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# CourseErrors Found in 2021 Study Materials P1.T3. Financial Markets & Products

#### Nicole Seaman

##### Director of FRM Operations
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Please use this new thread to let David and I know about any errors, missing/broken links, etc. that you find in the 2021 materials that are published in the study planner under P1.T3. Financial Markets & Products. This will keep our forum much more organized. We appreciate your cooperation!

PLEASE NOTE: Our Practice Question sets already have links to their specific forum threads where you can post about any errors that you find. This thread is for any other materials (notes, spreadsheets, videos, etc.) where you might find errors.

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#### bollengc

##### Member
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hello,
a feedback on 3-FMP-10-Ch10-Fin-Fwds-v3

Page 10: the phrasing of the Hull example is not 100% clear:
If a long forward contract to purchase a non-dividend-paying stock in 3 months is currently priced at $40. Here is from the video where there is no ambiguity: And page 14: 1000*exp(r_f*T) corresponds to the 1000 units of foreign ccy at T and not zero. Same page 14: in case forward exchange rate vary from 0.7651 -> should be 0.7206 (value of F0 computed just above?) thanks, Camille #### Jaskarn ##### Active Member Hi @Nicole Seaman , book 3 chapter banks page 6. I think this case is for JP Morgan chase and not Morgan stanley. ( We studied this in book 1) For instance, when the Morgan Stanley trader known as the London Whale lost more than$6 billion in 2012, could Morgan Stanley have predicted the loss?
Further, could Morgan Stanley have predicted that two former traders would face criminal
charges and the bank would be faced to pay more than \$1 billion in fines because of the
issue? Perhaps, but probably not given that the predictability of such outcomes is nearly
impossible.

#### Garbanzo

##### New Member
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T3.CH11 Commodity Forwards and Futures. Study Notes page 7:

Did you mean "if the forward price is lower"? there is an arb opportunity if the price is higher because I can just sell the forward and carry the commodity with the extra convenience yield.

#### lushukai

##### Active Member
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Hi @Garbanzo ,

If the forward price is higher, it means that the commodity has financial and physical costs of storing. Therefore, when you short the forward (to sell the commodity in the future) and you carry the commodity, you have to pay for the financial and physical costs of storing (between now and when the forward matures) that effectively offsets the arb/profit opportunity.

#### Garbanzo

##### New Member
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but here we are talking about a forward price implied by the cost of carry model. we are given the storage costs.
i.e. if the market forward price is higher than the analytical price, there should be an arbitrage opportunity, which we can exploit by shorting the forward and carrying the commodity, accounting for the given storage costs and implied convenience yield.

#### lushukai

##### Active Member
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Hi @Garbanzo ,

I'm not sure if you are saying the forward price is higher than the output of the cost of carry model or higher than the current market price of the commodity.

If you are talking about the first (you are right in saying that there is an arb opportunity), but if you are talking about the second, I don't really see how there is an arb opportunity here. The cost of carry model (a simplified one) is given by:

F_0 = S_0 * exp(r + s)T

So if F_0 is higher than S_0, it is simply due to positive interest rates and storage cost. The reason why there cannot be an arbitrage (with reference to the second case), is because when you short the forward and carry the commodity, you are holding the commodity and you have to pay for its storage costs (and if you paid for the commodity using borrowed capital, the interest rate has to be paid). So the profit (you would have supposedly made) by shorting the higher forward price is "eaten up" by the amount you would have to pay in storing (s) your carried commodity and interest on the borrowed capital (r).

#### Garbanzo

##### New Member
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Thanks for taking the time to answer.
I understand the cost of carry model and the relationship between the forward and spot.
maybe I am just overcomplicating it and it simply meant 'higher forward price than spot price' as you say.
in that case it really is trivial.
However, I think it has to do with the introduction of the convenience yield into the model.
Later, there is the no arbitrage range, where the bottom formula's left part is what the original quote I posted is indicating as well ('forward price being higher than the commodity carried... implying no arbitrage'):

the only way I can understand that is that, because convenience yield is unobserved, if the forward price is higher (than the output of the carry model), it simply means that the implied convenience yield is lower. But this also means the convenience yield just "equates" the F_0_T price with the left hand "carry model price". so there cannot possibly be any arbitrage when convenience yield is involved.

I would understand if the left hand side was only an "equal". But the "lower than" does not make sense.
The right hand side is easy, the forward price must be less than or equal, otherwise we can short forward and carry.

