*
This is the second part of this paper. The first part was published in July 2005 issue of Bimaquest.
The rights and obligations of the buyer and seller in an options contract are not symmetrical, the buyer has the right, the seller has the obligation. By the very nature of the contract the buyer’s liability is limited to the premium but the seller has in principle an unlimited liability. Accordingly, the accounting treatment must differ for the buyer and the seller so as to reflect this non-symmetry.
Obviously, the bought option is an acquired asset because it has a potential to earn. Since options are usually short-term, the asset may be recognized as a current asset. In the case of the seller who carries the obligation, the treatment needs to be reasoned out more carefully. It is clear of course that the seller contracts an explicit liability at the strike price; in the case of a call option he is obliged to deliver money to purchase the U/L at this strike price and in case of a put option he is obliged to make a payment equal to the strike price. Accordingly, he must show a liability equal to the strike price. Of course since he is also entitled to receive value equivalents, money or the U/L, he must also record an asset of equal value.
The difficult part is the treatment of the option premium. Now anybody who sells an option expects the option premium he quotes to cover the losses in the event of exercise.
Then again there are option sellers who have positions in the U/L and are using these positions to earn additional income. These day-to-day facts suggest that the motivation for selling options is to earn revenue so that at the time of entry into the contract the option premiums received should be shown as revenue. This may be codified in a principle.
•
Professor & Faculty Associate, National Insurance Academy, Pune – 45, India.
•
E-mail: rajasparchure@niapune.com , uma@niapune.com.
Bimaquest - Vol. VI Issue I, January 2006 43

Derivaties Accounting – A New Option for the Future
Principle 1 : At the time of entry into an options contract the buyer will book the option premium paid as current asset. But the seller will credit the premium received in the P &
L Account.
But there is a qualification. Time is always against the holder of options. Therefore, when books are closed on the balance sheet date some portion of the option value would have been irretrievably decayed against the buyer and in favour of the seller so that only the unexpired portions of the contracted option premium can represent the residual values of the assets and liabilities. In effect the buyer should debit and the seller should credit the expired portion of the option premium to the P & L A/c. As for the unexpired portion the buyer will show it as an asset. However for the seller the unexpired portion will be shown only as a liability, the corresponding entry on the asset side being in the form of such assets as represent the investments of premiums received.
The next problem is to find a robust method for estimating the expired and unexpired portions of the option premium. Two methods suggest themselves. Allusion has been made to the time value decay of options. This can serve as one method. Another less elaborate method is the linear approximation method.
(i) Time Value Method
Under this method the expired portion is equal to the decline in the time value of the option from the contract date to the accounting date. This is easy to find for exchange traded options. But in case of OTC options only time value at the inception of the contract is known. In principle it would be possible to obtain an OTC quote for the same option on the accounting date and estimate the time value on that date as well. But, besides putting a burden on the accountant, it may be open to question and/or it may give scope for ambiguities. Therefore, for OTC options the time value decay may be estimated by a linear approximation method, i.e. with reference to the lapsed maturity in relation to the option maturity. For example a 3 month OTC option was transacted on 1 st
February, 2003 for a price of 30. Its time value was 20. When closing books on 31 st
March it may be supposed that 2/3 rd
of the time value has decayed and 1/3 rd
remains unexpired. Then
13.33 will be debited or credited by the buyer or seller to the P&L A/c respectively and
6.67 will be shown as current asset and liability respectively for the buyer and seller. For exchange traded options the expired value is simply the time value at contract date less the time value on accounting date and the unexpired portion will be the contracted option premium less the expired portion.
The other alternative is to use the linear approximation for the entire option premium. For example a 6 month option contract transacted on 1 st
March may be said to have lost 1/6 th
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Derivaties Accounting – A New Option for the Future of its value on the balance sheet date of 31 st
March. If it was bought / sold for 25 then the expired value would be 4.16 and the unexpired portion would be 20.84. The former would be debited / credited to the P&L A/c and the latter would be shown current asset and liability respectively for the buyer and seller.
The choice of method will be governed by two considerations – the nature of business of the entity and convenience of accounting. If the entity’s business entails transacting a large number of options contracts the linear method is recommended because of its convenience. If transactions in options are few and far between the more elaborate and accurate time value method is recommended.
In what follows we shall illustrate the application of the linear method which it may be pointed out, gives almost the same results as the time value method when the entity transacts a large number of in-the-money, at-the-money and out-of-the money contracts which will result in a linearisation of the otherwise non-linear decay of time value over the life of options.
Principle 2 : Expired option value must be calculated by the time value method or by the linear method. Although the time value method is recommended, entities having numerous options transactions may follow the linear method. In the case of OTC options only the linear method is feasible.
Before proceeding to give illustrations we need to dispose two matters. First, the realized gains and losses in respect of contracts that have been reversed / settled during the accounting period. We follow the principle stated in futures accounting.
Principle 3 – All realized capital gains or losses on delivery or reversal of transactions in options will be shown in the profit and loss account.
Second in respect of unrealized gains or losses. Here too as in the case of forwards and in keeping with the principle of conservatism the net losses should be provided for and net gains only disclosed. Now in case of the buyer the losses to be provided for will be equal to the excess of the strike price over the closing stock price on the balance sheet date subject to a maximum of the unexpired premium. In case of the seller the provision will be equal to the excess of closing stock price over the strike price and has of course no limit.
Principle 4 : Provision will be made for net losses with reference to U/L price but gains will only be disclosed .
