Q&A - Module 2 - Student
Q&A - Module 2 - Student
                                            T ( days to
                                 spot price settlemen Dividend      Dividend
                    Sr no           (Rs)                (Rs)          days
                                                 t)
                 Commodity
                   futures
                                                                    Expected
                                            T ( days to   Storage    price of
                                 spot price settlemen     cost (%     future
                    Sr no           (Rs)
                                                 t)         p.a.)   contract
                                                                       (Rs)
                      9           100.00        30        6.00%       100.91
                     10           100.00        25        4.00%       100.62
                Currency futures/forward
                       contracts
                                 Risk free
Cost of carry                    interest        5.00% p.a.                     compounded c
                                   rate
                Equity futures
                                            T ( days to
                                 spot price settlemen Dividend      Dividend
                    Sr no           (Rs)                (Rs)          days
                                                 t)
                      1           100.00        30         0.00
                      2           100.00        25         1.00      10.00
                      3           100.00        20         1.10      15.00
                      4           100.00        40         0.00
                      5             ?           30         0.00
                      6             ?           30         1.00      10.00
                      7           100.00         ?         0.00
                      8           100.00         ?         1.00      20.00
                 Commodity
                   futures
                                                                    Expected
                                 spot price T ( days to   Storage    price of
                    Sr no           (Rs)    settlemen     cost (%     future
                                                 t)         p.a.)   contract
                                                                       (Rs)
                      9           100.00        30        6.00%        ?
                     10           100.00        25        4.00%        ?
                Currency futures/forward
                       contracts
                                                   T ( days to domestic overseas
                                        spot price settlemen risk free (% risk free (%
                       Sr no               (Rs)
                                                        t)       p.a.)        p.a.)
                                        Risk free
  Basis,spread and cost of carry        interest        5.00% p.a.
                                          rate
net gain,margin
                             Actual
 Spot price     Expected     price of
adjusted for price of future future Implied cost of
                                      carry (% p.a.)
dividend (Rs) contract (Rs) contract
                               (Rs)
  100.00        100.41      100.65        7.88%
   99.00         99.34       99.80       11.73%
   98.90         99.17       99.43        9.76%
  100.00        100.55      101.10       10.00%
  100.09        100.50
   99.44         99.85
  100.00        100.76
   99.00         99.65
compounded continuously
                             Actual
 Spot price     Expected     price of
adjusted for price of future future Implied cost of
                                      carry (% p.a.)
dividend (Rs) contract (Rs) contract
                               (Rs)
  100.00        100.41      100.65        7.88%
   99.00         99.34       99.80       11.73%
     ?             ?           ?          9.76%
     ?             ?           ?         10.00%
     ?          100.50
     ?           99.85
     ?          100.76
     ?           99.65
                           Implied
Actual price Expected cost cost of    Convenience
  of future   of carry (% carry (%    yield (% p.a.)
contract (Rs)     p.a.)     p.a.)
  100.85           ?           ?            ?
  100.84           ?           ?            ?
             Expected
              price of Actual price of Expected
           future/forwa future/forwar cost of Implied cost of
                          d contract   carry (% carry (% p.a.)
            rd contract      (Rs)        p.a.)
                (Rs)
                 ?            65.51           ?              ?
                 ?              ?          4.00%          4.10%
compounded continuously
 ry after 15 days, no dividend and implied cost of carry 9% p.a. compounded continuously.
                 100.37                                   Basis         0.371
 ry after 15 days, dividend of 1 after 10 days and implied cost of carry 9% p.a. compounded continuously.
                  99.00         99.37                     Basis        -0.632
 compouded continuously) if basis is 2,spot is 100, expiry after 25 days and dividend is nil.
                  28.9%        102.00       100.00
 compouded continuously) if basis is 0.2,spot is 100, expiry after 35 days and dividend is 1 after 12 days.
                  12.5%         99.00       100.20       100.00
 pot of 100, storage cost @ 3% p.a., expiry after 20 days, convenience yield of -2.3% p.a. Risk free interest ra
                 10.30%        100.57
  ) is 0.4, near month spread @ 1.3 ( expiry 42 days away) and far month spread @ 2.4 ( expiry 71 days away
tinuously for the current month, near month as well as far month futures
  lied cost of carry ( % p.a.)
