Sir, when we are calculating the gain/loss on futures why are we dividing the difference of the futures prices by 400? and how did the figure 400 come to be?

We divide by 100 because the futures prices are equivalent fo %’s, and we divide by 4 because they are always 3 month futures and there are four 3 months periods in a year (so we are effectively applying one quarters interest).

Thanks for the great lecture. I have a question regarding the relationship between the interest rate and the price. For example, an interest rate of 6% is equivalent to a price of 94. What is the logic behind this relationship?

It is simply that in order to make the trading of futures simple (and for it to be the same sort of way people deal in shares i.e. buying at one price and selling at another price), they price the futures at 100 less the equivalent interest rate. So as you write, a futures price of 94 is equivalent to an interest rate of 6% (100 – 94).

Thanks for the reply. I have one follow-up question. Seems the future price tries to simulate the way stock prices work but they are not the same. For example, if a stock price rises from 90 to 92, then the gain should be calculated as (92 – 90)/90 = 2.22%. However, in case of future prices, the gain will be 2%.

It sounds like the futures price is just a scale from 0 – 100 so that people can easily tell whether the futures contract is rising or falling. Am I correct?

It is correct, but is not really of any relevance. In a perfect world (i.e. ignoring basis risk) the gain or loss will match the loss or gain on the underlying transaction, and that is the purpose of using futures as far as the financial manager is concerned.

Also sir I do not understand how come there existed 0.33% difference? I mean even if we take 0.5×1/3= .1666666(i know you told us off for rounding beyond 2 decimal places, but just for a moment, pardon me sir), which would give us a receivable of $533,333. calculating effective interest rate we still get 7.33335%. Which apparently means it has got nothing to do with rounding off. So then why exactly is this difference arising? Is it merely due to the existence of a non-zero basis amount, to say the least?

P.S.- I know you briefly mention something in the end regarding this, but it is not very clear to me.

Hi John, can I just say I love your lectures they explain everything so well! One thing that strikes me is that when dealing with the futures we will be receiving these monies when we close the contract which is at the start of the loan and therefore have the receipt sat in our bank account before loan interest is due in 6 months time, theoretically wouldn’t this be invested/used to pay off overdraft for example up until the date that the monies would be due and therefore an additional saving on interest/receipt from deposit can be achieved? why would we not factor this in? or have I missed something?

Sir but as far as equity futures are concerned the seller of futures(fresh position) is not allowed to use the receipts from short sell for own use, until he squares off his position. No doubt his position becomes positive and the amount rests in the broker’s accounts. But this makes sense because sometimes a trader’s position goes grossly wrong and hence to maintain the M2M margins etc. its always reagrded a safe tactic by broker to just let a trader’s gain accumulate to be used for rainy days.

So I do not understand why the core principle here is tweaked in case of interest-rate futures? How can short-sellers be allowed to withdraw the sums? What happens if their predictions goes for a toss? No increased margin requirements?

Your response would be very much appreciated sir! As always thanks for making such amazing and lucid lectures!

As far as interest rate futures (and exchange rate futures) are concerned, nobody is withdrawing anything. As I do explain in the lectures, using them is effectively gambling and you are not really buying or selling anything. You must have a ‘buy’ and a ‘sell’ (in either order depending on the nature of the underlying transaction) and at the end of the deal you receive any gain or suffer any loss (together with a refund of the deposit/margin that had been paid.

Hi Sir, when we calculating the futures price for 1 Jan, the futures price on 1 JAN will be lower than the Interest rate (94.00) on 1 JAN because of the futures price on 1 NOV is lower than the interest rate (91.00) on 1 NOV.

Is it this theory applicable to the currency futures as well? i am not sure when to deduct or when to add the unexpired basis risk.

Yes, it is applicable to currency futures. The spot rate and the futures price always move closer together over time, but whichever is higher ‘now’ will always be higher.

