CA, CFA(USA), CPA(USA) Praveen Khatod (Best Faculty in India for SFM & COST(SCM) 1
DERIVATIVES UNIT I – FUTURES & FORWARD
Q.2. Suppose that you enter into a short future…..
Solution:
Total loss before margin call triggers = 5,00,000 – 3,00,000
= 2,00,000
Required change in price = ₹ 2,00,000
1000 = ₹200 per gram
Therefore, an increase in price (since we are seller) of ₹200 will trigger the margin call.
If we do not meet the margin call then exchange/broker has the right to unilaterally
square off the position, adjust the losses against the margin already deposited & refund
back the balance amount if any.
Q.5. ABC Ltd., a non-dividend paying company is quoting…..
Solution:
(a) F = S0 x ert
= 85 x e0.08 x 6
12
= ₹ 85 x e0.04
= ₹ 85 x 1.04081
= ₹ 88.46885 ~ ₹ 88.47
(b) Since actual price (₹ 88) < futures fair price (₹ 88.47), therefore, futures contract
are undervalued, hence will long the futures & short the spot to earn risk free
gain of ₹ 0.47 (88.47 - 88).
(c) Since actual price (₹ 94) > futures fair price (₹ 88.47) therefore future contract
are overvalued, hence will short the futures & long the spot to earn risk free gain
of ₹ 5.53 (94 – 88.47)
Proof of Arbitrage Table for point (c)
Today On due date
Particulars Action Amount Action If ₹ 80 If ₹ 95
Futures Short @94 - Settle +14 -1
Spot Long (85) Short +80 +95
Loan Borrow @8%
p.a.cc
+85 Repay* (88.47) (88.47)
Net Arbitrage Gain 5.53 5.53
CA, CFA(USA), CPA(USA) Praveen Khatod (Best Faculty in India for SFM & COST(SCM) 2
*FV = PV x ert
= 85 x e0.08 x 6/12
= 85 x 1.04081
= 88.47
Q.6. X Ltd. a company that historically has not paid….
Solution:
F = S0 x ert
61.21 = S0 x e0.08 x 3
12
= S0 x e0.02
= S0 x 1.02020
S0 = 61.21 / 1.0202
= ₹ 60
Since Actual Spot Price (₹ 64) > Fair Spot Price (₹ 60), therefore, Stock in Spot is
Overvalued. Hence will Short in Spot & Long in Futures to earn risk free gain of ₹ 4
today (64 – 60)
Proof of Arbitrage Table
Today On due date
Particulars Action Amount Action If ₹ 50 If ₹ 70
Futures Long @61.21 - Settle (11.21) (8.79)
Spot Short 64 Long (50) (70)
Investment Invest @8%
p.a.cc
(60) Liquidate +61.21 +61.21
Net Arbitrage Gain +4 0 0
Note: Alternatively, we could have invested full amount of ₹ 64 and realized gain on
Due date which will be equivalent to Future Value of ₹ 64 compounded @ 8% p.a.
c.c. for 3 months
CA, CFA(USA), CPA(USA) Praveen Khatod (Best Faculty in India for SFM & COST(SCM) 3
Q.9. A 3-month forward contract on a stock….
Solution:
F = S0 x ert
96.50 = 92 x er x 3/12
1.04891 = e0.25r
Taking Log on both the sides
Ln (1.04891) = Ln (e0.25r)
Ln (1.04891) = 0.25r
Using Interpolation:
Ln 1.04 0.03922
0.01 Ln 1.04891 ? 0.00957
Ln 105 0.04879
Since, 0.01 = 0.00957
Therefore, 0.00891 = 0.00891 x 0.00957
0.01
= 0.008527
= 0.03922 + 0.008527
= 0.04774
Replacing Ln 1.04891 with 0.04774
0.4774 = 0.25r
Therefore, r = 19.098% p.a. compounded continuously
CA, CFA(USA), CPA(USA) Praveen Khatod (Best Faculty in India for SFM & COST(SCM) 4
Q.10. A forward contract on a share that is selling…..
Solution:
F = S0 x ert
100 = 97.05 x ert 6/12
1.0304 = e0.50r
Alternative-1: using ex table values
Since, e0.03 = 1.03045 ~ 1.0304
Replacing 1.0304 in the LHS of above equation by e0.03
e0.03 = e0.50r
when bases are same, powers can be compared
0.03 = 0.50r
r = 6% p.a.cc
Alternative-2: Using Log Natural
1.0304 = e0.50r
Taking Ln on both the sides
Ln (1.0304) = Ln (e0.50r)
Ln (1.0304) = 0.50r
Ln (1.03) 0.02956
0.01 1.0304 ? 0.00966
Ln (1.04) 0.03922
Since, 0.01 --- 0.00966
Therefore, 0.0004 --- ?
= .0004 x 00966
.01
= 0.0003864
= 0.02956 + 0.0003864
= 0.02995
Replacing Ln 1.0304 by 0.02995
0.02995 = 0.50r
r = 5.99 ~ 6% p.a.cc
CA, CFA(USA), CPA(USA) Praveen Khatod (Best Faculty in India for SFM & COST(SCM) 5
Q.14. Calculate the price of a 6 months futures contract
Solution:
Working Note 1: Calculation of PV of dividend income:
PV (I) = FV
ert
I = 2
e0.12 x 4/12
I = 2
e0.04
I = 2
1.04081
I = 1.92
Calculation of Fair Futures Price
F = (S0 – I*) x ert
F = (75 – 1.92) x e0.12 x 6/12
= 73.08 x e0.06
= 73.08 x 1.06184
= 77.60
Futures contract value = 77.60 x 100
= 7760
Since actual futures price (₹ 7400) < futures fair price (7760), therefore Futures
Contract are Undervalued. Hence, we will go Long Future & Short Spot & Invest the
proceeds at risk tree rate of return to earn risk free arbitrage gains of ₹ 360 (equivalent
to the extent of mispricing).
Proof of Arbitrage Table:
Today Dividend date On due date
Particulars Action Amt Action Amt Action If ₹ 70 If ₹ 80
Futures Long @
₹ 7400
- Short -400 +600
Spot Short 7500 Long -7000 -8000
Investment Invest
@12%
p.a.cc
7500 Liquidate +7963.80 +7963.80
Dividend Paid (200) - - -
Loan Borrow @
12% p.a.cc
for 2 month
+ 200 Repay -204.04 -204.04
Net Arbitrage Gain 360 360
CA, CFA(USA), CPA(USA) Praveen Khatod (Best Faculty in India for SFM & COST(SCM) 6
Since actual futures prices (₹ 7900) > fair futures price (₹ 7760), therefore, Futures
Contract are Overvalued. Hence, we will go Short in Futures & Long in Spot by
borrowing at risk free rate of interest to earn risk free arbitrage gain of ₹ 140.
Proof of Arbitrage Table:
Today Dividend date On due date
Particulars Action Amt Action Amt Action If ₹ 70 If ₹ 80
Futures Short @
₹ 7900
- Long +900 -100
Spot Long (7500) Short +7000 +8000
Loan Borrow
@ 12%
p.a. cc
+7500 Repay -
7963.80
-7963.8
Dividend Received 200 - - -
Investment Invest @
12% p.a.cc
for 2 month
(200) Liquidate +204.04 +209.04
Net Arbitrage Gain 140 140
CA, CFA(USA), CPA(USA) Praveen Khatod (Best Faculty in India for SFM & COST(SCM) 7
Q.18. An index consists of following four stocks…..
Solution:
Working Note 1: Calculation of present Market Cap
Stock Price No. of Shares M. Cap
A 50 10 500
B 80 5 400
C 20 5 100
D 100 5 500
Total M. Cap = 1500
Working Note 2: Calculation of PV of dividend income
= ₹ 10
e0.12 𝑥 1/12
= 10
e0.01
= 10
1.01005
= ₹ 9.90 x 10 lakh shares
= ₹ 99 lakhs
Calculation of Future Market Cap:
F = (S0 - I) x Crt
= (1500 - 99) x e0.12 x 3/12
= 1401 x e0.03
= 1401 x 1.03045
= ₹ 1443.66
Calculation of futures contract price on index (Using Cross Multiplication)
Market Cap Index Points
Since, 1500 lakhs equivalent to 12 pts
1443.66 ?
= 1443.66 x 1200
1500
= 1154.93 Pts ~ 1155 Pts
CA, CFA(USA), CPA(USA) Praveen Khatod (Best Faculty in India for SFM & COST(SCM) 8
Q.20. Nifty spot is 1300 points. You are considering…..
Solution:
Calculation of Theoretical Futures Value:
F = S0 x e(r - y) x t
= 1300 x e(0.08 – 0.02) x 3/12
= 1300 x e0.015
= 1300 x 1.015125
= ₹ 1319.67
Action: Since, Actual Futures Price (₹ 1325) > Fair (Theoretical) Futures Price
(1319.67), therefore, it is Overvalued. Hence, we will Short in Future & Long in Nifty
constituents by borrowing at risk free rates to earn arbitrage gain of ₹ 5.33 (1325 –
1319.67).
Q.25. The spot price of Wheat is ` 8000 per ton…
Solution:
F = (S0 + S) x e(r - c) x t
= (8000 + 300) x e(0.08 – 0.02) x 12/12
= 8300 x e0.06
= 8300 x 1.06184
= ₹ 8813.27
Q.27. The following information about copper scrap is given……
Solution:
Futures price
(1+Risk−free rate)1 = Spot price + PV of storage costs - PV of Convenience Yield
10,800
(1.12)1 = 10,000 + 500 - PV of Convenience Yield
Hence the Present Value of Convenience Yield is $857.14 per ton.
CA, CFA(USA), CPA(USA) Praveen Khatod (Best Faculty in India for SFM & COST(SCM) 9
Q.31. Identify the action to be taken in terms of the hedging through Nifty…….
Solution:
S. No. Stock
Beta
Stock
Position
Stock Value
(` in Lakhs)
Hedging
required
Action in
futures
Amount
(` in Lakhs)
(i) 1.0 Short 10 Full Long 10
(ii) 0.25 Long 25 50% Short 3.125
(iii) 3.40 Long 60 110% Short 224.4
(iv) 0.75 Short 55 None - -
(v) 1.4 Short 35 140% Long 68.6
Q.36. A portfolio manager owns 3 stocks……
Solution:
(a)
Security MV of security Proportion Beta Beta Portfolio
1 400 Lacs 4/13 1.1 0.34
2 600 Lacs 6/13 1.2 0.55
3 300 Lacs 3/13 1.3 0.3
1300 Lacs 1.19
Security Proportion Beta Portfolio Beta
Portfolio P 1.19 p x 1.19
Risk free 1 – p 0 0
0.8
p = 67.23 %
(1— p) = 32.77%
1300 Lacs
Instead of selling the existing portfolio for 426 lacs for risk free securities the portfolio
manager can use stock index futures to hedge the operations.
