Suppose that the spot price…
$begingroup$
Suppose the spot price of gold is $300 per ounce and the risk-free
interest rate for one year is 5%. What is a reasonable value for the one-year forward price of gold?
The answer is $315, right?
Suppose the one-year forward price of gold is $340. Argue as follows: borrow 300 dollars for a year and buy one ounce of gold. Then short a forward contract to sell the gold in one year time. Show this will lead to a risk-free profit (arbitrage) and the the one-year forward price of gold must be $315.
This comes down to $340 - $315 = $25 , right?
I suppose that the $315 here cones again from the $300*105% ? right?
Then assume the one-year forward price of gold is $300. Argue as follows: sell the gold, then invest the proceeds and long a one-year forward on gold. Show again that this will lead to a risk-free profit (arbitrage) and the one-year forward price of gold must be $315.
I'm confused cause of this part. So if anybody could help?
thanks in advance
I don't know what goes wrong with the notation but when I design the question I don't have a problem until I upload the text. Therefor I wanted to upload an image. enter image description here
valuation-theory
edited Jan 4 at 6:18
max_zorn
3,36361329
asked Jan 4 at 4:12
Nicolas CloetNicolas Cloet
121
$endgroup$
add a comment |
$begingroup$
Suppose the spot price of gold is $300 per ounce and the risk-free
interest rate for one year is 5%. What is a reasonable value for the one-year forward price of gold?
The answer is $315, right?
Suppose the one-year forward price of gold is $340. Argue as follows: borrow 300 dollars for a year and buy one ounce of gold. Then short a forward contract to sell the gold in one year time. Show this will lead to a risk-free profit (arbitrage) and the the one-year forward price of gold must be $315.
This comes down to $340 - $315 = $25 , right?
I suppose that the $315 here cones again from the $300*105% ? right?
Then assume the one-year forward price of gold is $300. Argue as follows: sell the gold, then invest the proceeds and long a one-year forward on gold. Show again that this will lead to a risk-free profit (arbitrage) and the one-year forward price of gold must be $315.
I'm confused cause of this part. So if anybody could help?
thanks in advance
I don't know what goes wrong with the notation but when I design the question I don't have a problem until I upload the text. Therefor I wanted to upload an image. enter image description here
valuation-theory
edited Jan 4 at 6:18
max_zorn
3,36361329
asked Jan 4 at 4:12
Nicolas CloetNicolas Cloet
121
$endgroup$
2
$begingroup$
The notation went funny because dollar signs are used here to delimit "math mode" based on LaTeX. In order to have a dollar sign show up, put a backslash in front of it. (I've edited this fix into your post - it should show up soon)
$endgroup$
– jmerry
Jan 4 at 4:26
$begingroup$
Waw, that really is an eye-opener to me! Thanks for helping me out! As you might have figured. I'm new to this website.
$endgroup$
– Nicolas Cloet
Jan 4 at 6:22
add a comment |
$begingroup$
Suppose the spot price of gold is $300 per ounce and the risk-free
interest rate for one year is 5%. What is a reasonable value for the one-year forward price of gold?
The answer is $315, right?
Suppose the one-year forward price of gold is $340. Argue as follows: borrow 300 dollars for a year and buy one ounce of gold. Then short a forward contract to sell the gold in one year time. Show this will lead to a risk-free profit (arbitrage) and the the one-year forward price of gold must be $315.
This comes down to $340 - $315 = $25 , right?
I suppose that the $315 here cones again from the $300*105% ? right?
Then assume the one-year forward price of gold is $300. Argue as follows: sell the gold, then invest the proceeds and long a one-year forward on gold. Show again that this will lead to a risk-free profit (arbitrage) and the one-year forward price of gold must be $315.
I'm confused cause of this part. So if anybody could help?
thanks in advance
I don't know what goes wrong with the notation but when I design the question I don't have a problem until I upload the text. Therefor I wanted to upload an image. enter image description here
valuation-theory
edited Jan 4 at 6:18
max_zorn
3,36361329
asked Jan 4 at 4:12
Nicolas CloetNicolas Cloet
121
$endgroup$
Suppose the spot price of gold is $300 per ounce and the risk-free
interest rate for one year is 5%. What is a reasonable value for the one-year forward price of gold?
The answer is $315, right?
Suppose the one-year forward price of gold is $340. Argue as follows: borrow 300 dollars for a year and buy one ounce of gold. Then short a forward contract to sell the gold in one year time. Show this will lead to a risk-free profit (arbitrage) and the the one-year forward price of gold must be $315.
This comes down to $340 - $315 = $25 , right?
I suppose that the $315 here cones again from the $300*105% ? right?
Then assume the one-year forward price of gold is $300. Argue as follows: sell the gold, then invest the proceeds and long a one-year forward on gold. Show again that this will lead to a risk-free profit (arbitrage) and the one-year forward price of gold must be $315.
I'm confused cause of this part. So if anybody could help?
thanks in advance
I don't know what goes wrong with the notation but when I design the question I don't have a problem until I upload the text. Therefor I wanted to upload an image. enter image description here
valuation-theory
valuation-theory
edited Jan 4 at 6:18
max_zorn
3,36361329
asked Jan 4 at 4:12
Nicolas CloetNicolas Cloet
121
edited Jan 4 at 6:18
max_zorn
3,36361329
asked Jan 4 at 4:12
Nicolas CloetNicolas Cloet
121
edited Jan 4 at 6:18
max_zorn
3,36361329
edited Jan 4 at 6:18
max_zorn
3,36361329
edited Jan 4 at 6:18
max_zorn
3,36361329
3,36361329
asked Jan 4 at 4:12
Nicolas CloetNicolas Cloet
121
asked Jan 4 at 4:12
Nicolas CloetNicolas Cloet
121
asked Jan 4 at 4:12
Nicolas CloetNicolas Cloet
121
121
2
$begingroup$
The notation went funny because dollar signs are used here to delimit "math mode" based on LaTeX. In order to have a dollar sign show up, put a backslash in front of it. (I've edited this fix into your post - it should show up soon)
$endgroup$
– jmerry
Jan 4 at 4:26
$begingroup$
Waw, that really is an eye-opener to me! Thanks for helping me out! As you might have figured. I'm new to this website.