Hi John, For my understanding please, are the rates under a futures the actual rate we would be locking in to borrow at, or are they just locking in a future base rate (on top of which the bank would add our risk spread, here 1%)? I realise we are only using futures here to hedge the risk and not to actually borrow at the futures specified rate, but I’m curious if I understand.So if we wished to use the January futures and take out a loan at the end of January, would the 6.5% (Price 93.5) be the total interest rate or would it only replace LIBOR as the base rate, with a further risk-spread added by the bank (here, 1%). Many thanks.

If the loan were to be taken on the closing date for the futures (in your example, January) then the 6.5% would replace LIBOR and the actual interest payable would be higher due to the credit risk applicable to the company.

Hello John. Since the loan is to start in 2 months, 1 Nov – 1 Jan. shouldn’t the interest be calculated for two months on the future? so rather than dividing by 400, shouldn’t it be (93.5-90.83)/100*2/12?

so in order to hedge it more accurately, i tried with 120m (40*6/2) as future contract size since it is only for 2 months and we should be getting the equivalent amount of interest within 2 months. but still, i got the same answer as you did, effective interest as 7.33%.

so i know your final answer still correct, but shouldn’t we taking future contract size 120m rather than 80m?

Interest is calculated for the period of the loan. There is no interest between now and the date the loan starts because you are not owing anything during that period!!

Can you advice: You have used the price of the futures as at January (93.5) to find the basis point on Nov 1st. If the Futures date was March, would you have used 93.35 against 94 to calculate the basis?

sindi2012 says

Hi John

Example 4

May you please explain the reason why the effective interest of 7.33% was more than the 7%

John Moffat says

Because the futures price changes by 2.67 whereas the interest rate changes by 3. The difference is 0.33.

hhashmi says

Sir, when we are calculating the gain/loss on futures why are we dividing the difference of the futures prices by 400? and how did the figure 400 come to be?

John Moffat says

I do explain this in my lectures!!

We divide by 100 because the futures prices are equivalent fo %’s, and we divide by 4 because they are always 3 month futures and there are four 3 months periods in a year (so we are effectively applying one quarters interest).

sopingyuen says

Hello John,

Thanks for the great lecture. I have a question regarding the relationship between the interest rate and the price. For example, an interest rate of 6% is equivalent to a price of 94. What is the logic behind this relationship?

John Moffat says

It is simply that in order to make the trading of futures simple (and for it to be the same sort of way people deal in shares i.e. buying at one price and selling at another price), they price the futures at 100 less the equivalent interest rate. So as you write, a futures price of 94 is equivalent to an interest rate of 6% (100 – 94).

sopingyuen says

Thanks for the reply. I have one follow-up question. Seems the future price tries to simulate the way stock prices work but they are not the same. For example, if a stock price rises from 90 to 92, then the gain should be calculated as (92 – 90)/90 = 2.22%. However, in case of future prices, the gain will be 2%.

It sounds like the futures price is just a scale from 0 – 100 so that people can easily tell whether the futures contract is rising or falling. Am I correct?

John Moffat says

It is correct, but is not really of any relevance. In a perfect world (i.e. ignoring basis risk) the gain or loss will match the loss or gain on the underlying transaction, and that is the purpose of using futures as far as the financial manager is concerned.

Noah098 says

Also sir I do not understand how come there existed 0.33% difference? I mean even if we take 0.5×1/3= .1666666(i know you told us off for rounding beyond 2 decimal places, but just for a moment, pardon me sir), which would give us a receivable of $533,333. calculating effective interest rate we still get 7.33335%. Which apparently means it has got nothing to do with rounding off. So then why exactly is this difference arising? Is it merely due to the existence of a non-zero basis amount, to say the least?

P.S.- I know you briefly mention something in the end regarding this, but it is not very clear to me.

Many thanks!

cbassett says

Hi John, can I just say I love your lectures they explain everything so well! One thing that strikes me is that when dealing with the futures we will be receiving these monies when we close the contract which is at the start of the loan and therefore have the receipt sat in our bank account before loan interest is due in 6 months time, theoretically wouldn’t this be invested/used to pay off overdraft for example up until the date that the monies would be due and therefore an additional saving on interest/receipt from deposit can be achieved? why would we not factor this in? or have I missed something?