No. of futures contracts to be purchased/sold = Total value of portfolio x (β2 − β1)
Value of 1 stock index
Here,
β1 = Existing Beta index
β2 = New Beta Index
Dispose & Substitute (bal fig)
= 426
Retain 67.23% x 1300 lacs
= 874
CA, CFA(USA), CPA(USA) Praveen Khatod (Best Faculty in India for SFM & COST(SCM) 10
Instead of changing the composition of the portfolio the portfolio manager shall retain
the entire portfolio & should go short for stock index futures
No. of SIF contracts = 1300 lacs x (0.8−1.19)
1350 x 100
= (375) contracts - Sold
Negative Quantity indicates sale of contracts & Positive Quantity indicates Purchases.
(b) No. of future contract to increase the beta from 1.19 to 1.5 the portfolio manager
buy 299 contracts
No. of SIF contracts = 1300 lacs x (1.5−1.19)
1352 x 100
= 299 contract - Buy
Q.37. The portfolio composition of Mr. X is given below……
Solution:
Let Fe, be, Fc, bc, Ff, bf, Fp & bp are the fund and beta values of equity, cash, index
futures and portfolio respectively.
Let n = No of future contracts
Beta for cash = 0
Then we have,
Fe x be + Fc x bc + Ff x bf = Fp x bp
or 8,00,000 x 0.69 + 2,00,000 x 0 + (930 x 200 x n x 1) = 1.1 x 10,00,000
or 5.52+ 1.86 n = 11
or 0.186 n = 5.48
or n = 2.946 i.e. 3 future contracts.
CA, CFA(USA), CPA(USA) Praveen Khatod (Best Faculty in India for SFM & COST(SCM) 11
Q.38. A company is long 10MT of copper @ ` 474 per kg (spot)……
Solution:
The optional hedge ratio to minimize the variance of Hedger's position is given by:
H = ρσS
σF
Where
σS = Standard deviation of ∆S
σF = Standard deviation of ∆F
ρ = coefficient of correlation between ∆S and ∆F
H = Hedge Ratio
∆S = change in Spot price
∆F = change in Future price
Accordingly,
H = 0.75 x 0.04
0.06 = 0.5
No. of contract to be short = 10 x 0.5 = 5
Amount = 5000 x ₹ 474 = ₹ 23,70,000
Q.46. The following information is available about standard gold. ….
Solution:
FP
(1+Rf)t = SP + PVS - PVC
PVC = SP + PVS - FP
(1+Rf)t
Accordingly,
= ₹ 15600 + ₹ 900 - ₹ 17100
(1+0.085)1
= ₹ 15600 + ₹ 900 - ₹ 15760
= ₹ 16500 - ₹ 15760 = ₹ 740
CA, CFA(USA), CPA(USA) Praveen Khatod (Best Faculty in India for SFM & COST(SCM) 12
Q.47. Mr. A bought a futures contract of Britannia that……
Solution:
(a) Working Note 1: PV of dividend income:
= 5
e0.08 x 12/12
= 5
1.08329
= 4.616
Calculation of fair futures prices:
F = (S0 - I) x ert
= (200 – 4.616) x e0.08 x 1
= 195.384 x e0.08
= 195.384 x 1.08329
= ₹ 211.66
(b) F = (S0 - I) x ert
= [186 – 4.616] x e0.08 x 1
= 181.384 x 1.08329
= ₹ 196.49
(c) Gain / (loss):
Absolute terms = (211.66 – 196.49) x 1000
= 15170
% terms = 211.66−196.49
211.66
= 7.17%
(d) Margin call:
Maintenance margin = ₹ 10000 per contract
Initially margin deposited was ₹ 20000 but after loss of ₹ 15170 position comes
to below maintenance margin of ₹ 10000 i.e. comes down to ₹ 20000 - ₹ 15170
= ₹ 4830, therefore, Amount of margin call will be ₹ 15170 [20000 - 4830] in order
to bring back the Maintenance Margin amount of ₹ 20000.
CA, CFA(USA), CPA(USA) Praveen Khatod (Best Faculty in India for SFM & COST(SCM) 13
UNIT II - OPTIONS
Q.55. A stock with a current market price of ` 50 has the following…….
Solution:
Exercise Price Spot Price Total Premium Intrinsic Value Extrinsic Value
40 50 10 10 -
48 50 7 2 5
50 50 5 0 5
55 50 3 0 3
62 50 1 0 1
Q.56. A put option on Abhishek Industries stock has an exercise price……
Solution:
Calculation of Value of Put
Exercise Price Spot Price Value of Put Option
VP = Max (E-S1 , 0)
20 16 4 (20 - 16)
20 18 2 (20 - 18)
20 20 0
20 22 0
20 24 0
Q.57. A call option has an exercise price of ` 50. On the expiry date…….
Solution:
Call Option Exercise Price = ₹ 50
Spot price on maturity date (S1) = ₹ 60
(i) Call is priced at ₹8:
Fair VC = Max (S1 – E, 0)
= Max (60 – 50, 0)
Fair VC = 10
Since, Actual VC (₹ 8) < Fair VC (₹ 10), therefore, Call Option is undervalued, Hence,
we will Buy Call Option & Sell in Spot to earn risk free arbitrage gain of ₹ 2.
Particulars Stock Amount
Buy CO Ex Price = ₹ 50 (8)
Exercise CO +1 (50)
Sell Stock in Spot -1 60
Net Arbitrage Gain ₹ 2
CA, CFA(USA), CPA(USA) Praveen Khatod (Best Faculty in India for SFM & COST(SCM) 14
(ii) Call is priced at ₹ 12:
Since actual VC (₹ 12) > Fair VC (₹ 10), therefore, Call Option is overvalued. Hence,
we will Sell Call Option & Buy Stock in spot to earn risk free arbitrage gain of ₹ 2.
Particulars Stock Amount
Sell CO Ex Price = ₹ 50 12
CO Exercised on us -1 50
Buy Stock in Spot +1 (60)
Net Arbitrage Gain 2
Q.58. A put option has an exercise price of ` 100. On the expiry date……
Solution:
Calculation of FV of Put Option:
Fair VP = Max (E – S1, 0)
= Max (100 – 80, 0)
Fair VP = 20
(i) Since Actual VP (₹ 14) < Fair VP (₹ 20), therefore, Put Option is
undervalued. Hence, we will Buy PO & Buy in Spot to earn risk free
arbitrage gain of ₹ 6.
Proof of Arbitrage:
Particulars Stock Amount
Buy PO Ex. Price = ₹ 100 (14)
Buy Stock in spot +1 (80)
Exercise PO -1 100
Net Arbitrage Gain 6
(ii) Since Actual VP (₹ 23) > Fair VP (₹ 20), therefore, Put Option is
overvalued. Hence, we will Sell PO & Sell in Spot to earn to risk free
arbitrage gain of ₹ 3.
Proof of Arbitrage:
Particulars Stock Amount
Sell PO Exercise Price = ₹ 100 23
PO Exercised on us +1 (100)
Sell in spot -1 80
Net Arbitrage Gain ₹ 3
CA, CFA(USA), CPA(USA) Praveen Khatod (Best Faculty in India for SFM & COST(SCM) 15
Q.61. The shares of Wipro Ltd. are selling at ` 550 per share…….
Solution:
(i) Pay off table for holder of Call Option
Exercise Price Stock Price Gross Payoff Less: Premium
Paid
Net Pay
Off
560 500 0 -40 -40
560 520 0 -40 -40
560 540 0 -40 -40
560 560 0 -40 -40
560 580 20 -40 -20
560 600 40 -40 0
560 620 60 -40 20
560 640 80 -40 40
(ii) Pay off graph for Mr. Balwant:
(iii) Pay off table for Writer of Call Option:
Exercise Price Stock Price Premium
received
Less: Gross Payoff Net Pay Off
560 500 40 0 40
560 520 40 0 40
560 540 40 0 40
560 560 40 0 40
560 580 40 -20 20
560 600 40 -40 0
560 620 40 -60 -20
560 640 40 -80 -40
CA, CFA(USA), CPA(USA) Praveen Khatod (Best Faculty in India for SFM & COST(SCM) 16
(iv) Pay off graph for Call Writer:
Q.62. The CMP of TCS Computers Ltd. is ` 120. Mr. Raju buys three……
Solution:
(i) Pay off table for holder of Put Option
Exercise Price Stock Price Gross
Payoff
Less:
Premium
Paid
Net Pay Off
110 85 25 -8 17
110 90 20 -8 12
110 95 15 -8 7
110 100 10 -8 2
110 105 5 -8 -3
110 110 0 -8 -8
110 115 0 -8 -8
110 120 0 -8 -8
110 125 0 -8 -8
CA, CFA(USA), CPA(USA) Praveen Khatod (Best Faculty in India for SFM & COST(SCM) 17
(ii) Pay off graph for Mr. Raju:
(iii) Pay off table for Writer of Put Option:
Exercise Price Stock Price Premium
received
Less: Gross Payoff Net Pay Off
110 85 8 -25 -17
110 90 8 -20 -12
110 95 8 -15 -7
110 100 8 -10 -2
110 105 8 -5 +3
110 110 8 0 +8
110 115 8 +5 +8
110 120 8 +10 +8
110 125 8 +15 +8
(iv) Pay off graph for Put Writer:
CA, CFA(USA), CPA(USA) Praveen Khatod (Best Faculty in India for SFM & COST(SCM) 18
Q.65. A put and a call option each have an expiration date 6 months……
Solution:
(a) VS + VP = VC + PV of Ex Price
$9 + $2 = VC + $10
(1+0.03)
VC = 1.29
(b) VS + VP = VC + PV of Ex Price
VS = $4 + $10
(1.03) - $1
VS = 12.71
(c) VP = VC + PV of Ex Price - VS
= $5 + 10
(1.03) – 12
VP = 2.71
Q.75. A company’s share price is now $60. Six months hence……
Solution:
(a) Step-1: Calculate delta (∆)
∆ = Spread in Option Values
Spread in Stock Prices
= $ 10−$0
$75−$50
∆ = 0.40
Now, perfectly hedged position can be created in either of the following two ways:
(i) Buy 0.40 shares & Sell 1 CO or
(ii) Buy 1 CO & Sell 0.40 shares
Let us assume that we Sell 0.40 share & Buy 1 CO
CA, CFA(USA), CPA(USA) Praveen Khatod (Best Faculty in India for SFM & COST(SCM) 19
(b) Calculation of value of hedged position on maturity dates:
Possible stock
prices on maturity
Value of Shares Value of CO Net Inflow/
(Outflow)
$ 75 (30)
[0.4 shares x $ 75]
+10 ($20)
$ 50 (20)
[0.4 shares x $ 50]
- ($20)
The value of perfectly hedged position would be $20 outflow irrespective of the
stock price outcome.