$endgroup$
– Nicolas Cloet
Jan 4 at 6:22
add a comment |
2
$begingroup$
The notation went funny because dollar signs are used here to delimit "math mode" based on LaTeX. In order to have a dollar sign show up, put a backslash in front of it. (I've edited this fix into your post - it should show up soon)
$endgroup$
– jmerry
Jan 4 at 4:26
$begingroup$
Waw, that really is an eye-opener to me! Thanks for helping me out! As you might have figured. I'm new to this website.
$endgroup$
– Nicolas Cloet
Jan 4 at 6:22
2
2
$begingroup$
The notation went funny because dollar signs are used here to delimit "math mode" based on LaTeX. In order to have a dollar sign show up, put a backslash in front of it. (I've edited this fix into your post - it should show up soon)
$endgroup$
– jmerry
Jan 4 at 4:26
$begingroup$
The notation went funny because dollar signs are used here to delimit "math mode" based on LaTeX. In order to have a dollar sign show up, put a backslash in front of it. (I've edited this fix into your post - it should show up soon)
$endgroup$
– jmerry
Jan 4 at 4:26
$begingroup$
Waw, that really is an eye-opener to me! Thanks for helping me out! As you might have figured. I'm new to this website.
$endgroup$
– Nicolas Cloet
Jan 4 at 6:22
$begingroup$
Waw, that really is an eye-opener to me! Thanks for helping me out! As you might have figured. I'm new to this website.
$endgroup$
– Nicolas Cloet
Jan 4 at 6:22
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Your first part is correct.
For the second part, if the forward price of gold is the same as the spot price then you can sell the gold today for $$300$ and put the money into an account earning $5%$ interest. At the same time you go long on a one year forward contract. This means you agree to pay $$300$ an ounce a year from now.
In a year you have $$315$ from the return on your investment so you can buy your gold back and earn a free $$15$. That's what arbitrage is. Since everyone would do this it would drive the forward price up to $$315$.
answered Jan 4 at 7:09
John DoumaJohn Douma
5,51211319
$endgroup$
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3061314%2fsuppose-that-the-spot-price%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Your first part is correct.
For the second part, if the forward price of gold is the same as the spot price then you can sell the gold today for $$300$ and put the money into an account earning $5%$ interest. At the same time you go long on a one year forward contract. This means you agree to pay $$300$ an ounce a year from now.
In a year you have $$315$ from the return on your investment so you can buy your gold back and earn a free $$15$. That's what arbitrage is. Since everyone would do this it would drive the forward price up to $$315$.
answered Jan 4 at 7:09
John DoumaJohn Douma
5,51211319
$endgroup$
add a comment |
$begingroup$
Your first part is correct.
For the second part, if the forward price of gold is the same as the spot price then you can sell the gold today for $$300$ and put the money into an account earning $5%$ interest. At the same time you go long on a one year forward contract. This means you agree to pay $$300$ an ounce a year from now.
In a year you have $$315$ from the return on your investment so you can buy your gold back and earn a free $$15$. That's what arbitrage is. Since everyone would do this it would drive the forward price up to $$315$.
answered Jan 4 at 7:09
John DoumaJohn Douma
5,51211319
$endgroup$
add a comment |
$begingroup$
Your first part is correct.
For the second part, if the forward price of gold is the same as the spot price then you can sell the gold today for $$300$ and put the money into an account earning $5%$ interest. At the same time you go long on a one year forward contract. This means you agree to pay $$300$ an ounce a year from now.
In a year you have $$315$ from the return on your investment so you can buy your gold back and earn a free $$15$. That's what arbitrage is. Since everyone would do this it would drive the forward price up to $$315$.
answered Jan 4 at 7:09
John DoumaJohn Douma
5,51211319
$endgroup$
Your first part is correct.
For the second part, if the forward price of gold is the same as the spot price then you can sell the gold today for $$300$ and put the money into an account earning $5%$ interest. At the same time you go long on a one year forward contract. This means you agree to pay $$300$ an ounce a year from now.
In a year you have $$315$ from the return on your investment so you can buy your gold back and earn a free $$15$. That's what arbitrage is. Since everyone would do this it would drive the forward price up to $$315$.
answered Jan 4 at 7:09
John DoumaJohn Douma
5,51211319
answered Jan 4 at 7:09
John DoumaJohn Douma
5,51211319
answered Jan 4 at 7:09
John DoumaJohn Douma
5,51211319
answered Jan 4 at 7:09
John DoumaJohn Douma
5,51211319
5,51211319
add a comment |
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3061314%2fsuppose-that-the-spot-price%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
2
$begingroup$
The notation went funny because dollar signs are used here to delimit "math mode" based on LaTeX. In order to have a dollar sign show up, put a backslash in front of it. (I've edited this fix into your post - it should show up soon)
$endgroup$
– jmerry
Jan 4 at 4:26
$begingroup$
Waw, that really is an eye-opener to me! Thanks for helping me out! As you might have figured. I'm new to this website.
$endgroup$
– Nicolas Cloet
Jan 4 at 6:22