To illustrate consider an example of a naked 6 month call option contract at strike of 110 at a premium of 30. Suppose the balance sheet date falls after 1 month and both buyer and
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Derivaties Accounting – A New Option for the Future seller have an open position on that date. Suppose also that price of the U/L on the balance sheet date is 105 so that the call option is out of the money and the option is quoted at 10. The P&L A/c and Balance sheet of the buyer will be as follows :
Call Option Premium
(Expired)
Provision for Loss on call
Option
20 P & L Account Balance
5
25
Liabilities Amount
Equity
Provision for Loss on call option bought
30
5
Assets
Call Option Premium 30
Amount
(-) Expired Premium 20 10
35 35
If we mark the above balance sheet to market there will be no difference in entries as provision has been made for the losses.
In the case of the seller in order to bring out the provisioning method clearly, suppose that the U/L price on the balance sheet date is 120 so that the call option is in the money and the option price is 35. The seller’s financial statements would be as follows;
Particulars Amount Particulars Amount
Unexpired Premium 10 Premium on option sold 30
Variation Margin (110
– 120)
10
P & L Account Balance 10
30 30
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Derivaties Accounting – A New Option for the Future
Liability on Sold option
Unexpired Premium
Variation Margin
P & L A/c Balance
110
10
10
10
Call Option sold
Bank / Investment
140
110
30
140
Observe the difference between the balance sheets of the seller vis-à-vis the buyer. It shows much greater leverage and risk because of the presence of the obligation under the option contract.
Principle 5 : Mark to Market Reserve will be made for gains with reference to U/L price and option price .
If the above balance sheet were to be marked to market, it will be as follows:
Liabilities Amount Assets Amount
Liability on Sold option
Unexpired Premium
MTM reserve on option
(120- 110)
110
10
Call Option sold
Bank / Investment
10
Provision for loss on option sold
10
P & L A/c Balance 10
150
120
30
150
Consider now the case of an agent who owns the U/L and sells say a call option on it; to illustrate, he owns a stock bought at 70 and sells a 6 month call at a strike of 110 at a premium of 30. The principle of the net open position will now come into operation.
Principle 6 : The value of the net open position in the U/L must be shown on the face of the balance sheet.
The agent in our example has a net open position of zero. For the sake of simplicity suppose the call option is sold on the balance sheet date. Then the balance sheet would be
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Derivaties Accounting – A New Option for the Future
Liabilities Amount Assets Amount
Equity 70 70
Unexpired premium
Liability on call
Option sold
30
40
Bank (Premium)
Call Option sold (Net Open
Position)
30
40
140 140
Observe that the value of the net open position (which is zero) is 40, it being the difference between the price locked in for delivery and the purchase price. Observe that the balance sheet shows no leverage.
A similar position will be observed in the case of an agent who owns the stock and buys a
6 month put option at a strike price of 70, equal to his holding price. Once again the net open position is zero and so is its value.
Liabilities Amount Assets
Put Option premium
100
Amount
70
30
100
The above statements shown at historical cost do not fully reveal the dynamics of the transaction though they do show absence of leverage and risk. The dynamics of price changes are revealed if the U/L and the option are marked to market. Thus suppose the covered call seller closes his books when the market price of the stock is 130 and the option price is 50. The MTM balance sheet will be
Liabilities Amount Assets Amount
MTM Reserve
Investment 60
Call Option 20
Loss on call option
Unexpired premium
80
20
30
Call options
P & L A/c Balance
Bank (premium received)
230
50
20
30
230
There is no diminution in net worth or increase in provision because the transaction is a hedge – the loss on the sold call is offset by gains on the U/L and in turn the increase in the value of call option sold.
In the case of the protective put buyer suppose the closing price is 50 then the MTM balance sheet will be :
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Derivaties Accounting – A New Option for the Future
Liabilities Amount Assets
Equity 70 Investment 70
Less : Provision for
Unexpired premium
Provision for loss on option
30
20
diminution in value 20
Put Options Premium
P & L A/c
120
Amount
50
30
40
120
Of course we may also mark to market the option positions where secondary market quotes are available. The effect will be identical.
Having tested shallow waters let us venture further. Suppose an agent buys a 90 strike call for 40 and sell a 110 strike call for 30 both of 3 months’ maturity. This is called buying a bullish call spread in the language of the trader. Suppose for simplicity that the spread is struck on the balance sheet date. The net open position is zero and its value is
10, the difference in the option premiums. His balance sheet would be
Equity
Liabilities Amount Assets Amount
10 Spread premium 10
10 10
If he does the reverse viz. he sells the 90 strike call and buys the 110 strike call the treatment is not so simple. He now has a bearish call spread for which he receives the option price spread which he must keep in reserve and invest. But this will not suffice because even though his net open position is zero he is exposed to risk equal to the difference in strike prices viz. 20 which is not covered and must be recognized as a liability; he has agreed to deliver the U/L at 90 and take delivery at a higher price of 110.
If the closing U/L price stands below 90 his balance sheet would be
Unexpired spread Premium
Liability on call Spread
10
20
Bank
Call Spread
30
10
20
30
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Derivaties Accounting – A New Option for the Future
If however the U/L’s price on the balance sheet date stands at 100 there is an unrealized loss of 10 which must be provided for and which will reduce the net liability on the spread to 10. The balance sheet will be
Liabilities Amount Assets Amount
Unexpired spread Premium
Provision for Loss
10
10
Bank
P&L A/c
Liability on Spread 10 Call Spread
30
10
10
10
30
We may state this as a principle.