          =LN(E65/$E$64)*365/F65
          =LN(E66/$E$64)*365/F66
          =LN(E67/$E$64)*365/F67
                                                                        day
              type of                    underlying                    count
            instrument     entry price    security     entry basis
                                                                       expiry
              future          121            X             2           30
              future          165            y             3           30
              future          201            Z             4           30
              future          306            A             2           30
               stock          103            B                         30
mpute net gain in INR for stock portfolio for X,Y,Z and A of 100 shares each
 te % gain over expiry cycle if average margin for x and Y is 20% and that for A & Z is 25% of the notional en
remain with the broker till expiry
d that for stock Y is 0.7%. On day 15, basis for X is 0.7% and that for Y is 0.9%.
 position in one stock only. Expiry on t=30.
mpounded continuously), time to expiry is 10 days and average margin 20% of entry notional value.
p by 5% during the 10 day period. Position held till expiry.
                        Exit price                            105
 rgin is 20% and maintenance level is 12%. At what price would the margin call be made?
           =100+(E93-F93)
mple in Q6 above and the price went to 109, but the customer did not respond to the margin call.
 off? Lot size : 2500.
               2500000
                500000
               -225000
                275000
                 300000
fficient to support outstanding position of 6 lots
                 250000
 ent to support outstanding position of 5 lots
pounded continuously.
                                                                    market
                                                                    price of
                                                    exit      exit underlyi
              day count for exit of position       price      basis          gain - Q1 gain - Q2
                                                                     ng on
                                                                      exit
                           30                                          110   -1100    -900
                           20                                1         175    1100    1300
                           30                                          220   -1900   -2300
                           10                                1         280    2500    2400
                           30                                          110    -700       -
                                                                              -100     500
d that for A & Z is 25% of the notional entry value, 30% for stock B
or Y is 0.9%.
          % gain                                  23.7%
e margin call be made?
                    1      Compute basis in case spot is 100, expiry after 15 days, no dividend and
                           Actual future price
                    2      Compute basis in case spot is 100, expiry after 15 days, dividend of 1 aft
                           Adjusted spot
                    3      Compute implied cost of carry ( % p.a. compouded continuously) if bas
                           Implied cost of carry
                    4      Compute implied cost of carry ( % p.a. compouded continuously) if bas
                           Implied cost of carry
                    5      Compute basis for a commodity with spot of 100, storage cost @ 3% p.
                           Basis                    ?
                           Spot is 100, basis ( expiry 12 days away) is 0.4, near month spread @ 1.
                    6      cost of carry in % p.a. compouded continuously for the current month,
                                              Actual price       days       Implied cost of carry ( %
                           spot                   100.0
                           current                  ?             12              ?
                           near                     ?             42              ?
                           far                      ?             71              ?
               compounded continuously
 r month spread @ 1.3 ( expiry 42 days away) and far month spread @ 2.4 ( expiry 71 days away). Calculate
r the current month, near month as well as far month futures
 ied cost of carry ( % p.a.)
 continuously.
a. compounded continuously.
dividend is nil.
                  1
                                        entry
                               # of    long/sh   day count for      type of
                       Sr no   units                 entry        instrument
                                         ort
                         1     100        L            0             future
                         2     100        L            0             future
                         3     100        S            0             future
                         4     100        S            0             future
                         5      0         S            0              stock
                      Compute net gain in INR.
2 In case of the example in Q1 above, recompute net gain in INR for stock
5 Entry is short position at 100. Initial margin is 20% and maintenance lev
                  6 If 10 lots were sold at entry in the example in Q5 above and the price w
                    How many lots would need to squared off? Lot size : 2500.
                                            day day count
           entry    underlying     entry   count for exit of     exit     exit
           price     security      basis                        price     basis
                                           expiry position
            121          X           2       30         30
            165          y           3       30         20                  1
            201          Z           4       30         30
            306          A           2       30         10                  1
            103          B                   30         30
over expiry cycle if average margin for x and Y is 20% and that for A & Z is 25% of the notional entry value
h the broker till expiry
d continuously), time to expiry is 10 days and average margin 20% of entry notional value.
 ring the 10 day period. Position held till expiry. No dividends expected.
