T3. Markets & Prdts (McDonald and Geman)
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skoh,
- no, crack spread can be various combinations of (typically although hardly necessary as it's a convergence/divergence pair trade) X = Y+Z, you can see it is roughly based on outputs and inputs, see http://forum.bionicturtle.com/threads/t3-markets-prdts-mcdonald-and-geman.6443/
- See http://www.bionicturtle.com/how-to/article/strip-and-stack-hedge-products
also, Hull Chapter 3.6 discusses stack and roll. The FRM's most important "case" of stack hedge (and its problems) is Metallgesellshaft
Hi David,
From the same chapter : Question 187.4- calculate the lease rate under continuous and annual compounding.
For the continuous lease rate, we used to conventional lease rate formula stated in the chapter: riskless - 1/T*LN(F/S)
However, im not familiar with the annual compounding formula: annual lease rate = (1 + riskless) / [F/S)^(1/T)] - 1.
Can you please tell me how did we get this formula ?!
From the same chapter : Question 187.4- calculate the lease rate under continuous and annual compounding.
For the continuous lease rate, we used to conventional lease rate formula stated in the chapter: riskless - 1/T*LN(F/S)
However, im not familiar with the annual compounding formula: annual lease rate = (1 + riskless) / [F/S)^(1/T)] - 1.
Can you please tell me how did we get this formula ?!
RiskNoob
Active Member
Hi jeff-1984,
It can be derived from annual compound version of the cost of carry (Hull Ch.5, continuous compounding) model
- continuous version: F = S*e^[(r - delta_c)*T], where delta_c is lease rate (continuous compounding)
- equivalently, the annual compounding version of cost of carry model of the above would be:
F = S*(1+r - (1 + delta_a))^T
Playing around with algebra and we can find delta_a (annual lease rate) = (1 + riskless) / [F/S)^(1/T)] - 1.
But I wouldn't bother memorizing the annual lease rate in my opinion, as long as we know 1. the basic (cts) cost of carry model (Hull Ch. 5) and 2. converting compounding frequency (Hull Ch.4), we should be able to derive one rate to other other, or vise versa.
Thanks,
RiskNoob
It can be derived from annual compound version of the cost of carry (Hull Ch.5, continuous compounding) model
- continuous version: F = S*e^[(r - delta_c)*T], where delta_c is lease rate (continuous compounding)
- equivalently, the annual compounding version of cost of carry model of the above would be:
F = S*(1+r - (1 + delta_a))^T
Playing around with algebra and we can find delta_a (annual lease rate) = (1 + riskless) / [F/S)^(1/T)] - 1.
But I wouldn't bother memorizing the annual lease rate in my opinion, as long as we know 1. the basic (cts) cost of carry model (Hull Ch. 5) and 2. converting compounding frequency (Hull Ch.4), we should be able to derive one rate to other other, or vise versa.
Thanks,
RiskNoob
Hi
I am still confused between Normal Contango, Normal Backwardation, Contango and Backwardation. Is it that
For normal Contango,
The current spot price is less than future price and the spot will rise up to the future?
For normal Backwardation,
The current future price is less than the spot price and the spot will decrease to match the future?
I am still confused between Normal Contango, Normal Backwardation, Contango and Backwardation. Is it that
For normal Contango,
The current spot price is less than future price and the spot will rise up to the future?
For normal Backwardation,
The current future price is less than the spot price and the spot will decrease to match the future?
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RiskNoob
Active Member
Hi skoh,
David posted an excellent article regarding the topic above few years ago, definitely recommended to read:
http://www.bionicturtle.com/how-to/article/contango_backwardation_expected_future_price
RiskNoob
David posted an excellent article regarding the topic above few years ago, definitely recommended to read:
http://www.bionicturtle.com/how-to/article/contango_backwardation_expected_future_price
RiskNoob
Thanks RiskNoob,
The way I think about it is, "contango" and "backwardation" are just fancy lingo for, respectively, an upward-sloping curve (what you'd expect for most commodities) and inverted (high convenience yield). So these are, contango if S(0)< F(0) and backwardation if S(0)>F(0). The (0)s are relevant b/c these terms simply characterize the shape of a forward curve that you can currently observe, today time (0).