Principle 7 : Whenever there are sold calls at lower strikes than bought calls and/or there are sold puts at higher strikes than bought puts the difference in strike prices must be recognized as liability (and an equivalent asset) to the extent they are not provided for.
Consider next the treatment for straddles. A trader buys both a call and a put option at strike of 100 at 10 and 30 each with expiry of 3 months. Assuming once again for convenience that the position is taken on the balance sheet date, his balance sheet would be :
Unexpired Option Premium 40 Bank 40
Note that the buyer of the straddle would never have to make a provision for unrealized losses since he can only gain; the seller of the same straddle would of course recognize two liabilities, to make delivery of the U/L at 100 and to take delivery at 100, i.e. a liability of 200. Also he must make provisions, if the ruling price is greater than 100 there is an unrealized loss on the sold call and if the ruling price is lesser than 100 there is an unrealised loss on the sold put. The provision will of course be duly reduced from the liability according to principle 7. Thus, suppose the U/L’s price stands at 80 and there is an unrealized loss of 20 on the sold put. The balance sheet would be
Liabilities Amount Assets
Unexpired Premium
Provision for Loss on
Put option
Liability on Straddle
40
20
80
Bank
P & L A/c
Receivable from
Straddle
140
40
20
80
140
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Derivaties Accounting – A New Option for the Future
Observe that the balance sheet of the straddle seller shows high leverage, a “debt : equity” ratio of 100 : 40 but the buyer’s book shows nil leverage. The same observation holds for the seller of the spread in the earlier example in relation to the buyer of the spread.
The foregoing discussion has prepared the ground for a generalization to a situation where a trader has several open positions in calls and puts of various maturities at various strikes. Calculations will now be more detailed for four reasons :
(i) The unexpired portions of the option premiums will have to be calculated by linear interpolation from the contract date to the balance sheet date with reference to the expiry date.
(ii) The average price of the bought or sold positions in the option contracts corresponding to each strike and each expiry date will have to be calculated.
(iii) The liability due to selling calls at strikes lower than buying calls and vice versa for put options would have to be recognized.
(iv) Provisions for unrealized loses on the net open position at the ruling price of the U/L must be calculated.
Consider an example with multiple call options. Suppose that the net outstanding positions (i.e. after netting bought and sold call options at each strike and each expiry date and taking realized gains / losses to the revenue account) are as follows. Suppose also that we are closing books on December 31, 2003.
Expiration Day
Strike
15/1/04
15/ 2/04
15/3/04
90 100 110
+5 (30)
-10 (40)
-6 (50)
-6 (23)
+5 (32)
+8 (45)
+8 (18)
-4 (25)
-2 (36)
+ 7
- 9
0
Of course each of the 9 outstanding positions in the table will have its own “history”.
Suppose the January 2004 90-strike calls have the following history.
No. Contracted Date Contracted Price
+2 1/12/03 30
+2 11/12/03 32
+1 21/12/03 26
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Derivaties Accounting – A New Option for the Future
Then the average price for the position +5, January 2004, 90-strike calls will be :
30 * 2
+
32
5
* 92
+
26 * 1
=
30
This is the figure shown in brackets next to the position. A similar calculation should be made for all the other positions. To keep things simple however let us suppose that all the remaining positions were taken on the same day, 15 December 2003 at the average prices shown in brackets.
The option premium on the net position of 2 sold calls (read directly from the extreme southeast corner of the table above) is arrived at by adding across the 9 positions,
(30 x 5) + (8 x 8) + …. (-2) (36) = -196 showing that a net premium of 196 is received.
This must be split into the expired and unexpired portions to be respectively considered in P&L A/c and shown as liability on the balance sheet. To find this is the next step.
Each of the 9 positions in the table will have its own “history”. For the January 15, 2004
90-strike call as on 31 December, 2003 this history will be as follows :
Contracted Date Expired Period
Till Balance Sheet
1/12/03
Date
30
11/12/03
21/12/03
20
10
45
35
25
15/45 x 30 = 10
15/35 x 32 = 13.71
15/25 x 26 = 15.60
And since there are +2, +2 and +1 contract numbers the unexpired option value will be
(10 x 2) + (13.71 x 2) + (15.60 x 1) = 63.02
The expired value will of course be 150 – 63.02 = 86.98. The unexpired option premium for all the positions will be as follows :
The sum of all these is the unexpired option premium for the net open position. It is –
109.98 and the expired portion is –86.02. Thus 86.02 will be credited to revenue account and 109.98 will be shown as unexpired option premium liability.
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Derivaties Accounting – A New Option for the Future
Now the difficult part – the determination of liability in terms of delivery of the U/L
1
. The principle that is a natural analog of that applied in the case of futures and principles of prudence &consistency may be stated.
Principle 8 : The liability under a net open sold position in a series of option contracts of one type, either call or put, on an U/L will be the sum of :
(i) Liability of the net sold position at the weighted average strikes at which there are net sold contracts (See Note 3). In our example all the sold contracts are at 90 strike so that liability to be shown on the balance sheet will be 90 x
2 = 180. In general the formula is :
( X ) ( NOP )
=
⎛
⎜⎜
Σ
X i
Σ
N
N i i
⎞
⎟⎟ ( NOP ) where N i
denotes sold contracts at strike X i
.
(ii) Liability due to the difference between the strike prices of sold options and the strike prices of bought options in the cases in which the latter exceeds the former.