(c) PV of Guaranteed Outcome:
= − (−$20)
1.03
= $19.42
Calculation of VC today: + ∆ SO – VC = PV of guaranteed outcome
0.40 x $60 – VC = +19.42
VC = $4.58
Q.77. In above problem, calculate the value of the European put……
Solution:
Alternative-1:
VP Probability VP x P
0 .125 0
0 .125 0
0 .125 0
20 .125 2.5
0 .125 0
20 .125 2.5
20 .125 2.5
50 .125 6.25
VP on maturity 13.75
Calculation of PV of VP:
VP = 13.75
(1.0010)3
= 13.71
Alternative-2:
VS + VP = VC + PV of Ex Price
5000 + VP = 8.72 + 5020
(1.0010)3
VP = 13.69
CA, CFA(USA), CPA(USA) Praveen Khatod (Best Faculty in India for SFM & COST(SCM) 20
Q.79. A company’s stock is currently traded in the market at ` 80…….
Solution:
We will calculate VC on each & every node & compare its value with all the subsequent
nodes then select the highest one.
After 1
Year
After 2
Year
If option is exercised
after 1 Year
If option is exercised
after 2 Year
Vc (Max of
both Vc
88
VC = 13
96.8
VC = 21.8
13 x 0.90
(1.08)1
= 10.83
[21.8 x 0.90+4.2 x 0.10] x 0.90
(1.08)2
= 15.46
15.46 79.2
VC = 4.2
72
VC = 0
79.2
VC = 4.2
0 x 0.10
(1.08)1
= 0
[4.2 x 0.90+0 x 0.10] x 0.10
(1.08)2
= 0.32
0.32 64.8
VC = 0
VC as of today 15.78
Calculation of probabilities:
Rf = % Upside x P + % downfall x (1 - P)
0.08 = .10 P + (-.10) (1 - P)
0.08 = .10 P - .10 + 0.10P
0.18 = 0.20P
P = .90
1 – P = 0.10
CA, CFA(USA), CPA(USA) Praveen Khatod (Best Faculty in India for SFM & COST(SCM) 21
Q.81. From the following data for certain stock, find the value of a call option……
Solution:
Applying the Black Scholes Formula,
Value of the Call option now:
C = SN (d1) – Ke(- rt) N(d2)
d1 = Ln (S/K) + (r + σ2 / 2) t
σ√t
d2 = d1 - σ√t
d1 = Ln (1.0667) + (12%+(0.08))
0.5
.40 √0.5
= 0.0645+(0.2)0.5
0.40 x 0.7071
= 0.1645
0.2828
= 0.5817
d2 = 0.5817 – 0.2828
= 0.2989
Nd1 = N (0.5817)
= 0.7195
Nd2 = N (0.2989)
= 0.6175
C = SO x N(d1) - E x N(d2)
ert
= 80 x Nd1 - 75
1.0060 x Nd2
= 80 x 0.7195 - 75 x 0.6175
1.0060
= 57.56 - 74.55 x 0.6175
= 57.56 - 46.04
= ₹ 11.52
Where,
C = Theoretical call premium
S = Current stock price
t = time until option expiration
K = option striking price
r = risk-free interest rate
N = Cumulative standard normal distribution
e = exponential term
σ = Standard deviation of continuously compounded
annual return.
Ln = natural logarithm
CA, CFA(USA), CPA(USA) Praveen Khatod (Best Faculty in India for SFM & COST(SCM) 22
Q.86. The market received rumour about ABC corporation’s tie up…..
Solution:
Cost of Call and Put Options
= (₹ 2 per share) x (100 share call) + (₹ 1 per share) x (100 share put)
= ₹ 2 x 100 + 1 x 100
= ₹ 300
(i) Price increases to ₹43. Since the market price is higher than the strike price of the
call, the investor will exercise it.
Ending position = (- ₹ 300 cost of 2 option) + (₹ 1 per share gain on call) x 100
= - ₹ 300 + 100
Net Loss = - ₹ 200
(ii) The price of the stock falls to ₹ 36. Since the market price is lower than the strike
price, the investor may not exercise the call option.
Ending Position = (- ₹ 300 cost of 2 options) + (₹4 per stock gain on put) x 100
= - ₹ 300 + 400
Gain = ₹ 100
Q.87. Mr. A purchased a 3-month call option for 100 shares in XYZ Ltd…..
Solution:
Since the market price at the end of 3 months falls to ₹ 350 which is below the exercise
price under the call option, the call option will not be exercised. Only put option
becomes viable.
₹
The gain will be:
Gain per share (₹ 450 - ₹ 350) 100
Total gain per 100 shares 10,000
Cost or premium paid (₹ 30 x 100) + (₹ 5 x 100) 3,500
Net gain 6,500
CA, CFA(USA), CPA(USA) Praveen Khatod (Best Faculty in India for SFM & COST(SCM) 23
Q.88. An investor purchased Reliance November Futures (600 shares lot size)……
Solution:
Particulars Computation Amount
Futures
Gain on settlement of futures
(1180 – 1150) x 600 shares x 1 lot +18000
Transaction cost (brokerage) on
purchase of Futures
1150 x 600 x 0.045% (310.50)
Transaction cost (brokerage) on sale
of Futures
1180 x 600 x 0.045% (318.60)
Net gain on Futures 17370.90
Call Option
Loss on premium of CO (16 – 10) x 600 shares (3600)
Brokerage on Selling CO (1190 – 10) x 0.045% x 600 shares (318.60)
Brokerage on Buying CO (1190 - 16) x 0.045% x 600 shares (316.98)
Net Loss on Options (4235.58)
Overall profit for investor 13135.32
Solution of Options Strategy related questions
89. Mr. Ramesh owns 10,000 shares……
Solution:
Since, Mr Ramesh own 10,000 Shares and feels that due to bad news stock price may
fall then he should do hedging in order to protect his spot position.
If he is highly bearish then he should Buy Put Option.
Alternatively, If he is mildly bearish then he should Sell Call Option.
90. A highly diversified portfolio….
Solution:
Current value of portfolio `15 lakhs, B=0.50 Put Option with Ex. Price = `9500, Premium
= `1000, Lot Size = 50
No. of Options to be traded = 15,00,000 x 0.50
9500 x 50 = 1.579 ~ 2 Put Options should be bought
CA, CFA(USA), CPA(USA) Praveen Khatod (Best Faculty in India for SFM & COST(SCM) 24
91. Rakesh is bullish to a limited extent
Solution:
Given
Call option Ex. Price Premium Put Option Ex. Price Premium
`1100 `55 `1000 `45
`1200 `20 `900 `15
Two strategies are possible in the bullish market
(a) Buy CO EL & Sell CO EH
(b) Buy PO EL & Sell PO EH
800 900 1000
0
1100
0
1200
0
1300
0
(+65) (+65)
Premium
Buy CO EL 1100 55 Paid
Sell CO EH 1200 20 Recd
35 Net Paid
(-35) (-35) (-35) (-35) -40
-30
-20
-10
0
10
20
30
40
50
60
70
N
e
t
p
a
y
o
f
f
(a)
Stock prices on maturity date
800 900 1000
0
1100
0
(+30) (+30)
Ex. Premium Premium
Buy PO EL 900 15 Paid
Sell PO EH 1000 45 Recd
30 Net Recd
(-70) (-70) -80
-60
-40
-20
0
20
40
60
80 N
e
t
p
a
y
o
f
f
(b)
Stock price on maturity date
CA, CFA(USA), CPA(USA) Praveen Khatod (Best Faculty in India for SFM & COST(SCM) 25
92. Gangaram is bearish on the stocks of Geodesic……
Solution:
Bearish
Two strategies are possible in the bearish market
(a) Sell CO EL & Buy CO EH
(b) Sell PO EL & Buy PO EH
(a) Sell CO EL & Buy CO EH
(-7) (-7) (-7)
100 110 120 130
(+3) (+3)
Ex. Premium Premium
Sell CO Ex. PriceL `110 5 Receive
Buy CO Ex. PriceH `120 2 Paid
3 Receive
-15
-10
-5
0
5
10
15
N
e
t
p
a
y
o
f
f
Stock price on maturity date 140
(-2) 80 90 100 110
(+8) (+8)
Ex. Premium Premium
Sell PO EL 90 2 Receive
Buy PO EH 100 4 Paid
2 Paid
-15
-10
-5
0
5
10
15
N
e
t
p
a
y
o
f
f
Stock price on maturity date 120
(b) Sell PO EL & Buy PO EH
(-2) (-2)
CA, CFA(USA), CPA(USA) Praveen Khatod (Best Faculty in India for SFM & COST(SCM) 26
