Few doubts on Market Risk....

[Chintan]

Hi David,

I've a few doubts in Mrkt Risk...

1) On Pg 81 of Hull (Hedging Strategies Using Futures)...in the airline example for hedging agnst price increase of
jet fuel, can we use the foll formulas ?

Variance = E (X^2) - {E(X)^2}
Covariance = E(XY) - { E(X) * E(Y) }

I used the above formulas and the answer is quite close to that given in the text book but not exactly
the same....

2) On Pg 123, it has been mentioned that margin does not represent cost to investor,
bcoz interest is paid on margin account ? Is interest really available on margin deposits ??

3) On Pg 25 of your notes, it is mentioned tht normal backwardation is wen the fut price >
Expected Futures Spot Price ???.....Is this a typo ?

4) While computing conversion factor, we have to reduce the accrued interest....
but why not the present value of accrued interest, since the same will be realized only
at the end of the period.....

5) For computing conversion factor, it is mentioned tht maturity is rounded down to the
nearest 3 months - so it presumably means tht it is rounded down to multiples of 3 months - right ?

6) For floating part in a swap, the rate is determined at the beginning of the period and the
payment is done at the end of the period...but this doesnt get reflected in the examples given
in the study notes....we have considered the cash flows at time 0.25, 0.75 and 1.25 and accordingly
applied the discounting factors ?

7) Can the upper bound of european put shud be considered as Strike Price or
"Present value of strike price" since the same will be exercised only on
expiry dates

Thanks in advance...

Chintan

 

[David Harper CFA FRM]

Hi Chintan,

1) On Pg 81 of Hull (Hedging Strategies Using Futures)...in the airline example for hedging agnst price increase of
jet fuel, can we use the foll formulas ?
Variance = E (X^2) - {E(X)^2}
Covariance = E(XY) - { E(X) * E(Y) }
I used the above formulas and the answer is quite close to that given in the text book but not exactly
the same....

Not the first b/c that is variance of single variable (X)
On the second, yes, you are onto the right idea, but the optimal hedge is to minimize the portfolio VARIANCE where portfolio includes the spot asset and the hedge:
MINIMIZE variance where
Variance (X+Y) = varX + varY - (2)(Cov X, Y)

2) On Pg 123, it has been mentioned that margin does not represent cost to investor,
bcoz interest is paid on margin account ? Is interest really available on margin deposits ??

To what do these page number refer, is this not Hull 6th Edition?
Yes, margin accounts pay/accrue interest, typically. I don't know the context but probably means a margin account is not a real opportunity cost. Difference between depositing $100 and getting back only $100 in the future (that's erosion, an direct loss of opportunity cost) versus $100 plus interest. If $100 + interest, i've been compensated for opportunity cost.

3) On Pg 25 of your notes, it is mentioned tht normal backwardation is wen the fut price >
Expected Futures Spot Price ???.....Is this a typo ?

Yes, i see that, you are right, the last note is typo. Graphics/above are correct. I'll fix

4) While computing conversion factor, we have to reduce the accrued interest....
but why not the present value of accrued interest, since the same will be realized only
at the end of the period.....

5) For computing conversion factor, it is mentioned tht maturity is rounded down to the
nearest 3 months - so it presumably means tht it is rounded down to multiples of 3 months - right ?

You might want to look at the member XLS called "2008 FRM: Hull (derivatives): cheapest to deliver (CTD)"
I detailed the CF calculation here.

* Everything does get discounted to PV. I see your point, but i think the XLS will clarify: when the rounding falls on 3/9 months, the PV() calculation is done + 3 months, THEN discounted back 3 months. By the end, everything has been PV'd

* Yes, you will see this also in my replicated XLS; i.e., rounded to nearest 3 months. Then use one of two rules.


6) For floating part in a swap, the rate is determined at the beginning of the period and the
payment is done at the end of the period...but this doesnt get reflected in the examples given
in the study notes....we have considered the cash flows at time 0.25, 0.75 and 1.25 and accordingly
applied the discounting factors ?

Yes, true this: "the rate is determined at the beginning of the period and the
payment is done at the end of the period" - This gives the future value (FV) column

Then PV column is discounting those cash flows back. So, yes, discounting is done.


7) Can the upper bound of european put shud be considered as Strike Price or
“Present value of strike price” since the same will be exercised only on
expiry dates

Yes, agreed, my upper bound should be p <= discounted [Strike]. Nice catch.

Thanks, David