In our example there are two such cases. Firstly there are 7 sold options at strike of 90 corresponding to 7 bought at 100 and secondly there are another
2 sold at 90 corresponding to 2 bought at 110. The liability due to them will be
(100 – 90) x 7 + (110 – 90) x 2 = 110
This figure will be added to 180 which is liability due to 2 sold calls to give
290. Note that step (ii) will apply even when the net open position is long.
The last step concerns provisioning for unrealized losses. Suppose the stock price stands at 105 on the balance sheet date. The 11 short positions at 90strike will each shown an unrealized loss of 15 giving a total of 165. But the
7 long positions at 100-strike will show unrealized gain of 5 each, i.e. 35.
Now since the prices of a series of call options on a U/L move in the same direction it is the net unealised loss that must be considered, i.e., 130.
Accordingly, 130 will be provided for in the P&L A/c and the provision shown in the balance sheet. The effect of this would however be to recognize a net liability of 290-130 = 160 in the U/L.
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Derivaties Accounting – A New Option for the Future
An identical procedure applies to transactions in a series of put options on an
U/L excepting for one difference, viz. that the liability on the net open position in put options will be topped up in all cases where the strikes of sold puts are greater than the strikes of bought puts.
When there are net open positions in calls as well as puts these too must be combined to find the net open position in the U/L. Four possibilities can arise which are shown below :
Calls Puts
(1) - +
Net Open (2) + -
Position (3) + +
(4) - -
The option premium on the overall position would of course be the sum total of the option premiums paid and received at the average option price at each strike and each expiry date, i.e.,
Σ
C it
N ict
+
P it
N ipt
N i
> 0 for bought
N i
< 0 for sold
And C and it
P are the average call and put option prices. The split of this into the it expired portion and the unexpired portions will be made in the same manner as has been illustrated above with reference to a series of call options.
To recognize the liability in the U/L the net open positions will be combined depending upon the pattern of signs shown above. For example, if both NOP’s show bought positions, say +2 and +5 then there is no liability on the U/L. If both positions show sold positions, say –5 and –3, then the liability on the U/L will be 5 X c
+
3 X p
where X c and X are the weighted average strike prices of sold calls and sold puts respectively. p
If the NOP’s in calls and puts are of opposite sign, e.g. –5 and +3, then 3 sold calls are matched to 3 bought puts and 2 sold calls remain. The matched position will be considered as 3 short futures (the obligations of selling calls get combined with the rights
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Derivaties Accounting – A New Option for the Future and puts, X
+ c
X p
)
/ 2 which gives a liability of
3
(
X
+ c
X p
)
2
To this must be added the liability due to 2 sold calls at X to give c
L
=
3
(
X c
+
X p
)
+
2 X c
2
As before the net liability recognized will depend on the stock price ruling on the balance sheet date and the provisions for net losses that it leads to.
In practice yet another round of matching and netting will be required if there is a net open position in the futures on the U/L as well. For example suppose the net open positions are –5, -3 and +4 in calls, puts and futures on the same U/L. The matching of –5 and –3 gives 3 short futures at a price
(
X c
+
X p
/
)
2 . This offsets 3 out of the 4 long futures at average price F with the shortfall if any of the price of bought futures below the price of shorted futures bearing provided, viz.
3
(
X c
+
X p
−
F
)
2 otherwise a disclosure for unrealized gains. There remain 2 short calls and 1 long futures.
Clearly 1 position can be offset and liability recognized only if there is a shortfall of the average futures price below the average strike of the sold call,
( X c
−
F )( 1 ) otherwise zero. Finally there remains 1 short call at average strike X whose implied c liability is X . The sum of provisions and liability will be, c
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Derivaties Accounting – A New Option for the Future
X c
+ max( 0 , X c
−
F )
+ max( 0 , 3
⎛
X
+ c
2
X p −
F
This net open position in derivatives taken as a whole must finally be combined with position in the spot to evaluate the grand net position in the U/L.
The accounting method proposed for derivatives on an U/L generalizes very comfortably to derivatives on derivatives as well , i.e., contracts such as options on futures and options on options. It will suffice to give only one example.
Consider the case of options on futures. The buyer will show the unexpired portion of the option premium as asset, making the necessary provisions and booking all realized profits and losses during the accounting period. The seller will do all of the above and in addition recognize the liability on the U/L, which is now a futures contract at the relevant striking price. There will be only one difference - if the contract goes to delivery the buyer will expense the option premium, the seller will take credit for the revenue and both will have an open position, bought and sold respectively, in the futures contract which will be shown as liability by the seller and asset by the buyer after making provisions for unrealized losses depending upon the market price of the futures contract that rules on the accounting date.
Of course when calculating the values of the net open position account must be taken of the position in the U/L as well as the U/L of the U/L.
Positions in index derivatives, whether futures or options, pose some special problems.
Index derivatives like all other derivatives may be used to speculate, hedge or arbitrage but unlike other derivatives considered so far their U/L is a generalised index, not a specific asset. Thus in a situation where an index fund manager uses index derivatives there is no problem whatsoever for accounting, everything said so far applies exactly and without modification.
There is no problem in the other kind of situation as well i.e. where the agent has no position, short or long, in any of the stocks that constitute the index. The problem lies in the intermediate case where the agent has a position in some of the stocks constituting the index and others which do not constitute the index. But even here there is no problem in
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Derivaties Accounting – A New Option for the Future those cases in which there are no short positions in stocks and there is a long position in the index futures or index calls. So the problem really arises in 2 cases.
(i) Where some of the stocks constituting the index are held and index futures and index calls are shorted or index puts purchased.