93. For each of the following cases, name the strategy adopted….
Solution:
Type of
option
Ex. Price
(buy)
Ex. Price
(sell)
Premium
(buy)
Premium
(sell)
(i) Call option 60
(EL)
70
(EH)
9 4 Buy CO EL & sell CO EH
= Bull Spread
(ii) Call option 80
(EH)
75
(EL)
2 6 Buy CO EH & sell CO EL
= Bear Spread
(iii) Put option 70
(EH)
65
(EL)
9 5 Buy PO EH & sell PO EL
= Bear Spread
(iv) Put option 50
(EL)
60
(EH)
4 11 Buy PO EL & sell PO EH
= Bull Spread
(i) Bull spread: - Buy CO EL & sell CO EH
Ex. Price Premium Stock Price Gross Pay Net Pay Off
60 9 Paid 60 0 -9
70 4 Recd 70 0 +4
5 Paid Net -5
(ii) Bear Spread :- Buy CO EH & sell CO EL
Ex. Price Premium Stock Price Gross Pay Off Net Pay off
80 2 Paid 80 0 -2
75 6 Receive 75 0 +6
+4
50 60 70 80
(+5) (+5)
(-5) (-5) -10
-5
0
5
10
N
e
t
p
a
y
o
f
f
Stock price on maturity date
BEP
(-1) (-1) 70 75 80 85
(+4) (+4)
-10
-5
0
5
10
N
e
t
p
a
y
o
f
f
Stock price on maturity date
BEP
CA, CFA(USA), CPA(USA) Praveen Khatod (Best Faculty in India for SFM & COST(SCM) 27
(iii) Bear Spread :- Buy PO EH & Sell PO EL
Ex. Price Premium Stock Price Gross Pay-off Net payoff
Buy 70 9 Paid 70 0 -9
Sell 65 5 Receive 65 0 +5
-4 Paid
(iv) Bear Spread :- Buy PO EL & Sell PO EH
Ex. Price Premium Stock Price Gross Pay off Net pay off Buy 50 4 paid 50 0 -4
Sell 60 11 Receive 60 0 +11
+ 7
(-4) (-4) 60 65 70 75
(+1) (+1)
-10
-5
0
5
10
N
e
t
p
a
y
o
f
f
Stock price on maturity date
BEP
40 50 60 70
(+7) (+7)
(-3) (-3)
-10
-5
0
5
10
N
e
t
P
a
y
o
f
f
Stock price on maturity date
BEP
CA, CFA(USA), CPA(USA) Praveen Khatod (Best Faculty in India for SFM & COST(SCM) 28
94. A call option on Adani Exports Ltd……
Solution:
Call option EP `50 Premium `4
Put option EP `50 Premium `5
(a) Buy a CO & Buy a PO with same Ex. Price
Buy CO `50 `4 paid
Buy PO `50 `5 paid
`9 net paid
(b) If you expect stagnant markets
Sell CO Ex. price `50 premium `4 receive
Sell PO Ex. Price `50 premium `5 receive
`9 receive net
40 50 60 70
(+11)
-10
-5
0
5
10
N
e
t
p
a
y
o
f
f
Stock price on maturity date
(-9)
(+1)
40 50 60 70
(+9)
-10
-5
0
5
10
N
e
t
p
a
y
o
f
f
Stock price on maturity date (-1)
(-11)
(-1)
(+1)
(-11)
(+11)
CA, CFA(USA), CPA(USA) Praveen Khatod (Best Faculty in India for SFM & COST(SCM) 29
95. A call option on ABB Ltd. with an exercise…..
Solution:
CO Ex. Price `50 premium `4
PO Ex. Price `45 premium `3
(a) If you expect high volatility
Buy CO Ex. Price `50 premium `4 paid
Buy PO Ex. Price `45 premium `3 paid
`7 net paid
(b) If you expect stagnant markets
Sell CO ex. Price `50 premium `4 receive
Sell PO ex. Price `45 premium `3 receive
`7 net receive
40 45 50 55
(+3)
-10
-5
0
5
10
N
e
t
p
a
y
o
f
f
Stock price on maturity date
(-2) (-2)
(-7) (-7)
60
40 45 50 55
(+7)
-10
-5
0
5
10
N
e
t
p
a
y
o
f
f
Stock price on maturity date
(-3)
(+2)
(+7)
60
(+2)
CA, CFA(USA), CPA(USA) Praveen Khatod (Best Faculty in India for SFM & COST(SCM) 30
96. An investor anticipates bearish volatility…..
Solution:
Strip – Bearish Volatility
Qty. Ex. Price Premium
Buy PO 2 `100 `7 * 2 Paid
Buy CO 1 `100 `9 * 1 Paid
`23 Net Paid
Pay off table
Ex. Price Stock Price Premium Gross Pay-off Qty Net Pay-off
PO `100 `100 `7 0 2 -14
CO `100 `100 `9 0 1 -9
-23 Net Paid
98. An investor notices a call option…..
Solution:
Straps
Qty. Total premium
Buy CO Ex. Price `80 premium `6 2 12 paid
Buy PO Ex. Price `80 premium `7 1 7 paid
19 net paid
30
80 90 100 110
(+17)
-20
-10
0
10
20
N
e
t
P
a
y
o
f
f
Stock price on maturity date
(-23)
(-13)
-30
120 (-3) (-3)
70 80 90
(-9) -20
-10
0
10
20
N
e
t
p
a
y
o
f
f
Stock price on maturity date
(-19)
(+1)
CA, CFA(USA), CPA(USA) Praveen Khatod (Best Faculty in India for SFM & COST(SCM) 31
99. A stock is selling at ` 62……
Solution:
Butterfly
For volatile market – using CO
Premium Qty. Total premium
Sell CO EL `55 10 receive 1 10
Buy CO EM `60 7 paid 2 14
Sell CO EH `65 5 receive 1 5
1 net receive
For volatile market – using PO
Qty Total premium
Sell PO EL 70 Prem 6 receive 1 6
Buy PO EM 75 Prem 9 Paid 2 18
Sell PO EH 80 Prem 14 receive 1 14
2 Net receive
50 55 60 65
(+1)
-10
-5
0
5
10
N
e
t
p
a
y
o
f
f
Stock price on maturity date (-4)
(+1)
70
(+1) (+1)
60 65 70 75
(+2)
-5
0
5
N
e
t
p
a
y
o
f
f
Stock price on maturity date (-3)
(+2)
80
(+2) (+2)
85
CA, CFA(USA), CPA(USA) Praveen Khatod (Best Faculty in India for SFM & COST(SCM) 32
For stable market – using CO
Qty Premium Total premium
Buy CO EL 1 55 10 10
Sell CO EM 2 60 7 14
Buy CO EH 1 65 5 5
-1 Net paid
For stable market – using PO
Qty Premium Total premium
Buy PO EL 1 70 6 6
Sell PO EM 2 75 9 18
Buy PO EH 1 80 14 14
-2 Net paid
(-1) 55 50 60 65
-10
-5
0
5
10
N
e
t
p
a
y
o
f
f
Stock price on maturity date
(-1)
70
(+4)
(-1) (-1)
65 70 75 80
-10
-5
0
5
10
N
e
t
p
a
y
o
f
f
Stock price on maturity date
(-2)
85
(+3)
(-2) (-2) (-2)
CA, CFA(USA), CPA(USA) Praveen Khatod (Best Faculty in India for SFM & COST(SCM) 33
FOREIGN EXCHANGE RISK
MANAGEMENT Q.11. A New Delhi Banker has offered….
Solution:
1 CY£ = ₹ 98.6033
1 NZ$ = ₹ 31.0021
(i) NZD $ / CYP i.e.
NZ$
CY£ =
NZ$
₹ x
₹
CY£
= 1
31.0021 x 98.6033
= 3.1805
1 CY£ = NZ$ 3.1805
(ii) CYP / NZD i.e.
CY£
NZ$ =
CY£
₹ x
₹
NZ$
= 1
98.6033 x 31.0021
= 0.3144
1 NZ$ = CY£ 0.3144
Q.15. Consider the following quotations in Mumbai…..
Solution:
1 AED = ₹ 13.75
1 SEK = ₹ 6.25
1 NZD = ₹ 29
1 INR = € 0.0148
(a) 1 AED = SEK 2.20
SEK
AED =
SEK
INR x
INR
AED
= 1
6.25 x 13.75
= 2.20
(b) 1 NZD = € 0.4292
€
NZD =
€
INR x
INR
NZD
= 0.0148 x 29
= 0.4292
CA, CFA(USA), CPA(USA) Praveen Khatod (Best Faculty in India for SFM & COST(SCM) 34
Q.16. Consider the following and determine the cross rates….
Solution:
1. 1 NOK = ₹ 6.44
1 GBP = ₹ 47.10
1 GBP = NOK 7.3137
NOK
GBP =
NOK
₹ x
₹
GBP
= 1
6.44 x 47.10
= 7.3137
2. 1 AUD = USD 0.6051
1 AUD = USD 0.6051
(a) 1 INR = USD 0.0209
USD
INR =
USD
AUD x
AUD
INR
= 0.6051 x 1
28.97
= 0.0209
(b) 1 USD = INR 47.8764
INR
USD =
INR
AUD x
AUD
USD
= 28.97 x 1
0.6051
= 47.8764 ~ 47.88
3. 1 GBP = INR 74.5 – 75.00
1 GBP = $ 1.62 – 1.63
1 $ = INR 45.7055
Bid (INR
$) = Bid (
INR
GBP) x Bid (
GBP
$)
= 74.5 x 1
1.63
= 45.7055 ~ 45.71
Ask (INR
$) = Ask (
INR
GBP) x Ask (
GBP
$)
= 75 x 1
1.62
= 46.2963 ~ 46.30
CA, CFA(USA), CPA(USA) Praveen Khatod (Best Faculty in India for SFM & COST(SCM) 35
Q.17. Suppose the exchange rate between US dollar and the French franc…..
Solution:
$ 1 = FF 5.90
1 £ = $ 1.50
1 £ = FF 8.85
FF
£ =
FF
$ x
$
£
= 5.90 x 1.50
= 8.85
Q.21. Calculate the merchant rates given the following interbank…..
Solution:
1. Merchant Bank Bid Rate = Interbank Bid Rate – Buying Margin
= 66.3250 – 0.030%
= ₹ 66.3051 ~ 66.31
Merchant Bank Ask Rate = Interbank Ask Rate + Selling Margin
= 66.4525 + 0.130%
= 66.5389 ~ 66.54
1 GBP = ₹ 66.31 – 66.54
2. Merchant Bank Bid Rate = 32.2525 – 0.025%
= 32.244 ~ 32.24
Merchant Bank Ask Rate = 32.3500 + 0.125%
= 32.3904 ~ 32.39
1 DEM = ₹ 32.24 – 32.39
3. Merchant Bank Bid Rate = 44.44000 – 0.080%
= 44.4044 ~ 44.04
Merchant Bank Ask Rate = 44.5100 + 0.150%
= 44.5768 ~ 44.58
1$ = ₹ 44.04 – 44.58
CA, CFA(USA), CPA(USA) Praveen Khatod (Best Faculty in India for SFM & COST(SCM) 36
Q.23. An all-inclusive 15-day trip covering Paris-Rome-Vienna…….
Solution:
Particulars Amount in
Foreign Currency
Relevant Rate Amount in ₹
Traveler’s cheque $ 15,500 ₹ 47.60 737800
Amount paid to travel agent - - 25000
Gifts – Europe € 1200 ₹ 50.98 61176
Gifts - London £ 750 ₹ 77.11 57832.5
Contingency Amount $ 275 ₹ 48.23 13263.25
Total tour cost ₹ 895071.75
Q.40. Deep Sea Fishing Co Ltd concluded an export order for….