"normal backwardation" and "normal contango" are not observable, because they concern the relationship between observed F(0) and unobserved E[S(t)] the expected future spot price. There isn't really a chart we can look at for normal backwardation. Thanks,
The way I think about it is, "contango" and "backwardation" are just fancy lingo for, respectively, an upward-sloping curve (what you'd expect for most commodities) and inverted (high convenience yield). So these are, contango if S(0)< F(0) and backwardation if S(0)>F(0). The (0)s are relevant b/c these terms simply characterize the shape of a forward curve that you can currently observe, today time (0).
"normal backwardation" and "normal contango" are not observable, because they concern the relationship between observed F(0) and unobserved E[S(t)] the expected future spot price. There isn't really a chart we can look at for normal backwardation. Thanks,
RiskNoob
Active Member
Hi Jeff,
Sorry there is a hole in my cost of carry formula for annual compounding above - this is not true (F = S*(1+r - (1 + delta_a))^T)
lease rate (delta, annual compounding) is an negative factor for the cost of carry model, so the correction would be
F = S* (1 + r)^T * ( 1 + delta ) ^(-T)
= S * [ (1 + r)/(1 + delta) ]^T
Notice that the above formula is consistent with the interest rate parity theorem from Ch15, Saunders (by setting r_f = delta, annual compounding)
Let's do some algebra:
F/S = [ (1 + r)/(1 +delta) ]^T
(F/S)^(1/T) = (1 + r)/(1 +delta)
(1 +delta) = (1 + r)/[(F/S)^(1/T)]
delta = (1 + r)/[(F/S)^(1/T)] - 1
Hope this helps this time...
RiskNoob
Sorry there is a hole in my cost of carry formula for annual compounding above - this is not true (F = S*(1+r - (1 + delta_a))^T)
lease rate (delta, annual compounding) is an negative factor for the cost of carry model, so the correction would be
F = S* (1 + r)^T * ( 1 + delta ) ^(-T)
= S * [ (1 + r)/(1 + delta) ]^T
Notice that the above formula is consistent with the interest rate parity theorem from Ch15, Saunders (by setting r_f = delta, annual compounding)
Let's do some algebra:
F/S = [ (1 + r)/(1 +delta) ]^T
(F/S)^(1/T) = (1 + r)/(1 +delta)
(1 +delta) = (1 + r)/[(F/S)^(1/T)]
delta = (1 + r)/[(F/S)^(1/T)] - 1
Hope this helps this time...
RiskNoob
Praveen_India
Member
''Lease rate
The lease rate is to commodities what the dividend is to financial assets: it is the rate received
by the owner of a consumption asset from the investor for borrowing the asset. Lease rate
payment is clearly a benefit to the owner of the asset. Accordingly, it has the effect of
lowering forward price. To see this, just imagine that the forward price was not impacted by
the lease rate. The owner of the commodity could exploit this by leasing his commodity to a
short seller, and turn around in the market and sell the forward at the higher price, thus
earning a risk-free payment equal to the present value of the lease rate.
“It is important to be clear about the reason a lease payment is required for a commodity
and not for a financial asset” (McDonald)"
-from the notes (Markets and Products(McDonald))
Hi David/Forum,
Similar to how the owner of commodity can give that commodity on lease and earn lease rate, cant the owner of financial asset lend his asset to a short seller and earn some money and thus reducing the forward/futures price. And also he would be entitled to dividends, if any, during the lease time.
Please help understand.
Thanks,
Praveen
The lease rate is to commodities what the dividend is to financial assets: it is the rate received
by the owner of a consumption asset from the investor for borrowing the asset. Lease rate
payment is clearly a benefit to the owner of the asset. Accordingly, it has the effect of
lowering forward price. To see this, just imagine that the forward price was not impacted by
the lease rate. The owner of the commodity could exploit this by leasing his commodity to a
short seller, and turn around in the market and sell the forward at the higher price, thus
earning a risk-free payment equal to the present value of the lease rate.