(ii) Where there are some short and long positions, partly in stocks constituting the index and partly not, and there are long or short positions in index derivatives.
What if any is the net open position in these circumstances and how is it to be valued? To begin with it is generally true that stocks tend to move up and down together, those in the indexes and those outside. More generally indexes tend to move up and down together and worldwide experience shows that it to be so. It is for this reason that fund managers hedge their positions in individual stocks or portfolios by opposite positions on index derivatives when they are trading on the “specific risks” of those stocks. In fact in these cases they do not want to short individual stock futures for example because that would be self defeating. That being so there is no harm in regarding long stocks and short index futures (or short index calls or long index puts) as reducing the net open position of the fund manager. Thus the value of the net open position will in this case be simply the value of stocks held minus the value of index futures / calls shorted or index puts purchased. There would not of course be any meaning to the net physical open position.
To be sure there is bound to be a basis risk viz. the risk that all stocks would not move exactly with the index but this would show itself in the net capital gains and losses on the positions. And these capital gains and losses must necessarily be considered to be shortterm unless the positions have been held for period longer than one year.
When there are some short and long positions in stocks and long or short positions in the index derivatives however the positions will have to be matched in the following way to calculate the value of the net open position;
1. Long positions in stocks (+) with short index futures plus short index calls
2. plus long index puts (-).
Short positions in stocks with long index futures plus long index calls plus
3. short index puts (-).
The sum of the two above, given the sign conventions + for bought and – for sold, which will be the effective net positions when signs differ and the sum when signs are the same.
This of course raises the question about the treatment to be accorded to the presence of individual stock options as well. But that’s no problem provided we consider only the net long and short positions in individual stocks in steps (1) and (2).
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Derivaties Accounting – A New Option for the Future
Swaps, eg. fixed rate for floating rate or vice versa involve exchanges of interest coupons on an U/L notional amount. Implied in every swap deal is a deal in derivatives as is revealed by the equation of value for swaps,
Fixed Rate A/L = Floating Rate A/L + Long Interest Rate Put – Short Interest Rate Call i.e. a holder of a fixed rate asset / liability buys an interest rate put option (quoted for the sake of exposition in interest rate terms instead of the usual asset price terms) and sells an interest rate call at a striking interest rate equal to the fixed rate. In other words he shorts an interest rate futures contract implicitly.
Thus an agent who swaps a fixed rate liability for a floating rate liability without owning a floating rate asset is buying (back) an interest rate futures contract. Now in a swap typically the exchange of interest coupons is made with interest calculated on the notional amount. The value of the net open position will not however be the notional amount, which only serves as the base for the calculation, but the present value of the difference between the interest coupons that are swapped. And this is equal to, n t
Σ
=
1
( FixedRate
−
FloatingRa te
( 1
+
Fixed
( Notional
Rate ) t
Amount ) where n is the maturity of the swap arrangements and t denotes the time periods at which the interest rate on the floating rate instruments is reset and | | denotes absolute value.
(Needless to say that in the above calculation the fixed rate floating rate pertains to the reset period). Obviously the value of the swap which, because it contains a position in the interest rate futures, must be shown both as a liability and an asset on the balance sheet. If the maturity of the swap arrangements exceeds the accounting period this value must of course be periodically amortised.
Consider an example. Suppose there is a manufacturing corporate that has Rs.1000 worth of real assets supported by Rs.1000 worth of fixed rate loans at 9% p.a. It can swap this for a floating rate liability at B + 2% where B is the benchmark rate which is currently
6%. Suppose net return on fixed assets is 15%. Also suppose the reset period for the floating rate loan is 1 year and the corporate considers a 2 year swap. The value of the swap will be :
17 .
59
=
( 9 %
−
8 %) ( 1000 )
( 100 ) ( 1 .
09 )
+
( 9 %
−
8 %) ( 1000 )
( 100 ) ( 1 .
09 )
2
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Derivaties Accounting – A New Option for the Future
The balance sheet will at the start of the year when the swap also is assumed to commence will be
Liabilities Amount Assets
(Floating) Loan
Swap Liability
1000
17.59
Assets
Value of Net Open Position
1017.59
Amount
1000
17.59
1017.59
For the simplicity suppose that B does not change over the two years then the P&L A/c extract for year 1 will be
Particulars Amount Particulars Amount
Amortisation of Swap 8.42
Profit 70
8.42
158.42 158.42
The amortisation charge of 8.42 is arrived at by subtracting from the annuity represented by difference in rates of interest the first year’s interest on the present value of the swap.
Note that this implies the use of the annuity method of depreciation . In subsequent years the depreciation / amortisation charge will simply rise by a factor of 1.09 for each year.
The balance sheet at year 2 will be.
Liabilities Amount Assets Amount
(Floating) Loan 1000 Assets 1000
Liability on Swap 17.59
(-) Amortisation 8.42 9.17
Value of Swap
Position 17.59 9.17
(-) Amortisation 8.42
1009.17 1009.17
The P&L A/c of the second year will be the same as above except that the amortisation will now be 9.17 giving once again a profit of 70 and the balance sheet at the end of the second year will simply show (fixed rate) loans and asset worth 1000 since the swap has expired. Of course in reality the profit figure will depend on how the benchmark rate B moves, being greater for declines in B and lower for increases in B. If B doesn’t move then the corporate saves 1% in interest cost and raises it income by 10 every year which is what is shown. (At the fixed rate net profit would be 150 – 90 = 60).