Solution:
(a) Estimating rupee inflow for the contract value
Contract Value 1,825 x 10 18,250 USD
Down Payment 18,250 x 1/4 4,562.50 USD
Installments 18,250 x 3/4 13,687.50 USD
Payment Dollars Rate INR
Down Payment 4,562.5 45.5 207,594
Installments 13,687.5 45.4 621,413
829,007
(b) Actual receipt amounted to ₹ 8,28,457 as shown in the table below. The actual
receipts have been lower than the amount estimated on contract date.
Computing actual receipts
Nature of payment Dollar Amount Rate Rupees
Advance payment 4,562.50 45.50 2,07,593
Shipment 1 1,368.75 45.40 62,141
Shipment 2 1,368.75 45.30 62,004
Shipment 3 1,368.75 45.20 61,867
Shipment 4 1,368.75 45.30 62,005
Shipment 5 1,368.75 45.20 61,867
Shipment 6 1,368.75 45.00 61,594
Shipment 7 1,368.75 45.50 62,278
Shipment 8 1,368.75 45.70 62,552
Shipment 9 1,368.75 45.60 62,415
Shipment 10 1,368.75 45.40 62,141
8,28,457
(c) Difference: ₹ 550. It arises on account of differences in exchange rates as
between the date on which the transaction is initially recorded, and the date(s)
on which payments are received. This is inherent in any transaction involving
foreign currency.
(d) Type of Risk: The type of exchange risk involved is known as Transaction Risk.
CA, CFA(USA), CPA(USA) Praveen Khatod (Best Faculty in India for SFM & COST(SCM) 37
Q.46. IG Ltd. has exported goods worth Kuwaiti Dinars 20,000……..
Solution:
Since it is a case of Exporter, therefore, Relevant rate will be Investment Rate
(a) Evaluation of both the alternatives
Particulars If Lead the Receipt If Lag the Receipt
Amount Receivable KWD 20000 KWD 20000
Conversion Rate 1 KWD = ` 175 1 KWD = ` 176.75
Amount in ` terms ` 35,00,000 ` 35,35,000
Add: Interest @ 6% p.a. for 90 days ` 52500
[` 35,00,000 x 6% x
90/360]
-
Total Amount at the end of 90 days ` 3552500 ` 35,35,000
Decision: It is better to Lead the Receipt since it results in Incremental inflow of `
17,500.
(b) Amount Receivable at the end of 90 days, If Lead = ` 35,00,000x (1 + 0.03 x 90/360) = ` 35,26,250.
Decision: It is better to Lag the Receipt since it results in Incremental Inflow of `
8,750
Q.47. An Indian importer has to settle an import for $ 1,30,000……..
Solution:
If importer pays now, he will have to buy US$ in Spot Market by availing overdraft
facility. Accordingly, the outflow under this option will be
₹
Amount required to purchase $130000 [$130000 x ₹ 48.36] 6286800
Add: Overdraft Interest for 3 months @15% p.a. 235755
6522555
If importer makes payment after 3 months then, he will have to pay interest for 3
months @ 5% p.a. for 3 month along with the sum of import bill. Accordingly, he will
have to buy $ in forward market. The outflow under this option will be as follows:
$
Amount of Bill 130000
Add: Interest for 3 months @5% p.a 1625
131625
Amount to be paid in Indian Rupee after 3 month under the forward purchase contract
₹ 6427249 (US$ 131625 x ₹ 48.83)
Since outflow of cash is least in (ii) option, it should be opted for.
CA, CFA(USA), CPA(USA) Praveen Khatod (Best Faculty in India for SFM & COST(SCM) 38
Q.49. The following 2-way quotes appear in the foreign exchange market…..
Solution:
(i) US $ required to get ₹ 25 lakhs after 2 months at the Rate of ₹ 47/$
Therefore, ₹ 25,00,000
₹ 47 = US $ 53191.489
(ii) ₹ required to get US$ 2,00,000 now at the rate of ₹ 46.25/$
Therefore, US $ 200,000 x ₹ 46.25 = ₹ 92,50,000
(iii) Encashing US $ 69000: now vs 2 month later
Proceed if we can encash in open mkt $ 69000 x ₹ 46 = ₹ 31,74,000
Opportunity gain
= 31,74,000 x10
100 x
2
12 ₹ 52 900
Likely sum at end of 2 months 32,26,900
Proceeds if we can encash by forward rate:
$ 69000 x ₹ 47.00 32,43,000
It is better to encash the proceeds after 2 months and get opportunity gain.
Q.55. An exporter expects the next remittance of €115,000/-…….
Solution:
By taking forward cover the exporter freezes his receipt at € 1,15,000 x ₹ 67 = ₹
77,05,000.
• If the spot rate turns out to be higher at ₹ 68 he misses out on receiving the extra
₹ 1,15,000. This is because under the forward contract he is obliged to sell at ₹
67.
• If the spot rate was lower at ₹ 66 and had he not taken forward cover, he would
have received Re 1 per € less, i.e. he would have received ₹ 1,15,000 less.
Hence, he has gained by forward cover.
CA, CFA(USA), CPA(USA) Praveen Khatod (Best Faculty in India for SFM & COST(SCM) 39
Q.58. You, a foreign exchange dealer of your bank, are informed that……
Solution:
Amount realized on selling Danish Kroner 10,00,000 at ₹ 6.5150 per Kroner = ₹
65,15,000.
Cover at London:
Bank buys Danish Kroner at London at the market selling rate.
Pound sterling required for the purchase (DKK 10,00,000 + DKK 11.4200) = GBP
87,565.67 Bank buys locally GBP 87,565.67 for the above purchase at the market
selling rate of ₹ 74.3200.
The rupee cost will be = ₹ 65,07,88
Profit (₹ 65,15,000 - ₹ 65,07,881) = ₹ 7,119
Cover at New York:
Bank buys Kroners at New York at the market selling rate.
Dollars required for the purchase of Danish Kroner (DKK10,00,000/7.5670)
= USD 1,32,152.77
Bank buys locally USD 1,32,152.77 for the above purchase at the market selling rate
of ₹ 49.2625.
The rupee cost will be = ₹ 65,10,176.
Profit (₹ 65,15,000 - ₹ 65,10,176) = ₹ 4,824
The transaction would be covered through London which gets the maximum profit of ₹
7,119 or lower cover cost at London Market by (₹ 65,10,176 - ₹ 65,07,881) = ₹ 2,295
Q.60. You are expecting to receive US $ 500,000 any time between…….
Solution:
You are going to receive $. The money may reach you either three months or six
months from today. When you approach the bank with this issue the Bank will take a
conservative view, and will reckon that the worst happens.
Since in the transaction you will sell and the bank will buy dollars, the relevant rate is
Bid rate for $ namely 67.65 and 67.50. The worse rate is ₹ 67.50 (Remember, banker
always wins). This will give you fewer rupees than the rate of 67.65. The bank will
quote a rate of 67.50, for a six month forward option contract, with an option for you to
deliver $ between three and six months.
CA, CFA(USA), CPA(USA) Praveen Khatod (Best Faculty in India for SFM & COST(SCM) 40
Q.61. You are expecting to pay SGD 100,000 any time between three and six months……
Solution:
You are going to PAY SGD any time between three months and six months from today.
When you approach the bank with this issue the Bank will take a conservative view,
and will reckon that the worst happens.
Since in the transaction you will buy and the bank sell buy SGD, the relevant rate is
Ask rate for SGD namely 55.00 and 55.35. The worse rate is ₹ 55.35 (Remember,
banker always wins). This will make you pay more rupees than the rate of 55.00. The
bank will quote a rate of 55.35 for a six-month forward option contract, with an option
for you to buy SGD between three and six months.
Q.63. The finance director of P Ltd., has been studying exchange rates…….
Solution:
FORWARD MARKET HEDGE:
Since, we are an importer and we have to pay $ 51 lakh in 3 months, therefore, relevant
rate is Ask rate i.e. 1 $ = ₹ 45
Outflow under forward = $ 51,00 000 x ₹ 45
Cover = ₹ 22,95,00,000
MONEY MARKET HEDGE:
Step-1: Identify
Since, we are an importer, therefore we have FC liability
Step-2: Create
We will create FC denominated asset equivalent to PV of FC denominated liability
discounted at USA deposit rates.
= $ 51,00,000
(1+0.08 x 3/12)
= $ 5000000
Step-3: Borrow
Borrow in India. Since after borrowing ₹ we have to Sell ₹ and Buy $ therefore,
Relevant Rate is Ask Rates.
CA, CFA(USA), CPA(USA) Praveen Khatod (Best Faculty in India for SFM & COST(SCM) 41
1$ = ₹ 40 – 42
= $ 50,00,000 x ₹ 42
= ₹ 21 crores
Step-4: Convert
Convert ₹ to $ at spot ask rate.
= $ 21 crores
₹ 42
= $ 50,00,000
Step-5: Invest
Invest in USA, $ 50,00,000 at deposit rate i.e. 8% p.a. for 3 months
Step-6: FV of Borrowings
= ₹ 21,00,00,000 + (₹ 21,00,00,000 x 0.16 x 3
12)
= ₹ 21,84,00,000
Step-7: Settle
Use the proceeds from deposit in USA to meet the import obligation.
Decision: Company should opt for money market hedge strategy, this would meet the
expectation of finance director to achieve a cost not more than ₹ 22,00,00,000.
Q.67. ABC Technologic is expecting to receive a sum of US$ 4,00,000…….
Solution:
The company can hedge position by selling future contracts as it will receive amount
from outside.
Number of Contracts = $ 4,00,000
$ 1,000 = 40 contracts
Gain by trading in futures = (₹ 45 - ₹ 44.50) 4,00,000 = ₹ 2,00,000
Net Inflow after 3 months = ₹ 44.50 x ₹ 4,00,000 + 2,00,000 = ₹ 1,80,00,000
Effective Price realization = ₹ 1,80,00,000
₹ 4,00,000 = ₹ 45 per US$
CA, CFA(USA), CPA(USA) Praveen Khatod (Best Faculty in India for SFM & COST(SCM) 42
Q.72. On march 1, 2015, B Ltd. bought from a foreign firm electronic equipment…….
Solution:
Option (A): Forward hedge
Cost at forward rate = $1,00,000 (9,00,000/9)
Cost at current spot rate = $ 90,000 (9,00,000/10)
Exchange Loss = $ 1,00,000 - $ 90,000 = $ 10,000
Tax shield on exchange loss = $10,000 x 0.40 = $ 4000
Net Cost of using forward market = $ 1,00,000 - $ 4000 = $ 96000
Option (B): Money Market Hedge
Post tax interest rates in US and LC are 7.2% and 4.8% respectively. Each LC
deposited at 4.8% now grows into LC 1.012 in 3 months.