John Moffat says

You are right in that there is a timing element here, but we ignore it for the exam 馃檪

Noah098 says

Sir but as far as equity futures are concerned the seller of futures(fresh position) is not allowed to use the receipts from short sell for own use, until he squares off his position. No doubt his position becomes positive and the amount rests in the broker’s accounts. But this makes sense because sometimes a trader’s position goes grossly wrong and hence to maintain the M2M margins etc. its always reagrded a safe tactic by broker to just let a trader’s gain accumulate to be used for rainy days.

So I do not understand why the core principle here is tweaked in case of interest-rate futures? How can short-sellers be allowed to withdraw the sums? What happens if their predictions goes for a toss? No increased margin requirements?

Your response would be very much appreciated sir!

As always thanks for making such amazing and lucid lectures!

John Moffat says

Equity futures are not in the syllabus.

As far as interest rate futures (and exchange rate futures) are concerned, nobody is withdrawing anything. As I do explain in the lectures, using them is effectively gambling and you are not really buying or selling anything. You must have a ‘buy’ and a ‘sell’ (in either order depending on the nature of the underlying transaction) and at the end of the deal you receive any gain or suffer any loss (together with a refund of the deposit/margin that had been paid.

belindalau says

Hi Sir, when we calculating the futures price for 1 Jan, the futures price on 1 JAN will be lower than the Interest rate (94.00) on 1 JAN because of the futures price on 1 NOV is lower than the interest rate (91.00) on 1 NOV.

Is it this theory applicable to the currency futures as well? i am not sure when to deduct or when to add the unexpired basis risk.

Thank you.

John Moffat says

Yes, it is applicable to currency futures. The spot rate and the futures price always move closer together over time, but whichever is higher ‘now’ will always be higher.

belindalau says

thank you,sir.

John Moffat says

You are welcome 馃檪

Cathal says

Hi John,

For my understanding please, are the rates under a futures the actual rate we would be locking in to borrow at, or are they just locking in a future base rate (on top of which the bank would add our risk spread, here 1%)? I realise we are only using futures here to hedge the risk and not to actually borrow at the futures specified rate, but I’m curious if I understand.So if we wished to use the January futures and take out a loan at the end of January, would the 6.5% (Price 93.5) be the total interest rate or would it only replace LIBOR as the base rate, with a further risk-spread added by the bank (here, 1%). Many thanks.

John Moffat says

If the loan were to be taken on the closing date for the futures (in your example, January) then the 6.5% would replace LIBOR and the actual interest payable would be higher due to the credit risk applicable to the company.

Cathal says

Brilliant John. Helps me understand the basis calculation here better i.e. LIBOR/spot rate vs future’s rate. Thanks a mil.

ashrf16 says

Hello John.

Since the loan is to start in 2 months, 1 Nov – 1 Jan. shouldn’t the interest be calculated for two months on the future? so rather than dividing by 400, shouldn’t it be (93.5-90.83)/100*2/12?

so in order to hedge it more accurately, i tried with 120m (40*6/2) as future contract size since it is only for 2 months and we should be getting the equivalent amount of interest within 2 months. but still, i got the same answer as you did, effective interest as 7.33%.

so i know your final answer still correct, but shouldn’t we taking future contract size 120m rather than 80m?

John Moffat says

Interest is calculated for the period of the loan. There is no interest between now and the date the loan starts because you are not owing anything during that period!!

claudia1 says

Hello John,

Is there a premium charged on futures?

John Moffat says

No – no premium 馃檪

hadehola says

Hello John.

Can you advice: You have used the price of the futures as at January (93.5) to find the basis point on Nov 1st. If the Futures date was March, would you have used 93.35 against 94 to calculate the basis?

John Moffat says

93.50 is the price of January futures as at 1 November (not as at January!)

If March futures had been used then we would have taken 93.35 against 94.