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Make now a variation. Suppose the corporate is one whose assets of 100 consist of floating rate instruments yielding B+3%. Now a swap of the liability at 9% for a liability at B +2% will amount to a net open position in floating rate instruments equal to zero and since the notional amount is also equal to value of assets, no liability will be recognized on the balance sheet. If, however, the swap is for 500 notional amount then there is residual mismatch whose value will be,
2
Σ t
=
1
[ 9 %
−
( B
+
2 )%](
( 1
+
0 .
09 ) t
500 ) and will be shown on the balance sheet. The application of the principle of net open position once again demonstrates ‘leverage’ in the balance sheet of one who has such a position as compared to one who hasn’t. Only, for swaps, the net open position must be reckoned with reference to assets for liability swaps and with reference to liabilities for asset swaps.
The method for swap accounting suggested above is almost identical with that recommended by FASB in SFAS 133 with two exceptions. Firstly, the present value of the swap payoff is not reflected in the balance sheet of FASB. Secondly, the present value is recalculated each year depending upon the floating rate in the market, it is not amortised over the life of the swap. On the first point, our treatment is consistent with our stand that transactions in derivatives must be reflected on the face of the balance sheet so that leverage in the structure of liabilities can be identified. On the second point, the treatment is consistent with expensing over a period of time the asset value implicit in derivatives contracts.
The Income Tax Act does not have any specific provision regarding taxability of gains or losses from derivatives. The only provisions which have an indirect bearing on derivative transactions are sections 73(1) and 43(5). Section 73(1) provides that any loss, computed in respect of a speculative business carried on by the assessee, shall not be set off except against profits and gains, if any, of speculative business. Section 43(5) of the Act defines a speculative transaction as a transaction in which a contract for purchase or sale of any commodity, including stocks and shares, is periodically or ultimately settled otherwise than by actual delivery or transfer of the commodity or scrips. It excludes the following types of transactions from the ambit of speculative transactions:
1. A contract in respect of stocks and shares entered into by a dealer or investor therein to guard against loss in his holding of stocks and shares through price fluctuations;
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Derivaties Accounting – A New Option for the Future
2. A contract entered into by a member of a forward market or a stock exchange in the course of any transaction in the nature of jobbing or arbitrage to guard against loss which may arise in ordinary course of business as such member.
These provisions of Income Tax Act give rise to two issues;
1.
2.
How to distinguish a speculative transaction with that of non-speculative one?
What should be the tax treatment of gains / losses on a derivative transaction which are generally for a short term but used to offset the gains / losses on an underlying held for long term?
1. As per Act provisions, a transaction is speculative, if
1. it is in commodities, shares, stock or scrips
2.
3. it is settled otherwise than by actual delivery the participant has no underlying position
4. it is not for jobbing/arbitrage
But again, one has to prove that the transaction was a non-speculative one to set off the losses against any business income. The accounting method suggested in the paper automatically takes care of these requirements. Suppose there is an underlying position against which derivative transactions are entered, only the net open position is accounted for. If both underlying and derivatives are liquidated simultaneously, the gain or loss on one position will offset loss or gain on the other position, in case of a perfect, complete hedge. If the hedge is not perfect, for example, when underlying is hedged by index derivative, there will be a basis risk whose effect on income will in any case be captured by the usual accounting rules. In fact, the proposed accounting system itself simplifies the procedure for segregating the speculative and hedging transactions for the income tax authorities!
If all the positions in NOP, say U/L and derivatives, are not liquidated simultaneously, there will be a question as to how this may be taxed? One may say that realized gains or losses shown in the revenue account may be taxed as speculative gains / losses. This will be too stringent for the trader who entered the transaction for managing price risk.
There will be two situations of this nature: 1) when the U/L (derivative) position will be making a loss and the derivative (U/L) is sold to book profits. 2) when the U/L
(derivative) position will be in profit and the derivative (U/L) is sold to book losses.
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•
Under (1) above, the accounting procedure illustrated in the paper calls for making provision for unrealized losses and showing realized gains or losses in the revenue account. Under the present taxation rules, though it is not permissible, the taxable income, may be defined to adjust provision for unrealized gains against the realized losses.
•
Under (2) above, both the positions may be marked to market and the realized losses to be set off against marked to market reserve, before arriving at the taxable income
•
All the realized losses may be allowed to be carried forward.
4. The second issue relating to long term and short term transactions can also be easily settled by taking into account the nature of capital gains / losses of the underlying. Long term gains / losses of the underlying may be set off against the short-term gains / losses on derivatives. If it is a perfect hedge, there will not be any tax liability. If not, the tax treatment on derivatives would be similar to the treatment of gains / losses on underlying.
It may be appropriate in concluding this paper to make an unforgivably brief comparison of the accounting system proposed in this paper vis-à-vis those of ICAI (2003), FASB
(1998) and IASC (2000) on 2 key issues viz.,
1. Recognition of assets and liabilities
2. Recognition of income and expense
To begin at home, the ICAI system appears to be a “transaction based system” which recognises the option premium alone as asset and liability in the books of both buyers and sellers. These are marked to market and continue in the books until they are closed out by cash settlement / delivery or expire. Realised gains are recognised in the P&L A/c. In case of futures contracts only the margin accounts with the exchange which are marked to market are reflected in the balance sheet. This is done for both buyers and sellers.
Surprisingly the ICAI guidance note is silent on the margin accounts of sellers of options which are marked to market. The ICAI system does, however, conform to the principle of conservatism in recognising and making provisions for unrealised losses. Overall the
ICAI philosophy seems to be to consider derivatives as being transactions only with the
Exchange and in which only the money flows to and from the Exchange are material.