A Inc, should buy and invest LC 8,89,328 (9,00,000/1.012) for 3 months
Spot purchase and deposit at 4.8% (LC) 8,89,328
Payment accumulated of LC deposits to make payment to LC Supplier 9,00,000
Exchange rate for spot purchase $1 = 10 LC
Borrow US $ at 7.2% to finance spot purchased 88,932.80
Repay $ loan with interest (88,932.80 x 1.018) 90,533.59
Option (C) No hedge
Cost at future spot Rate = $ 1,12,500 (9,00,000/8)
Cost at Current spot rate = $ 90,000 (9,00,000/10)
Exchange loss = $ 1,12,500 - $ 90,000 = $ 22,500
Tax shield on exchange loss = $ 22,500 x 0.40 = $ 9000
Net cost if not hedged = $ 1,12,500 - $ 9,000 = $ 1,03,500.
The money market hedge (Option B) is best.
CA, CFA(USA), CPA(USA) Praveen Khatod (Best Faculty in India for SFM & COST(SCM) 43
Q.73. PQ an UK company, has a substantial portfolio of its trade…..
Solution:
Note that this for the is not a pure money market hedge, as no discounting takes place
in order for the amount borrowed to equal the amount due.
(i) Method 1 £
Borrow PV of $ 5 m now and convert into sterling
($ 5,000,000/1.035) = $ 4830918 converted at £ 1 = $ 1.4455 3,342,039
Method 2
Sell $ 5m forward at 1.4165: that is for 3,529,827
Borrow PV of £ 3,529,827 discounted at 5.75% that is
(£ 3,529,827 / 1.0575) 3,337,898
Method 1 gives £ 4,141 more than Method 1, therefore, Method 1 is preferable.
(ii) The spot rate is today's rate. In this question, $ 1.4455 could be exchanged for
£ 1 today.
The forward rate is the rate which could be agreed for delivery at some specified
future date. In this question the bank is agreeing to purchase $ 1.4165 for £ 1 in
12 months' time.
The relationship between the two is a function of interest-rate differentials. In
effect, the bank would protect its position by borrowing $ 1.4455, paying interest
at 3.5 per cent bringing it up to $ 1.4961, then, lending £1 on which it would earn
interest of 5.75 per cent, bringing it up to £ 1.0575. $ 1.4961/ £1.0575 = $ 1.4147
per pound. The bank divides by a higher figure to earn a margin.
Exchange rates and interest rates are subject to such volatility that it is not safe to
regard the forward rate as a reliable predictor of what the spot rate will be at the
appropriate future date. If future spot rates were predictable there would be no
need to hedge. However, it is argued that in the long term the various rates are
reconcilable; for example, a country with relatively high interest rates will cede
growth opportunities to others, and its economy will weaken.
(b) If the dispute is expected to be settled in due course, then the bank is likely to be willing
to extend the arrangement — but at a price which reflects the exchange rate at the
time originally specified. If there is no hope of the debt being settled, then PQ plc will
have to buy currency at the spot rate and deliver it to the bank on the agreed basis.
The actual solution could, of course, be anywhere between these two extremes, and a
`mixed' solution reached.
CA, CFA(USA), CPA(USA) Praveen Khatod (Best Faculty in India for SFM & COST(SCM) 44
Q.79. Nitrogen Ltd, a UK company is in the process of negotiating……
Solution:
(i) Receipt under three proposals
(a) Invoicing in Sterling
Invoicing in £ will produce = € 4 million
1.1770 = £ 3398471
(b) Use of Forward Contract
Forward Rate = € 1.1770 + 0.0055 = 1.1825
Using Forward Market hedge Sterling receipt would be € 4 million
1.1825 = £ 3382664
(c) Use of Future Contract
The equivalent sterling of the order placed based on future price (€ 1.1760)
= € 4.00 million
1.1760 = £ 3401360
Number of Contracts = £ 3401360
62,500 = 54 Contracts (to the nearest whole number)
Thus, € amount hedged by future contract will be = 54 x £ 62,500 = £ 3375000
Buy Future at € 1.1760
Sell Future at € 1.1785
€ 0.0025
Total profit on Future Contracts = 54 x € 62,500 x € 0.0025 = € 8438
After 6 months
Amount Received € 4000000
Add: Profit on Future Contracts € 8438
€ 4008438
Sterling Receipts
On sale of € at spot = € 4008438
1.1785 = € 3401305
(ii) Proposal of option (c) is preferable because the option (a) & (b) produces least receipts.
Alternative solution:
Assuming that 6 month forward premium is considered as discount, because generally
premium is mentioned in ascending order and discount is mentioned in descending order.
(i) Receipt under three proposals
(a) Invoicing in Sterling
Invoicing in £ will produce = € 4 milion
1.1770 = £3398471
CA, CFA(USA), CPA(USA) Praveen Khatod (Best Faculty in India for SFM & COST(SCM) 45
(b) Use of Forward Contract
Forward Rate = € 1.1770-0.0055 - 1.1715
Using Forward Market hedge Sterling receipt would be € 4 milion
1.1715 = £ 3414426
(c) Use of Future Contract
The equivalent sterling of the order placed based on future price (€ 1.1760)
= € 4.00 milion
1.1760 = £ 3401360
Number of Contracts = € 3401360
62,500 = 54 Contracts (to the nearest whole number)
Thus, € amount hedged by future contract will be = 54 x £62,500 = £3375000
Buy Future at € 1.1760
Sell Future at € 1.1785
€ 0.0025
Total profit on Future Contracts = 54 x £ 62,500 x € 0.0025 = € 8438
After 6 months
Amount Received € 4000000
Add: Profit on Future Contracts € 8438
€ 4008438
Sterling Receipts
On sale of € at spot = € 4008438
1.1785 = €3401305
(ii) Proposal of option (b) is preferable because the option (a) & (c) produces least receipts.
CA, CFA(USA), CPA(USA) Praveen Khatod (Best Faculty in India for SFM & COST(SCM) 46
Q.83. On 15th January you booked a forward sale contract for French Francs……
Solution
Since it is a case of Cancellation of Forward Contract on due date, therefore, Bank will
enter into Opposite Action with the Customer at Spot Merchant Rates.
Calculation of Cancellation Rate
Bid (₹
FFR) = Bid (
₹
$) x Bid (
$
FFR)
= 34.7900 x 1
5.0300
= ₹ 6.92
Interbank bid rate = ₹ 6.92
Less: Margin @ 0.15% = -0.15%
Merchant bank bid rate = ₹ 6.91
Original Action – Sell 1 FFR = ₹ 6.95
Opposite Action – Buy 1 FFR = ₹ 6.91
Gain 1 FFR = ₹ 0.04
Contract amount FFR 2,50,000
Total gain recoverable = ₹ 10000
from customer
Answer: Bank will recover ₹ 10000 from the customer. In addition, bank may also
recover minimum flat charges on account of cancellation request.
CA, CFA(USA), CPA(USA) Praveen Khatod (Best Faculty in India for SFM & COST(SCM) 47
Q.86. Suppose you as a banker entered into a forward purchase contract for US$ 50,000….
Solution
Since it is a case of extension of forward contract banker will cancel the original forward
contract by taking opposite action @ 5th June forward contract & will book new forward
contract for 5th July i.e. extended maturity.
Here, at the time of Cancellation, relevant rate is ask rate
Interbank Spot 5th June = 1 $ = ₹ 59.2425
Add: margin = 0.10%
Merchant bank spot 5th June ask rate = 1$ = 59.3017 ~ 59.3025
Original Action – Buy $ 1 = ₹ 59.6000
Opposite Action – Sell $ 1 = ₹ 59.3025
Loss $ 1 = ₹ 0.2975
Contract size = $ 500000
Total loss payable = ₹ 14875
Interbank 5th July bid rate = ₹ 59.6300 (bid rate)
Less: margin = 0.10%
Merchant bank 5th July bid rate = ₹ 59.5704 ~ ₹ 59.5700
Answer: Banker will pay ₹ 14875 to the customer as extension charges & will quote
new forward rate of $ 1 = ₹ 59.5700
CA, CFA(USA), CPA(USA) Praveen Khatod (Best Faculty in India for SFM & COST(SCM) 48
Q.94. The risk free rate of interest in USA is 8% p.a. and in UK is…….
Solution:
2 year Forward Rate will be calculated as follows:
F = S x e(ruk
- rus
)t
Where F = Forward Rate
S = Spot Rate
rUK = Risk Free Rate in UK
rUS = Risk Free Rate in US
t = Time
Accordingly,
F = 0.75e(0.05-0.08)2
= 0.75 x 0.9418
= 0.7064
Thus,
1 US $ = £ 0.7064
If forward rate is 1 US $ = 0.85 £ then an arbitrage opportunity exists. Take following
steps.
(a) Should borrow UK £
(b) Buy US $
(c) Enter into a short forward contract on US $
Accordingly,
The riskless profit would be
(a) Say borrow £ 0.7064e-(0.05) (2) = £ 0.6392 and invest in UK for 2 years.
(b) Now buy US $ at US $ 1e-(0.08)2 = US $ 0.8521, so that after two year
it can be used to close out the position.
(c) After two year the investment in US $ will become US $ 0.8521 e(0.08)
(2) = US $ 0.8521 x 1.1735 = 1 US $
(d) Sell this US $ for £ 0.85 and repay loan of £ 0.6392 along with interest
i.e £ 0.7064.
Thus, arbitrage profit will be
UK £ 0.85 — UK £ 0.7064 = UK £ 0.1436 say UK £ 0.144
CA, CFA(USA), CPA(USA) Praveen Khatod (Best Faculty in India for SFM & COST(SCM) 49
Q.96. Presently, the dollar is worth 140 yen in the spot market…….
Solution:
It has been assumed that we are based in Japan & hence given quotation becomes a
direct quote for us.
1+rh
1+rf =
f1
S0
1+0.04 x 360̅̅ ̅̅ ̅̅
90
1+Rf x 360̅̅ ̅̅ ̅̅90
= 138
140
Rf = 9.85% p.a.
Since, Actual Interest rate (7%) < Fair Interest rate (9.85%), therefore, an investor
should borrow in USA & Invest in japan to earn free arbitrage gain.
