# Cash and Carry..... again.

I decided to spend the day working on the problems I had previously punted, and made some solid progress but I am confused about a number of issues. I may be asking stupid questions but it’s late and im fried so I apologize in advance.

1.)When do you incorporate the borrowing cost in the cash and carry equation (e.g. borrowing at the risk free rate to finance the spot purchase)? For example problems 2.) (b) and © both do not incorporate the borrowing costs. The only thing I can think of is because they are actually purchasing a forward as a proxy for spot so there is no cash flow? I thought they had meant that the futures price was to be used as a proxy for the spot price but you are still buying spot…

2.) When calculating FV of storage costs, and borrowing costs for that matter, when do you simply multiple by (1+r)^t versus multiplying by e^(r*t) … I have seen it done both ways. For example problem 3 uses the first way whereas many of the examples use the latter

3.) While going through these problems, I realized that calculating the payoff on the cash and carry is simply as easy as subtracting the no arb price from the current futures price, so that is: [F0,T - S0*e^(rfr + storage costs - conv yield) *T] … so do we even really need to use the stupid table or can we just cut to the answer using the no arb model?

4.)When solving for the annualized return on a cash and carry, why do we have to use ln(VT/V0) = r * t/12 versus just doing a simple HPR and annualizing it… is this due to continuous versus normal compounding? Why do we even have to use continuous to calc a return?

5.) When are we suppose to use individual future value of storage costs and sum them all up versus convert it to a continuous rate by dividing the costs by the spot and simply throwing it in the exponent? The answers are slightly different both ways, and it is a massive shortcut to just convert to continous and solve the no-arb model.

I know thats alot of questions and probalby not 100% clear, but thanks in advance.

2.) When calculating FV of storage costs, and borrowing costs for that matter, when do you simply multiple by (1+r)^t versus multiplying by e^(r*t) … I have seen it done both ways. For example problem 3 uses the first way whereas many of the examples use the latter

This one is based on whether the “r” in question is discrete [1+r convention] or continuous [e^ convention].

1. the ln term again seems to be coming due to the continuous vs. the discrete compounding.

If the rate is defined as a continuous one instead of discrete time , there is no other way but to use the ln method.

by the way I’m sure you know that ln(VT/V0) = r * t/12 implies VT/V0 = e^(r*t/12) so the return is given by ret = VT/V0 - 1 = e^(r*t/12) - 1

Appreciate the input, but can you not convert discrete to continous just simply by dividing discrete by spot and then using continous formula? The difference is minor and saves several steps, you can go straight to the no-arb formula and be done in one step… has anybody noticed that ? (see point 3 above)

Also, any takers on question 1.)

1. I’m looking at page 204, CFAI book 5. Both 2b & 2c incorporate a rf loan to buy the asset

Cash and carry means you can sell the asset foward for more than it costs you to buy & store. Futures price is higher than the upper end of the no-arb range.

Steps:

1. Borrow at the rf

3. Pay to store it (so you never touch / see the commodity)

4. Sell the asset you now own foward

5. Wheh you close the position, deliver the asset to the owner of the foward & pay off your loan

6. Profit = Fwd price - (So*e^(rf + storage))

Also, on your discrete vs continous question:

When I solve these, I am going to stick to the no arb formula & range, which use continous compounding and netting of the benefits and costs. That’s the no arb range and that’s what should get you full credit.

You can see from another post I bumped up some confusion surrounding the reverse cash and carry question on the 2008 morning exam. Some guy e-mailed the CFAI organization and they gave him a cryptic answer that there were multiple responses that would have recieved full credit.

So, if there is a method you like, and it works, and its in the books, stick with it.

Good to know on the discrete vs continous. Makes my life easier.

My book is the 2011 text, not sure if has changed, the answers are on page 205 for me. I don’t see them borrowing to finance spot, otherwise the net outflow at time zero would be zero, not -3.00?

-3.00 doesn’t that mean they are borrowing the 3.00 dollars?

These are exellent questions… Here are my thoughts.

1.) When do you incorporate the borrowing cost in the cash and carry equation (e.g. borrowing at the risk free rate to finance the spot purchase)? For example problems 2.) (b) and © both do not incorporate the borrowing costs. The only thing I can think of is because they are actually purchasing a forward as a proxy for spot so there is no cash flow? I thought they had meant that the futures price was to be used as a proxy for the spot price but you are still buying spot…

– These questions are made to compare the rate of return from C&C(assume no borrowing) and the borrowing rate, and determine if there is any arbitrage opportunity. If C&C can earn a rate of return higher than the borrowing rate, C&C arbitrage is profitable. I know this is confusing – for any arbitrage calculation. Q2.C also tells that a negative rate of return may not make a reverse C&C arbitrage profitable – it may be simply caused by a convenience yield.

2.) When calculating FV of storage costs, and borrowing costs for that matter, when do you simply multiple by (1+r)^t versus multiplying by e^(r*t) … I have seen it done both ways. For example problem 3 uses the first way whereas many of the examples use the latter

– Q3: effective [monthly] interest rate: (1+r)^t – Q2: continuously compounding rate: e^(r*t)

3.) While going through these problems, I realized that calculating the payoff on the cash and carry is simply as easy as subtracting the no arb price from the current futures price, so that is: [F0,T - S0*e^(rfr + storage costs - conv yield) *T] …. so do we even really need to use the stupid table or can we just cut to the answer using the no arb model?

– I think your formula is the most accurate, while the dumb table is just an approximation. – I may be wrong, it’s probably make grades’ life easier. I’m amazed by the approximation, it’s pretty close.

4.) When solving for the annualized return on a cash and carry, why do we have to use ln(VT/V0) = r * t/12 versus just doing a simple HPR and annualizing it… is this due to continuous versus normal compounding? Why do we even have to use continuous to calc a return? – For 2.B&C, it compares the rate of return with the given interest rate, which is a continuously compouned rate.

5.) When are we suppose to use individual future value of storage costs and sum them all up versus convert it to a continuous rate by dividing the costs by the spot and simply throwing it in the exponent? The answers are slightly different both ways, and it is a massive shortcut to just convert to continous and solve the no-arb model.

– Don’t quite undertsand the question, so skip this one.

Great point on 1.) … you are likely correct, it is because you are comparing the returns to the borrowing rate to see if the rate is correct… that is why. Thanks.

I am NOT using that stupid table, im going straight to the no-arb formula.

Ques 1 C

Its gold (commodity) lent out question, why are we paying the lease rate upfront?

Since it is cash settled commodity transaction??

It depends on when to receive the lease payment…you earn FRF in this case.

BTW, how can an approximation work so perfectly?!

What do you mean by approximation? The table? If you look a the blue box examples and ignore all the unnecessary bullshit and go straight to the solution in the lower right, you will notice that it is simply the no arb formula minus the futures (for reverse cash and carry, other way around for cash and carry). All the table does is take a long ass time to get you there and confuse you in the process.

The 0.02 diff i believe comes from whether they account for lease payments up front, or at the end. CFGAY has done it both ways, and it is not clear which one is correct, or if it makes a difference since they will accept either way. Intuitively i would think it would come at the end, but who knows.

I meant the table in 1.C.

Whether it receives the lease payment upfront does make difference. Receiving upfront is consistent with the forward formula: S0*e^[(rfr - lease rate) *T]

This lousy arbitrage again:

P203, Q2B.

1. The storage cost is given in amount. Sometimes, it's given in %. (In schweser, it's continuously compounding) 2) The storage cost () is paid at the end of period.