 # Cash and Carry, The easy way

So I am presented with yet another will this work question.

The CFA goes through the whole long hullabaloo on Cash and Carry and reverse Cash and Carry

Without typing everything out, suffice it to say that the answer for number 6 on the 2008 exam is 2.19 cents for the long reverse cash and carry.

The “simple” way would be to say “well we receive the risk free and pay the lease” so…

Profit = Forward - Spot e(Rf-Lease)T

in this case its 316e(.05-.06)3/12 = 315.2199

Future is 3.13

Net we get 2.21…

Do we win? Or does CFAI say it has to be 2.19 and the long way? The difference is .02 cents on a 313 cent contract…

On a multiple choice it woudl be fine…but what about the essay

the first part of the question called to identify the 3 parts to the reverse cash and carry contract didn’t it?

So Short Spot (Overpriced), Invest Proceeds in the T-bill, (Pay Lease Rate) Buy Forward (underpriced)

Short Spot = -316 [@T0]

Invest Proceeds in T-Bill= +316 [@T0]

Net [@T0] = 0

@ T1 => Pay Lease Rate = -1 * [316 * e^(0.06*.25) - 316]= - 4.7787 [-1 * since we are paying]

@ T1 = Buy Forward = -313

@ T1 receive Interest on 316 invested = 316 * e^0.05*0.25 = 319,9748

Net @ T1 = -313 - 4.7787 + 319.9748 = 2.1961

It all depends on the # of points allocated.

I guess…it asked for the “two” components… only long futures and long a zero, no short or lease payment.

CPK, what is the lease rate is discretely compounded, do we also calculate the components like you did?

even then it should be Spot * Lease Rate …

E.g. if 6% were the discrete lease rate above … 316 * 1.06^0.25 - 316 = 4.6369 would be the lease rate that would be paid.

I think the guideline answer is not right here. Either the no arb range holds, or it doesn’t. And cpk’s answer is not in the no arb range.

No arb range is what?

So * e^rf*t = 316 * e^0.05 * 0.25 = 319.9747

Lower = S0 * e^(rf-d)*T = 316 * e^-0.025 = 308.1979

313 lies very much in that range.

Lower bound is 315.2109867

316e(0.05-0.06).25

Both of your very different lower bound are below that range.

No arb is no arb, your cannot be below.

And your comment about 313 being in the range makes no sense.

Yes my math was whack. I ended up doing 0.025 instead of 0.0025 above.

however given that this was a ARB transaction - the price HAD to lie outside the range. Without that Arb would not be possible.

They were asking you to do a reverse cash and carry ARB. How would you do that within a no-Arb transaction range?