% and maintenance level is 12%. At what price would the margin call be made?
above and the price went to 109, but the customer did not respond to the margin call.
ze : 2500.
           market price of underlying
                    on exit
                       110
                       175
                       220
                       280
                       110
Q2          If in Q1 above, average margin deployed on the future contract was 25% and it was o
              compute % net gain on the owned funds invested
            Assume transaction costs to be nil
            Margin                   25.225 =100.9*0.25
            % net gain                1.61% =C8/C13
Q3          If in Q2 above, the transaction costs are 0.2% for delivery based transactions and 0.0
              compute the revised % net gain on the owned funds invested. Price of the stock wen
            Net gain (Rs.)               -0.04 =C8-0.2%*100-0.03%*100.9-0.2%*110
            Amt invested             25.4553 =C13+0.2%*100+0.03%*100.9
            % net gain                -0.17% =C18/C19
Q4          With respect to Q1, 2 and 3 above; what is the minimum value of the futures contrac
            Fut price for            100.94 =100.9-C18
            no arbitrage
Q5          Further to Q4, what is the minimum implied cost of carry in terms of % p.a. necessary
            Compute using simple interest method , discrete compounding as well as continuous
            Simple interest          11.48% =+((C23-100)/100)*365/30
            Discrete comp.           12.10% =((C23/100)^(365/30))-1
            Cont. comp.              11.42% =+LN(C23/100)*365/30
Q7     Stock Z was borrowed from SLBM at borrowing cost of 0.7% p.a. ( including SLBM tra
       Stcok Z was sold at 100 and the future contract on Z was simultaneously purchased a
       Expiry of the futures contract is 30 days way
       No dividend expected.
       Transaction costs 0.25% for delivery and 0.05% for active futures.
       Fund received on selling the stock was first used in giving the margin for the futures c
       Compute net arbitrage gain on the expiry day. Stock price 105 at the time of expiry.
       Amt invested             74.9004 =100-99.2*0.25-100*0.0025-99.2*0.0005
       Int earned                   0.31 =+C57*0.05*30/365
       Trxn costs                   0.56 =100*0.0025+99.2*0.0005+105*0.0025
       SLBM cost                    0.06 =100*0.007*30/365
       Net gain                     0.49 =100-99.2+C58-C59-C60
Q8     Further to Q7 above, what should be the maximum futures contract price necessary
                        99.69 =99.2+C61
Q9     On day t=0, stock X was priced at 100 and its basis was at 1.2% of the stock price. On
       Stock X went up by 3% from t=0 to t=15. Stock Y went up by 4% in the same period.
       On day 15, basis for X was 0.7% and that for Y was 0.9%.
       Max capital available is 200
        Expiry on t=30.
       Compute optimum net arbitrage gain on expiry day based on the information given.
       Interest computed on simple interest basis and nil transaction costs.
       Stock X                  Future X Stock Y
t=0                     100.00 101.20                            150.00
t=15                    103.00 103.72                            156.00
                             net gain % gain
      only X                      1.20                           0.96%
      only Y                      1.05                           0.56%
      first X then Y              1.88                           1.10%
Q10   An HNI investor is expecting inflow of INR 100 cr on 5th Feb, 2019. This would be inv
      The investor is bullish about the budget to be presented on 1st Feb,2019 and wishes
      The following are the prices of various futures contracts as on 18th Jan, 2019
      Choose appropriate contract for hedging and compute the number of lots needed to
      Will the future contracts be sold or bought?
      Nifty31stjan2019                                           10937
      Nifty28thFeb2019                                           10967
      BankNifty31stJan2019                                       27560
      BankNifty28thFeb2019                                       27674
                         1215 =ROUNDDOWN(100*10^7/(75*10967),0)
Q11   A diversified fund with Beta of 1.2 and size of 12340 cr as on 19th jan,2018 wishes to
      Using the alternative futures contracts as in Q11 above, compute the number of lots
      Will the future contracts be bought or sold?
                       180524 hedging using Jan futures
                       180031 hedging using Feb futures
Q12   A company borrows USD 100m@ 2.4% p.a., sells spot USD@ 70 and buys 1 year forw
      The funds received by selling spot USD are invested at 7% p.a.