Step-1: Borrow: $ 100000
Step-2: Convert:
At spot rate
= $ 100000 x ¥ 140
= ¥ 14000000
Step-3: Invest: In Japan @ 4% p.a. for 90 days
Step-4: Forward cover: Enter into forward over $1 = ¥ 138
Step-5: FV of investment:
= ¥ 14000000 x (1 + 0.04 x 90/360)
= ¥ 14140000
Step-6: Re-convert:
At forward rate agreed earlier
$ 102463.77 = ¥ 14140000
¥ 138
Step-7: Repayment:
The borrowed amount along with interest
= $ 100000 x 1 + .07 x 90
360
= $ 101750
Step-8: Count arbitrage gain:
= $ 102463.77 - $ 101750
= $ 713.77 or ¥ 98500 ($ 713.77 x ¥ 138)
CA, CFA(USA), CPA(USA) Praveen Khatod (Best Faculty in India for SFM & COST(SCM) 50
Q.98. This is the beginning of a new accounting year……….
Solution:
Euroland opportunities: Spot 1 £ = € 1.50 (Indirect quote)
1st year
= 1+rh
1+rf =
S0
F1
= 1+0.06
1+0.05 =
1.50
F1
= F1 = 1.4858
£ 1 = € 1.4858
2nd year
1+rh
1+rf =
F1
F2 alternatively,
(1+rh)2
(1+rf)2 = S0
F2
1.06
1.05 =
1.4858
F2 or,
1.1236
1.1025 =
1.50
F2
F2 = 1.4717 F2 = 1.4718
£ 1 = € 1.4717
3rd year
1+rh
1+rf =
F2
F3
1+0.06
1+0.05 =
1.4717
F3
F3 = 1.4578
1 £ = € 1.4578
4th year
1+rh
1+rf =
F3
F4
1+0.06
1+0.05 =
1.4578
F4
F4 = 1.4440
1 £ = € 1.4440
CA, CFA(USA), CPA(USA) Praveen Khatod (Best Faculty in India for SFM & COST(SCM) 51
USA opportunity: Spot 1 £ = $ 1.60 (Indirect quote)
1st year 1+rh
1+rf =
S0
F1
1+0.06
1+0.07 =
1.60
F1
F1 = 1.6150
2nd year 1+rh
1+rf =
F1
F2
1.06
1.07 =
1.6150
F2
F2 = 1.6302
£ 1 = $ 1.6302
3rd year 1+rh
1+rf =
F2
F3
1.06
1.07 =
1.6302
F3
F3 = 1.6456
£ 1 = $ 1.6456
CA, CFA(USA), CPA(USA) Praveen Khatod (Best Faculty in India for SFM & COST(SCM) 52
Q.101. The United States Dollar is selling in India at ` 45.50…….
Solution:
(i) According to Interest Rate Parity Theorem, a country whose interest rates are
comparatively lower its currency will appreciate. On the contrary, whose rates
are higher will depreciate. In the present case, USA $ will appreciate & ₹ will
depreciate.
(ii) Using Interest Rate Parity Theorem,
1+rh x n/12
1+rf x n/12 =
F1
S0
1+0.08 x 6/12
1+0.02 x 6/12 =
F1
45.50
F1 = 46.85
1 $ = ₹ 46.85
(iii) % app/dep
On LHS currency i.e. $ = F1−S0
S0 x 100 x
12
n
= 46.85−45.50
45.50 x 100 x
12
6
= 5.93% p.a. Premium on $
On RHS currency i.e. ₹ = S0−F1
F1 x 100 x
12
n
= 45.50−46.85
46.85 x 100 x
12
6
= -5.76% p.a. Discount on ₹
CA, CFA(USA), CPA(USA) Praveen Khatod (Best Faculty in India for SFM & COST(SCM) 53
Q.102. Spot rate 1 US $ =` 48.0123….
Solution:
Spot Rate = ₹ 4000000 /83312 = 48.0123
Forward Premium on US$ = [(48.8190 — 48.0123)/48.0123] x 12/6 x 100
= 3.36%
Interest rate differential = 12% - 8%
= 4% (Negative Interest rate differential)
Since the negative Interest rate differential is greater than forward premium there is a
possibility of arbitrage inflow into India.
The advantage of this situation can be taken in the following manner:
1. Borrow US$ 83312 for 6 months
Amount to be repaid after 6 months
= US $ 83312 (1 + 0.08 x 6/12) = US $ 86644.48
2. Convert US$ 83312 into Rupee and get the principal i.e. ₹ 40,00,000
Interest on Investments for 6 months = ₹ 4000000 x 0.06
= ₹ 240000
Total amount at the end of 6 months = ₹ (4000000 + 240000)
= ₹ 4240000
Converting the same at the forward rate
= ₹ 4240000 / ₹ 48.8190
= US $ 86851.43
Hence the gain is US $ (86851.43 - 86644.48) = US$ 206.95 OR
₹ 10103 i.e., ($ 206.95 x ₹ 48.8190)
Evaluation of Decision to take Covered Interest Rate Arbitrage OR Uncovered Interest
Rate Arbitrage
CA, CFA(USA), CPA(USA) Praveen Khatod (Best Faculty in India for SFM & COST(SCM) 54
Expected Rate spot after 180 days
Future rate for 1 US $ (Xi) Probability (Pi) Xi Pi
₹ 48.7600 25% 12.19
₹ 48.8000 60% 29.28
₹ 48.8200 15% 7.323
48.7930
Converting the amount of investment and interest at the expected forward rate as
follows:
= ₹ 42,40,000/ ₹ 48.7930 = US$ 86,897.71
Hence the gain is US $ (86,897.71 - 86,644.48) = US$ 253.23 OR
₹ 12,356 i.e., ($253.23 x ₹ 48.7930)
Since the expected gain is more in case of uncovered interest arbitrage the arbitrageur
may go for same. However, this gain is not certain and since it just slightly higher than
the gain under Covered Interest Arbitrage therefore he may chose not go for uncovered
interest arbitrage as there as also chances of actual spot rate turning adverse.
Q.103. Given:
Spot GBP/USD 1.9845 – 1.985 …… Solution:
For spot bid rate:
1+rh−Invest
1+rf−Borrow =
F1 − Ask Rate
S0 − Bid Rate
1+0.04125 x 3/12
1+0.06125 x 3/12 =
F1 − Ask rate
$ 1.9845
F1 ask rate = $ 1.9747
For spot ask rate:
1+rh − Borrow
1+rf − Invest =
F1 − Bid rate
S0 − Ask rate
1+0.04375 x 3/12
1+0.05875 x 3/12 =
F1 − Bid rate
$ 1.9845
CA, CFA(USA), CPA(USA) Praveen Khatod (Best Faculty in India for SFM & COST(SCM) 55
F1 bid rate = $ 1.9747
3 m, F £ 1 = $ 1.9744 or more (ask rate)
3 m, F £ 1 = $ 1.9782 or less (bid rate)
Since, above rates acts as a no arbitrage zone the actual rates should fall in those zones & at
the same time satisfy Bid Ask Rate Rule i.e. Bid Rate < Ask Rate. Since it is not so in the
present case, therefore, we have switched bid rate & ask rates.
Accordingly.
3 m forward rate £ 1 = $ 1.9741 – 1.9782
Spot rate £ 1 = $ 1.9845 – 1.9855
Swap points = 98 - 73
Q.107. Following are the spot exchange rates quoted in three different forex markets…..
Solution:
The arbitrageur can proceed as stated below to realize arbitrage gains.
(i) Buy ₹ 1 from USD 10,000,000
At Mumbai 48.3 x 10,000,000
₹ 483,000,000
(ii) Convert ₹ 1 to GBP at London 483,000,000
77.52 GBP 6,230,650.155
(iii) Convert GBP to USD at New York
6,230,650.155 x 1.6231 USD = 10,112,968.26
There is net gain of USD = 10,112968.26 less 10,000,000
i.e USD = 112,968.26
CA, CFA(USA), CPA(USA) Praveen Khatod (Best Faculty in India for SFM & COST(SCM) 56
Q.108. Following are the foreign exchange rates:
$1 = ` 40.50 / 40.75….…
Solution:
Step 1: Calculation Cross currency rates using any 2 quotations say:
$ 1 = ₹ 40.50 – 40.75
$ 1 = £ 0.60 – 0.61
Bid rate (₹
£) = B (
₹
$) x B (
$
£)
= 40.50 x 1
0.61
= 66.39
Ask rate (₹
£) = ask rate (
₹
$) x ask rate (
$
£)
= 40.75 x 1
0.60
= 67.92
Therefore, £ 1 = ₹ 66.39 – 67.92 (Cross Currency)
However, £ 1 = ₹ 65 – 66 (actual quote)
Step-2: Check for Overlapping exchange rate concept to identity arbitrage
Since the Bid rate of Cross (₹ 66.39) > Ask rate of Actual quote, therefore there
exists arbitrage opportunity.
To earn risk free arbitrage gains, an arbitrageur should Buy £ with ₹ under
Actual Quote and Sell them under Cross Currency Quote.
Proof of Arbitrage:
Let us assume an arbitrageur has ₹ 100000 with him
Convert ₹ 100000 into £ = £ 1515.15
[₹ 100000/66]
Convert £ 1515.15 into $ = $ 2483.85
[£ 1515.15/0.61]
Convert $ 2483.85 into ₹ = ₹ 100596.13
[$ 2483.85 x ₹ 40.50]
Net arbitrage gain = ₹ 100596.13 - ₹ 100000
= ₹ 596.13
CA, CFA(USA), CPA(USA) Praveen Khatod (Best Faculty in India for SFM & COST(SCM) 57
Q.110. Imagine that the current Yen/Euro rate is Yen 120…….
Solution:
Today spot rate € 1 = ¥ 120, assuming we are based in Japan so given quote becomes
a direct quote for us:
Year 1 1+Ih
I+If =
Expected S1
S0
1.06
1.03 =
E(S1)
120
E(S1) 1 € = ¥ 123.4951 ~ ¥ 123.50
Year 2 1+Ih
I+If =
E(S2)
E(S1)
1.03
1.05 =
ES2
123.50
E(S2) 1 € = ¥ 121.1476 ~ ¥ 121.15
Year 3 1+Ih
I+If =
E(S3)
E(S2)
1.035
1.03 =
ES3
121.15
E(S3) 1 € = ¥ 121.7381 ~ ¥ 121.74
Q.114. In International Monetary Market……
Solution:
Buy £ 62500 x 1.2806 = $ 80037.50
Sell E 62500 x 1.2816 = $ 80100.00
Profit $ 62.50
Alternatively, if the market comes back together before December 15, the dealer could
unwind his position (by simultaneously buying £ 62,500 forward and selling a futures
contract. Both for delivery on December 15) and earn the same profit of $ 62.5.