#### lushukai

##### Active Member
Subscriber
Hi @Garbanzo ,

Later, there is the no arbitrage range, where the bottom formula's left part is what the original quote I posted is indicating as well ('forward price being higher than the commodity carried... implying no arbitrage'):
- I think what David is trying to explain is just that convenience yield lowers the forward price because of the nature of its exponent, which you probably already know F_0 = S_0 * exp(-y)T and I am ignoring the other terms here. Therefore, the introduction of the convenience yield lowers the forward price and is acceptable (as mentioned in the notes).

the only way I can understand that is that, because convenience yield is unobserved, if the forward price is higher (than the output of the carry model), it simply means that the implied convenience yield is lower. But this also means the convenience yield just "equates" the F_0_T price with the left hand "carry model price". so there cannot possibly be any arbitrage when convenience yield is involved.
- I feel you are not quite clear on the concepts (sorry), but this is what the forum is for - raising doubts and making your money's worth . Firstly, when you say the forward price is higher than output of the CoC model, you are talking about the market forward price (which is a result of market dynamics) and convenience yield is not the cause of this higher forward price (the convenience yield affects the model output). You need to be clear on the difference between 1. Market Price and 2. Model Output, they are not the same. The output of the CoC model at a point in time for a specific forward contract should always give the same forward price and is affected by the same variables - spot, interest rate, storage cost, convenience yield and TTM. I do not consider these as influences on the market price (though one can put in an argument).
- The "ranged" equation is simply saying that - if the market forward price (F_0) is between the model outputs (S_0*exp(r+u-y)T and S_0*exp(r+u)T), then arbitrage is unlikely (I would not say impossible). Actually, it is possible for arbitrage to take place when convenience yield is involved, you just have to violate the equation given below. For example, if F_0 < S_0*exp(r+u-y)T, one can long the forward and short the commodity to invest at the risk-free rate and pay cheaply for the commodity in the future (which is then used to pay back the initial short position).

I would understand if the left hand side was only an "equal". But the "lower than" does not make sense.
The right hand side is easy, the forward price must be less than or equal, otherwise we can short forward and carry.

- I guess I explained the "lower than" in my example above? Also, just thinking logically, if there is a positive convenience yield, it has to lower the left term S_0*exp(r+u-y)T = S_0*exp(r+u)T*exp(-y)T < S_0*exp(r+u)T = right side term. This is because exp(-y)T < 1.0 and thus must lower the left term.

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
I am sorry @Garbanzo because, I think you are correct that it is our mistake (sorry for the trouble @lushukai truly). This is about the convenience yield where the convenience yield is the essential distinction between an investment versus a consumption commodity. Investment commodities have no convenience such that arbitrage can always enforce F = S0*exp(r + c) where c = r + u - q or any subset of the tangle carry factors (r = financing, u = storage, q = dividend/income).

But a consumption has convenience (especially right now, today in a supply crunch!) and the point is that if the following inequality exists:

F0 < S0*exp(r + c) or realistically b/c consumption commodities don't throw off income:
F0 < S0*exp(r + u)

.... whereas arbitrageurs would typically sell commodity that is "trading rich" (too expensive) in this scenario, they are inhibited by the commodity's convenience (by definition convenience is the preference to hold for future use). Consumption commodity owners are reluctant to sell when convenience is high. Convenience yield blocks (or introduces friction into) the "short commodity" that is otherwise possible when the forward price is too low. Put again, for consumption commodities only (as their defining characteristic is convenience):

F0 > S0*exp(r + u) is not sustainable, arbitrageurs will exploit this with the short-forward/long-commodity trade. However;
F0 < S0*exp(r + u) is sustainable because everybody is reluctant to short the commodity, and this can persist and is explained by:
F0 = S0*exp(r + u + y); convenience, y, is the gap that defies arbitrage (persists) because it is a reluctance to sell the commodity

Convenience yield can also be viewed as embedded option value (optionality). In this way, you are correct @Garbanzo. Sorry for the typo(s), hope that clarifies.

Last edited:

#### Garbanzo

##### New Member
Subscriber
thank you @David Harper CFA FRM

@lushukai - convenience yield is an unobserved variable, so you cannot use the formula to determine if market price is off or not. you can only imply the convenience yield from the market price or somehow estimate it (introducing risk). That's why I was saying, an arbitrage (by definition a "riskless profit") is not possible when we introduce something unobservable.

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