Derivative contracts are accounted at face value, margin accounts in case of futures and premiums in case of options but the underlying positions are not considered at all. Also the ICAI system is silent on OTC derivatives contracts.
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In contrast, the FAS 133 is “motive-based” in which the distinction between “hedging” transactions and “speculative” transactions is given the centre-stage. Quite clearly and entirely justifiably the chief concern seems to be to ensure that hedge transactions are recognised for what they are and receive favourable tax treatment as compared to speculative transactions. However, the apparatus that reveals the distinction of hedging and speculation to the accountant is both complex and ambiguous : its chief requirement is the designation of a transaction to qualify for hedge accounting. Though the standard does not specify an appropriate method of assessing the effectiveness of the hedge, it requires that the method used for assessing the effectiveness of hedge to be specified at the time of designation and continued usage of the same method throughout the hedge period. Usually used tools are betas / correlation coefficients / volatilities. Although they are very useful statistical concepts, their use in this context give rise to a whole host of questions; how long should be the time-series, of what frequency, whether P-beta or Rbeta is relevant, whether covariance or semi covariance is the right idea, what to do if betas change over time, etc. etc. etc. These issues not only confound the job of the accountant but may also lead to suspicions and allegations of “creativity”. However, this standard of FASB does emphasize the need to recognize derivative instruments as assets and liabilities and the necessity to show all derivatives transactions on the balance sheet at fair value.
The IASB (IAS 39) follows “fair value” accounting and on balance sheet recognition of derivatives. Fair value means in the first place the market value but failing that it should be approximated by some scientific model eg. in case of options by the Black-Scholes model etc.
Both FASB and IASB recommend the method of hedge accounting and there is a feeling that hedge accounting is one of the main reasons for the complex nature of IAS 39 and
FAS 133. European countries try to evolve a method of accounting sans hedge accounting.
The accounting system proposed here combines the advantages of the transaction based and motive based approaches. The former is clearly accommodated in showing option premiums as assets and liabilities, making appropriate provisions for prudence and booking premium to revenue / expense both for exchange traded and OTC derivatives.
The latter too finds an explicit place because the net open position in derivatives is shown on the face of the balance sheet to reveal the liability in terms of the U/L. Both IASB and
FASB say that derivatives are assets and liabilities but show entries only for net rights or obligations under derivative contracts on the basis of change in fair values. We, on the other hand explicitly recognize the assets and liabilities and also show the effect of their recognition on the leverage in the balance sheet. Apart from this, there are strong similarities between the FASB procedure for hedge accounting and the proposed method.
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These are 1) the treatment of expired portion of option premium in terms of time value and 2) the principles of marked to market balance sheet
2
.
Note, however, that we have been under no necessity to pre-designate transactions as hedge, speculation or otherwise. Our position is that motives should not be written into the accounts by its author, motives should be revealed by the accounts to its reader.
Accordingly, the principles and rules that are devised to calculate the net open position and its value automatically bring out whether transactions in derivatives have on the whole been for hedging or for speculation. All of the statistical paraphernalia of FASB is completely avoided.
Apart from the synthesis that is sought to be achieved, we have sought to clarify in detail the procedures and rules to be applied in case of multiple, numerous and complex positions in derivatives. Such an exposition is woefully absent in the accounting literature on this subject, whether academic or official, which makes it difficult to understand derivatives accounting in a comprehensive way. This is the gap we have tried to fill.
Incidentally these procedures and rules fit an interesting acronym – NOMAD – meaning
Netting, Offsetting, Matching, Averaging and Differencing, but which, we hope, will give
“settled” and “stable” accounting results.
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Derivaties Accounting – A New Option for the Future
b)
Buyer Seller
I. At the time of Entry I. At the time of Entry
1. Call / Put Option 1. Bank A/c Dr
Premium A/c Dr
To Bank A/c
To Call / Put Option premium A/c
(For receipt of premium)
(Being recognition of asset & liability on option bought)
2. Call / put option sold A/c Dr
To Liability on call/put option sold
(Being recognition of asset & liability on option sold)
*3. Variable Margin A/c Dr
To Bank A/c
(For the payment of margin to Exchange)
II. Squaring up / Settlement II. Squaring Up / Settlement i). Squaring up a) Bank A/c Dr
To Call/Put Option
Premium A/c
(Being reversal of the bought position on options) i). a)
Squaring up
Call / Put Option
Premium A/c Dr
To Bank
(Being reversal of the sold options position) b) Liability on call/put option Dr
Call / Put option sold A/c
(Being the reversal of recognition entry) c) Profit on options A/c Dr
To P & L A/c
(Being Profit on reversal of options contract sold)
(premium on bought – sold)
P & L A/c Dr
To Loss on options A/c
(Being Loss on reversal of options contract)
Profit on options A/c
To Profit & Loss A/c
(Being profit on bought futures squared up)