“It is important to be clear about the reason a lease payment is required for a commodity
and not for a financial asset” (McDonald)"
-from the notes (Markets and Products(McDonald))
Hi David/Forum,
Similar to how the owner of commodity can give that commodity on lease and earn lease rate, cant the owner of financial asset lend his asset to a short seller and earn some money and thus reducing the forward/futures price. And also he would be entitled to dividends, if any, during the lease time.
Please help understand.
Thanks,
Praveen
Hi
May i put forward my 2 arguments.
1) The short seller borrows and sells it to buy it later. The dividends if any received by financial asset owner would be provided by the borrower himself otherwise from where he would get the dividend,thus the borrowing rate would be equal to dividend yield itself therefore what owner is getting in the end is the dividend yield itself. I am talking this in context of arbitrage the lender of financial assets would make riskless profit if he is getting some basis points more than dividends from borrower so in end he will receive riskless rate-div yield from forward+div yield+basis point =risk free rate plus some basis points but his earning should be the risk free rate only,arbitrage shall drive this extra basis points to 0 in the long term so in end he receives only the risk free rate. So in general the what remains as income from financial assets is the dividend yield and nothing else which is analogous to lease rate as sourve of income for physical commodities. Please see the broader picture and not details.
2) Also the term lease rate is more suited to physical commodity and is not used in context of financial assets so often but we usually associate dividend yield with them which is analogous to lease rate for physical commodity. We lease physical commodities and we lend financial assets.
Thanks
May i put forward my 2 arguments.
1) The short seller borrows and sells it to buy it later. The dividends if any received by financial asset owner would be provided by the borrower himself otherwise from where he would get the dividend,thus the borrowing rate would be equal to dividend yield itself therefore what owner is getting in the end is the dividend yield itself. I am talking this in context of arbitrage the lender of financial assets would make riskless profit if he is getting some basis points more than dividends from borrower so in end he will receive riskless rate-div yield from forward+div yield+basis point =risk free rate plus some basis points but his earning should be the risk free rate only,arbitrage shall drive this extra basis points to 0 in the long term so in end he receives only the risk free rate. So in general the what remains as income from financial assets is the dividend yield and nothing else which is analogous to lease rate as sourve of income for physical commodities. Please see the broader picture and not details.
2) Also the term lease rate is more suited to physical commodity and is not used in context of financial assets so often but we usually associate dividend yield with them which is analogous to lease rate for physical commodity. We lease physical commodities and we lend financial assets.
Thanks
Praveen_India
Member
Hi Shakti,
Right, the short seller will give the dividend back to the lender. If there are not any dividends paid during the lending/lease period short seller would give Only fees to the lender for borrowing the assets. And if there are dividends he would give dividend+fees to the lender.
Cost of carry model is considering only Dividend, however that extra income (fees) that lender earns by lending the financial asset to the short seller is not considered.
Or is it that the ''dividend'' term in the COC model impounds this fees also and not just the actual dividend?
Kindly share your thought.
Thank you,
Praveen
Right, the short seller will give the dividend back to the lender. If there are not any dividends paid during the lending/lease period short seller would give Only fees to the lender for borrowing the assets. And if there are dividends he would give dividend+fees to the lender.
Cost of carry model is considering only Dividend, however that extra income (fees) that lender earns by lending the financial asset to the short seller is not considered.
Or is it that the ''dividend'' term in the COC model impounds this fees also and not just the actual dividend?
Kindly share your thought.
Thank you,
Praveen
Hi
Yes this fees in itself is not determinist/is ambigous but the dividend yield which is known at the time of valuing the forward is ddeterministic.COC lay emphasis on just the dividend yield not the fees because dividend are more deterministic, i think they do not include the fees. In the end i would take the COC model as what it is rather tthan include fees also which would make the model more complicated.
Thanks
Yes this fees in itself is not determinist/is ambigous but the dividend yield which is known at the time of valuing the forward is ddeterministic.COC lay emphasis on just the dividend yield not the fees because dividend are more deterministic, i think they do not include the fees. In the end i would take the COC model as what it is rather tthan include fees also which would make the model more complicated.
Thanks
Praveen_India
Member
Thank you for your time and explanation Shakti.
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