038149977384

Obviously, I'm missing something here.

Answer 1

If the value of a stock goes up by 50% then the value of your investment also goes up by 50% as long as nothing else changed. You didn't buy more shares, you didn't sell any shares, or there were dividends.

This is also true for mutual funds and ETFs. This also ignores expenses. All investments have expenses.

If you invest $200 in an fund that follows the S&P 500 index, and over time the index goes up by 50% you should expect that the value of your investment is now $300.

If I start with an investment of $2,000 the same day as you. Then in the same time frame my investment would grow to $3,000.

If a rich person invests $2,000,000 over the same time period their investment would grow to $3,000,000.

Using the numbers provided in the edited question:

To be more specific, with a real world example...

I open a position with $200 when the SPX500 is at 4377.46 and I close the position when the SPX500 reaches 4486.98. The index has risen by 109.52 points. I'm told that for the $200 investment this would be a % increase of 50% meaning a profit of $100. Is this correct?

According to the sums provided by @flux this would work out this way:

$200 / 4377.46 = 0.0456885956696349 4486.98 * ($200 / 4377.46) = $205.0038149977384

Obviously, I'm missing something here.

One day one invests $200 in a mutual fund that follows the S&P 500. The current price of a share is 4377.46. That gets you 0.045689 shares.

(200/4377.46) or  0.045689 shares.

After it has risen by 109.52 points to 4486.98 the value has grown by

(109.52/4437.46)*100 = 2.052%

The just over 2.5% increase will translate to your investment being worth:

$200*1.0252 = $205.0038

Your confusion is at this point:

I'm told that for the $200 investment this would be a % increase of 50% meaning a profit of $100.

The value of the index didn't double. It went up by about 2.5%. Thus the value of your investment went up by 2.5%.

Answer 2

Let's say I open a position while the S&P 500 is at 4400 and after a few hours or days I close the position when the S&P 500 is at 4500. This would be in profit. But, would I make twice the $ profit if I open the position with $400 than if I opened it with $200?

Suppose 1 unit of S&P 500 (e.g. a hypothetical S&P 500 index fund) trades at $4400.

• You invest $400. Your $400 investment represents approximately 0.09 units of S&P 500 ($400 / $4400 ≈ 0.09). When 1 unit of S&P 500 rises to $4500, your 0.09 units is worth $409.09 ($4500 * [$400 / $4400] ≈ $409.09). The profit is approximately $9.09.

  • The rise from $4400 to $4500 is a rise of 2.27% ([4500 - 4400] / 4400 ≈ 0.0227).
  • The rise from $400 to $409.09 is also a rise of 2.27% ([409.09 - 400] / 400 ≈ 0.0227).

• You invest $200. Your $200 investment represents approximately 0.045 units of S&P 500 ($200 / $4400 ≈ 0.045). When 1 unit of S&P 500 rises to $4500, your 0.045 units is worth $204.55 ($4500 * [$200 / $4400] ≈ $204.55). The profit is approximately $4.55.

  • The rise from $4400 to $4500 is a rise of 2.27% ([4500 - 4400] / 4400 ≈ 0.0227).
  • The rise from $200 to $204.55 is also a rise of 2.27% ([204.55 - 200] / 200 ≈ 0.0227).

$4.55 * 2 ≈ $9.09

So yes, you would make twice the dollar profit with an investment of $400 than with an investment of $200.

Answer 3

The first two answers accurately explained the calculation. Your interpretation of the answer from @flux (your EDIT) is incorrect.

The percent gain is:

• [(Current value)- (Cost) / (Cost)]

(4486.98 - 4377.46)/4377.46 = 2.50% (109.52 gain)

If you were to invest $200, you'd make $5.

5/200 = 2.50%

Answer 4

tl;dr– Apparently OP invested in an index-fund with 20x leverage, and then that index-fund increased by ~2.5%, yielding ~50% profit.

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It sounds like you invested 200-USD in an index-fund.

The index went from 4377.46 to 4486.98, which is about a ~2.5% increase. And presumably would normally correspond to a ~2.5% profit.

Except, as you commented:

I have worked it out. I was using x20 leverage. <facepalm>

, so, yeah, ~2.5% times 20 is about ~50%.