(premium on sold – bought options)
Profit & Loss A/c Dr
To Loss on call/put options A/c
(Being Loss on options transaction reversed)
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Derivaties Accounting – A New Option for the Future
(ii) Cash Settlement a) Bank A/c Dr
To Profit on Options
Loss on Options A/c Dr
To Bank A/c
(Being reversal of the bought position on options)
*d)
Bank A/c Dr
To Variable Margin A/c
(Being the receipt of margins deposited)
(ii) Cash Settlement a) Liability on call/put option Dr
Call / Put option sold A/c
(Being reversal of recognition entry) b) Bank A/c Dr
To Profit on Options
Loss on Options A/c Dr
To Bank A/c b) Profit on options A/c
To Profit & Loss A/c
(Being profit on bought futures squared up)
(premium on sold – bought options)
Profit & Loss A/c Dr
To Loss on call/put options A/c
(Being Loss on options transaction reversed) c) P & L A/c Dr
To Call / Put Options
Premium A/c
(Being the unexpired portions of premiums in options contract settled)
(iii) Physical Settlement a) Stock / Investment A/c
Dr
To Bank A/c
(Being the receipt of U/L on Options Contract) b) P & L A/c Dr
To Call / Put Options
Premium A/c c)
(iii) Physical Settlement a) Bank A/c Dr
To Stock / Investment A/c
(Being the delivery of U/L on Options
Contract) b)
Profit on options A/c Dr
To P & L A/c
(Being Profit on reversal of options contract sold)
(premium on bought – sold)
P & L A/c Dr
To Loss on options A/c
(Being Loss on reversal of options contract)
Liability on call/put option Dr
Call / Put option sold A/c
(Being the reversal of recognition entry)
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Derivaties Accounting – A New Option for the Future
(Being the unexpired portions of premiums in options contract settled) b) Profit & Loss A/c Dr
To losses on
Provision
Options A/c for
(Being the losses on options contract)
*c) Bank A/c Dr
Margin A/c
(Being the receipt of margins deposited)
III. Open Positions a) P&L A/c Dr
Expired
Premium A/c option
(Being the entry for expensing the expired portion of option premium)
III. Open Positions a) P&L A/c Dr
To provision for Unexpired Premium
A/c
(Being the provision for unexpired option premium) b) Profit & Loss A/c Dr
To Variation Margin A/c
(Being the losses on options contract)
1. Total Transactions – Bought and sold separately
2. Realised Profit / loss on transactions settled / closed out.
3. Schedule of Net Open Position giving details on Number of U/L and derivatives
4. (Unrealised) Losses on Derivative Contracts
The above details be furnished separately for Options, Futures, Forwards and Swaps for each U/L i.e., Commodities, Interest Rates (Long term and short term separately),
Stocks, Indexes, Foreign exchange.
5. Initial margin paid other than by cash.
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Derivaties Accounting – A New Option for the Future
01 “Alternative Approaches to Testing Hedge Effectiveness under SFAS 133”,
J.D.Finnerty & D.Grant, Accounting Horizons , June, 2002.
02 Derivatives Core Module Workbook , National Stock Exchange of India Ltd, 2001.
03 “Financial Infrastructure and Public Policy - A Functional Perspective” Merton
R.C. & Z. Bodie, in Crane D.B. et. Al (eds) . The Global Financial System : A
Functional Perspective, Harvard Business School Press, Boston, 1995.
04 GAAP, 2001 , P.R.Delaney, R.Nach, B.J.Epstein, S.W.Budak, John Wiley & Sons,
Inc, 2001.
05 Guidance Note on Accounting for Futures and Options , Institute of Chartered
Accountants of India, 2003.
06 International Accounting Standards, 2001 , Taxman Publications (P) Ltd., New
Delhi, 2001.
07 “Using and Accounting for Derivatives: An International Concern”, L.E.Crawford,
A.C. Wilson & B.J.Bryan, Journal of International accounting, Auditing and
Taxation , January, 1997.
1
It is perfectly legitimate to take an average of strikes for bought positions and an average of strikes of sold positions. But bought and sold positions cannot be averaged.
Several methods suggest themselves. First is to simply value the whole position but that will not do as shown by the following example.
No.
Value
-11
- 990
+ 9
+ 990
- 2
0
There is a liability due to 2 net sold contracts but the value of the whole position does not show it. Another method is to value the net sold position of 2 at 90 to 180. This is correct for this example but runs into difficulty as shown below :
No.
Value
-10
- 900
+ 8
+ 800
- 2
-220
- 4
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How do we value the NOP ? At 90 or 110 ? This leads to the best approximation viz. valuation at the weighted average strike, viz.
( 90 x 10 )
+
( 110 x 2 )
=
93 .
33
12 with a liability of 93.33 x 4 = 373.33. This is the method used in the text. Of course the liability will be topped up for the strike price difference of bought over sold calls for 8 contracts, i.e. 10 x 8 = 80.
2
Suppose, an agent has bought 100 shares of XYZ Ltd for Rs.15 on 1 st
July, 2003. On
30 th
September, the value has risen to Rs.25. In order to protect the appreciation on shares, the agent buys an equal amount of put option on XYZ shares. The premium paid for acquiring 6 months at-the-money option was Rs.350. On 31 st
December, the share price was Rs.22 and put option value was Rs.515. Let us now compare the balance sheets of the agent prepared under FAS standard and our accounting method.
Balance sheet Extract under FAS 133
Equity / overdraft
Other Comprehensive
1850
Income
(exercise price – cost)
1000
Shares of XYZ Ltd
Valuation Allowance
(exercise price – cost)
Put option
Time value expired
1200
1000
135
(515 – 300 intrinsic value)
-------
2850
-------
2850
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Balance sheet Extract under our system (Under MTM accounting)
Amount Liabilities Amount Assets
Equity / overdraft 1500 Shares of XYZ Ltd
MTM reserve Put option
2200
515
(2200-1500) 700
Liability on Option 350
MTM reserve
(intrinsic value)
300
P&L A/C bal
(expired premium)
-------
135
-------
2850 2850
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