CA, CFA(USA), CPA(USA) Praveen Khatod (Best Faculty in India for SFM & COST(SCM) 58
Q.117. On January 28, 2005 an importer customer requested a Bank to remit Singapore Dollar
(SGD) 25,00,000 under an irrevocable LC. ……
Solution:
On January 28, 2005 the importer customer requested to remit SGD 25 lakhs.
To consider sell rate for the bank:
US $ = ₹ 45.90
Pound 1 = US $ 1.7850
Pound 1 = SGD 3.1575
Therefore, SGD 1 = ₹ 45.90∗ 1.7850
SGD 3.1575
SGD 1 = ₹ 25.9482
Add: Exchange margin (0.125%) ₹ 0.0324
₹ 25.9806
On February 4, 2005 the rates are
US $ = ₹ 45.97
Pound 1 = US $ 1.7775
Pound 1 = SGD 3.1380
Therefore, SGD 1 = ₹ 45.97∗ 1.7775
SGD 3.1380
SGD 1 = ₹ 26.0394
Add: Exchange margin (0.125%) ₹ 0.0325
₹ 26.0719
Hence, loss to the importer
= SGD 25,00,000 (₹ 26.0719 - ₹ 25.9806) = ₹ 2,28,250
CA, CFA(USA), CPA(USA) Praveen Khatod (Best Faculty in India for SFM & COST(SCM) 59
Q.135. Diva Jewellery Exporters, Delhi received orders…….
Solution:
WN#1 Calculation of Cross Currency Rates between ₹ and €
The relevant rate is Bid Rate since we have to sell €
If exposure is hedged
Bid Rate: ₹
€ =
₹
$ x
$
€
For January = 46.04 x 1.2803 = 58.945
For February = 46.11 x 1.2800 = 59.0208
For March = 46.13 x 1.2828 = 59.175564
If exposure is left uncovered
Bid Rate: ₹
€ =
₹
$ x
$
€
For January = 45.98 x 1.2786 = 58.790028
For February = 46.05 x 1.2806 = 58.97163
For March = 46.07 x 1.2811 = 59.020277
(i) If the exposure is hedged
Calculation of Expected Inflow under both the Invoicing Currency options
Month If Invoice in $ If Invoice in €
US$ Conversion
Rate
Equivalent
₹
€ Conversion
Rate
(Refer
WN#1)
Equivalent
₹
January 63950 $ 1 = ₹
46.04
2944258 50000 € 1 = ₹
58.945
2947250
February 96100 $ 1 = ₹
46.11
4431171 75000 € 1 = ₹
59.0208
4426560
March 128150 $ 1 = ₹
46.13
5911560 100000 € 1 = ₹
59.175564
5917556
CA, CFA(USA), CPA(USA) Praveen Khatod (Best Faculty in India for SFM & COST(SCM) 60
Choice of Currency for invoicing, if hedging is done
January – €
February – $
March – €
(ii) If the exposure is left uncovered
Calculation of Expected Inflow under both the Invoicing Currency options
Month If Invoice in $ If Invoice in €
US$ Conversion
Rate
Equivalent
₹
€ Conversion
Rate
(Refer
WN#1)
Equivalent
₹
January 63950 $ 1 = ₹
45.98
2940421 50000 € 1 = ₹
58.790028
2939501
February 96100 $ 1 = ₹
46.05
4425405 75000 € 1 = ₹ 58.97163
4422872
March 128150 $ 1 = ₹
46.07
5903871 100000 € 1 = ₹
59.020277
5902028
Choice of Currency for invoicing, if hedging is done
January – $
February – $
March – $
CA, CFA(USA), CPA(USA) Praveen Khatod (Best Faculty in India for SFM & COST(SCM) 61
Q.138. Task PLC is a UK based exporter. It…….
Solution:
Evaluation of MMH
Step 1: Identify
• The company has a foreign currency asset for $350,000.
Step 2: Create
• We must now create a liability
Step 3: Borrow
• Borrow in $ an amount which will mature in value to $ asset of Step 1
• Rate: 9% per annum or 2.25% per quarter.
• Borrowing: $ 350,000 / 1.0225 = S 342,300.
Step 4: Convert
• Sell $ and buy £.
• The relevant rate is the Ask rate, namely, 1.5905 per £.
• £ s received on conversion is (£ 342,300 /1.5905) = 215,215
Step 5: Invest
• £ 215,215 will be invested at 5% for 3 months
Step 6: Future Value
• FV of Investment = £ 217,904 [£ 215,2 l 5 x 1.0125]
Step 7: Settle
• The liability of $ 342,300 @ 2.25% per quarter matures to $ 350,000. This
will be settled with the amount of $ 350,000 receivable from customer.
Evaluation of Forward Cover
WN 1: Realization if forward contract is used
• Applicable rate is the 3-month Forward Ask Rate; $ 1.6140 per £
• Realization three months later = £ 350,000 / 1.6140. = £ 216,852
WN 2: Comparison of the two hedges
Under money market hedge, the amount is received NOW. Under forward contract,
money is received in future. We can compare these two figures, by either discounting
the "future receipts to its present value", or by compounding the spot receipts to its
"future value". We use the three-month deposit rate (at 5% p.a.) to compound the
present receipts, thus making it comparable to receipts under forward market rates.
Amount received by the company Now (£) 3 months later (£)
Forward Market 2,16,852
Money market hedge 2,15,214 2,17,904
Decision:
Money Market Hedge gives a higher £ realization and should be preferred.
CA, CFA(USA), CPA(USA) Praveen Khatod (Best Faculty in India for SFM & COST(SCM) 62
Q.139. Bask PLC is a UK based importer. It has………
Solution:
Part (a)
Step 1: Identify
• Transaction is import.
• Foreign currency liability of $ 350,000 exists
Step 2: Create
• We must create a Dollar Asset. To this end, importer has to generate dollar
funds.
Step 3: Borrow
• Borrow in Home Currency, Pounds, an amount equivalent to the PV of $
asset of 350,000.
• $ Deposit rate for applicable period is 2.5%.
• Amount of Borrowing = Present value of $ 350,000 discounted at 2.5% is $
3,41,463.
Step 4: Convert
• Relevant rate is spot Bid rate (Indirect quote; bid is on pounds) = 1.5865
• Actual borrowing $ 341,463 / 1.5865 would be £ 2,15,230.
Step 5: Invest
• The $ 3,41,463 is invested for 6 months at 2.5% per half year
Step 6: Future Value
• FV of Borrowing = £ 2,24,916 (£ 2,15,230 x (1 + 0.09 x 6/12))
Step 7: Settle
• $ Asset of 341,463 matures to $ 350,000
• This is used to settle the $ liability of 350,000 of Step 1
Part (b):
Compare the money market hedge and forward rate: We compare cost of purchase of
$ to yield maturity proceeds equivalent to import liability, and forward contract rates.
6 months later
Forward Market 2,25,733 (3,50,000/1.5505)
Money Market Hedge 2,24,916*
Decision: Maturity value of the cost of £-funds under money market hedge is lower
than quantum of £s involved for performing forward exchange contract at 1.5505.
Hence we must opt for money market hedging.
CA, CFA(USA), CPA(USA) Praveen Khatod (Best Faculty in India for SFM & COST(SCM) 63
Q.157. Given the following information:
Solution:
In this case, DM is at a premium against the Can$.
Premium = [(0.67 — 0.665) /0.665] x (12/3) x 100 = 3.01 per cent
Interest rate differential = 9-7 = 2 per cent.
Since the interest rate differential is smaller than the premium, it will be profitable to
place money in Deutschmarks the currency whose 3-months interest is lower.
The following operations are carried out:
(i) Borrow Cans 1000 at 9 per cent for 3- months;
(ii) Change this sum into DM at the spot rate to obtain DM
= (1000/0.665) = 1503.7
(iii) Place DM 1503.7 in the money market for 3 months to obtain a sum of DM
Principal: 1503.70
Add: Interest @ 7% for 3 months = 26.30
Total 1530.00
(iv) Sell DM at 3-months forward to obtain Can$= (1530x0.67) = 1025.1
(v) Refund the debt taken in Cans with the interest due on it, i.e.,
Can$
Principal 1000.00
Add: Interest @9% for 3 months 22.50
Total 1022.50
Net arbitrage gain = 1025.1 - 1022.5 = Can$ 2.6
CA, CFA(USA), CPA(USA) Praveen Khatod (Best Faculty in India for SFM & COST(SCM) 64
Q.160. You are given the following information by your banker:
Solution:
We have to work out the $/£ cross rates
$/£bid rate = ($/₹)bid x (₹/£)bid
= 1
(₹/$)ask x (₹/£)bid
= 1
48.75
= 1.4523
$/£ask rate = ($/₹)ask x (₹/£)ask
= 1
(₹/$)bid x (₹/£)ask
= 1
48.70
= 1.4548
$/£ cross rate = 1.4523/1.4548
Similarly we can work out the 6 months forward rate
(72.40
49.95)/(
72.50
49.85) = 1.4494/1.4544.
Suppose we borrow $100
To prevent arbitrage the following condition must be satisfied
100 (1 +0.04
2) > [100/(1.4548)] + (1 +
i
2) (1.4494)
102 > 99.6288 (2+i
2)
In other words ibid > 4.76%.
Suppose we borrow £ 100
To prevent arbitrage the following condition must be satisfied
100 (1 +i
2) >
100 x 1.4523
1.4544 x (1 +
0.035
2)
100 (1 +i
2) > 101.6030
iask > 3.21%
CA, CFA(USA), CPA(USA) Praveen Khatod (Best Faculty in India for SFM & COST(SCM) 65
Q.165. An authorized dealer in Chennai bought Japanese………..
Solution:
WN#1 Calculation of Cross Currency Rate applicable for remaining amount of JPY 30
million
The relevant rate is Bid Rate since we have to Sell JPY
Bid Rate: ₹
JPY=
₹
$ x
$
JPY= 65.02 x
1
111.80= ₹ 0.5816
i.e. JPY 100 = `58.16
Calculation of Gain / (Loss)
Particulars Computation Amount
Bank’s Outflow on Buying JPY from
an Exporter
JPY 50 mn x 58.21/100 (` 29,105,000)
Bank’s Inflow on Selling JPY locally JPY 20 mn x 58.25/100 ` 11,650,000
Bank’s Inflow on Selling remaining
JPY in Singapore
JPY 30 mn x 58.16/100 ` 17,448,000
Net Gain / (Loss) ₹ 7000