      If spot USD after 1 year is 73.5; compute net arbitrage gain in INR and in USD
Q13   A company borrows USD 100m @ 3.5% p.a. for a period of 1 year and buys forward U
      With the proceeds from this loan, the company pays back an outstanding domestic lo
      If the spot at the beginning of the year was INR 70 per USD and at the end of one yea
      Is this an example of arbitrage or hedging?
           Scenario 1 - pay back domestic loan
           Value of USD loan            100 USD mn
           Loan o/s after 1 year      103.5 USD mn
Cashflows? Rs. needed to close loan 7607.25 INR mn
Q14        A commodity having storage cost of 1.5% p.a. is bought in spot @ 100 . Future contra
           Average margin on the future contract is 25%
           Assume that the commodity purchase was funded by borrowing at 6% p.a. and marg
           Compute the net gain on the expiry day. Interest and storage cost computed using sim
                             0.18
                           0.73% 8.86% p.a.
12.10% =RRI(30/365,100,C23)
at 6% p.a.
005+103*0.0025
005+105*0.0025
at 1.2% of the stock price. On day t=0, stock Y was priced at 150 and its basis was 0.7% of the stock price.
p by 4% in the same period.
                                                                            lot size : 75
                                                                            lot size : 75
                                                                            lot size : 40
                                                                            lot size : 40
         buy futures
         =ROUNDDOWN(12340*10^7*1.2/(D87*75),0)
         =ROUNDDOWN(12340*10^7*1.2/(D88*75),0)
d of 1 year and buys forward USD at a premium of 5% on the spot to pay back this loan.
 ck an outstanding domestic loan which carried interest of 9.5% p.a.
USD and at the end of one year was INR 73 per 1 USD; compute the annual savings to the company.
                                                                          Assume all rates are based on
         Scenario 2 - do not pay back domestic loan
         USD loan in INR/ Value of domestic loan                                       7000
         Loan closure after 1 year                                                     7665
in spot @ 100 . Future contract on that commodity ( expiring 30 days later) is simultaneously sold at 100.8
orrowing at 6% p.a. and margin for the futures contract was paid from owned funds.
orage cost computed using simple interest method. Transaction costs nil.
                                                                           Sell -->
         buy
         stock                                                                           100
         future                                                                        101.5
         syn98                                                                           100
         syn100                                                                         99.9
         syn102                                                                        100.1
         syn104                                                                        101.3
                100.94 =   100+100*r/100*30/365
/365,100,C23)
 = Stock SP - Fut CP - trxn cost - SLBM cost + int earned
          USD mn liab
          INR mn asset
          USD mn asset         convert @ fwd rate
o the company.
 all rates are based on simple interest.
         INR mn
         INR mn              Savings
                                  57.75 INR mn
         Sell Future and buy syn100 - this will give max arbitrage gain
Define the following terms in the context of future/forward contracts
      1 Open interest
      2 SPAN margin
      3 Exposure margin
      4 Marking-to-market
      4 Basis
      5 Spread
      6 Implied cost of carry
      7 Notional value
      8 Contango
      9 Backwardation
     10 Interpretation of convenience yield
nge whereas forwards are traded over the counter. Futures are standardised contracts while forwards are not standardised.
n or possess an asset and decide to sell it whereas shorting is when you sell an asset without owning or possessing it in the futures market
s the expected rate and expected price of the future contract whereas the implied cost of carry considers the actual cost
o expiry, dividend, number of days to dividend, risk free rate of interest                  *=Adjusted Spot*EXP(RiskfreeRate*n/365)
basis, dividend, number of days to expiry, number of days to dividend                       *= 365*LN(Actual price/Adjusted Spot price)/n
risk free interest rate, storage cost, actual price of futures contract, number of days to expiry     *=Expected Cost of Carry - Implied Cost
ee rate in India, risk free rate in US
y, delivered on a particular day.
ges around the world
t some point in the future than the actual expected price of the commodity.
hes expiration, the futures contract trades at a higher price compared to when the contract was further away from expiration.
 for forward prices in markets with trading constraints. This makes it possible for backwardation to be observable.
ot standardised.
essing it in the futures market.
e actual cost
P(RiskfreeRate*n/365)
ice/Adjusted Spot price)/n
ed Cost of Carry - Implied Cost of Carry
ay from expiration.