Level 4 — ApplicationCommodities, Forex & Crypto

Commodities, Forex & Crypto

⏱ 60 minutes50 marksprintable — key stays hidden on paper

Level: 4 (Application — novel problems, no hints) Time limit: 60 minutes Total marks: 50

Instructions: Answer all questions. Show all working. Use $...$ notation for calculations where relevant. Round currency answers to 2 decimals unless stated otherwise.

Question 1 — Commodity Futures & Cost of Carry (12 marks)

A trader on MCX is analysing a gold futures contract (1 contract = 100 grams). The current spot price of gold is $\text{₹}6{,}200$ per gram. The relevant financing (interest) rate is 8% per annum, and storage + insurance costs amount to a further 1% per annum of spot value. The futures contract expires in exactly 3 months.

(a) Using the cost-of-carry model, compute the theoretical (fair) futures price per gram. Use simple (non-compounded) annualised carry. (4)

(b) The futures are actually trading at $\text{₹}6{,}380$ per gram. Identify whether the market is in contango or backwardation relative to spot, and state whether the futures are rich or cheap versus your fair value. (3)

(c) Describe the cash-and-carry arbitrage a trader would execute, and compute the arbitrage profit per contract (100 grams), ignoring transaction costs. (5)

Question 2 — Forex Pips, Cross Rates & USD/INR (12 marks)

A treasury desk observes the following quotes:

$EUR/USD = 1.0850$
$USD/INR = 83.20$
$GBP/USD = 1.2700$

(a) An Indian importer must pay $€500{,}000$ . Compute the cost in INR by first deriving the $EUR/INR$ cross rate. (4)

(b) The $USD/INR$ pair moves from $83.20$ to $83.65$ . For a standard USD/INR currency futures lot on NSE of $\$ 1{,}000$, compute the number of pips moved and the profit/loss in INR for a trader long 5 lots. (Take 1 pip = 0.0001 for INR quotes here as the desk convention, i.e. quote to 4 decimals.) (4)

(c) Classify each of the three pairs above as major, minor (cross), or exotic, and justify why $USD/INR$ falls into its category. (4)

Question 3 — Crypto Volatility & Position Risk (10 marks)

An investor buys $0.5$ BTC at $\$ 60{,}000 $per BTC and$ 8 $ETH at$ $3{,}000$ per ETH.

(a) Compute the total portfolio value at entry in USD. (2)

(b) One week later BTC falls 20% and ETH rises 12%. Compute the new portfolio value and the net percentage return of the portfolio. (5)

(c) The investor claims "diversifying across two cryptos removed most of my risk." Critically evaluate this claim in 2–3 sentences, referencing crypto correlation and volatility. (3)

Question 4 — Stablecoins, DeFi & Blockchain Reasoning (8 marks)

(a) A DeFi lending protocol offers 6% APY on a USD-pegged stablecoin deposit, while a bank offers 3% on rupee deposits. A trader wants to move $\text{₹}8{,}30{,}000$ into the stablecoin pool for one year. Using $USD/INR = 83.00$ , compute the USD deposited and the USD value after one year (simple interest). (3)

(b) State two distinct risks unique to this DeFi/stablecoin route that are absent from the bank deposit, and explain each in one line. (3)

Question 5 — Integrated Scenario (8 marks)

A macro fund holds three positions: (i) long crude oil futures on MCX, (ii) short USD/INR futures, (iii) long Bitcoin. News breaks that the US Federal Reserve unexpectedly raises interest rates sharply.

(a) For each of the three positions, state the likely directional impact (favourable / unfavourable) and give a one-line mechanism. (6)

(b) Which single position is likely the most volatile in response to this news, and why? (2)

End of paper.

Answer keyMark scheme & solutions

Question 1 (12 marks)

(a) Cost of carry (simple): $F = S \times (1 + (r + c)\times t)$

$r + c = 8\% + 1\% = 9\%$ p.a.; $t = 0.25$ yr → carry factor $= 0.09 \times 0.25 = 0.0225$ . (1)
$F = 6200 \times (1 + 0.0225) = 6200 \times 1.0225$ (2)
$F = \text{₹}6{,}339.50$ per gram. (1)

(b)

Futures $6{,}380 >$ spot $6{,}200$ ⇒ contango (futures above spot). (1)
Market futures $6{,}380 >$ fair $6{,}339.50$ ⇒ futures are rich/overpriced by $\text{₹}40.50$ /gram. (2)

(c) Cash-and-carry arbitrage (since futures overpriced):

Sell the futures at $6{,}380$ ; borrow funds and buy spot gold at $6{,}200$ ; carry (store) until expiry. (2)
At expiry: deliver gold against short future, receive $6{,}380$ . Cost of carrying = fair value $6{,}339.50$ . (1)
Profit per gram $= 6{,}380 - 6{,}339.50 = \text{₹}40.50$ . (1)
Per contract (100 g) $= 40.50 \times 100 = \text{₹}4{,}050$ . (1)

Question 2 (12 marks)

(a) $EUR/INR = (EUR/USD)\times(USD/INR) = 1.0850 \times 83.20 = 90.272$ (2)

Cost $= 500{,}000 \times 90.272 = \text{₹}4{,}51{,}36{,}000$ (₹4.5136 crore). (2)

(b) Move $= 83.65 - 83.20 = 0.45$ INR $= 4500$ pips (0.45 / 0.0001). (2)

Long ⇒ profit as rate rises. 5 lots $\times \$ 1{,}000 = $5{,}000$ notional.
P/L $= 5000 \times 0.45 = \text{₹}2{,}250$ profit. (2)

(c) (4)

$EUR/USD$ : major (contains USD + top-tier currency). (1)
$GBP/USD$ : major (USD + GBP). (1)
$USD/INR$ : exotic — pairs a major (USD) with an emerging-market currency (INR); lower liquidity, wider spreads, capital-control considerations. (2)

(Accept "minor/cross" only for pairs excluding USD; both EUR/USD and GBP/USD contain USD so are majors, not crosses.)

Question 3 (10 marks)

(a) Entry value $= 0.5\times60{,}000 + 8\times3{,}000 = 30{,}000 + 24{,}000 = \$ 54{,}000$. (2)

(b)

BTC new: $60{,}000 \times 0.80 = 48{,}000$ ; position $= 0.5\times48{,}000 = \$ 24{,}000$. (1)
ETH new: $3{,}000 \times 1.12 = 3{,}360$ ; position $= 8\times3{,}360 = \$ 26{,}880$. (1)
New total $= 24{,}000 + 26{,}880 = \$ 50{,}880$. (1)
Return $= (50{,}880 - 54{,}000)/54{,}000 = -3{,}120/54{,}000 = -5.78\%$ . (2)

(c) BTC and ETH are typically highly positively correlated, so holding both does not remove systematic crypto risk; both crash together in market-wide sell-offs. Diversification here only reduces idiosyncratic (asset-specific) risk, not the dominant market/volatility risk. (3)

Question 4 (8 marks)

(a)

USD deposited $= 8{,}30{,}000 / 83.00 = \$ 10{,}000$. (1)
After 1 yr at 6% simple: $10{,}000 \times 1.06 = \$ 10{,}600$. (2)

(b) Any two, one line each: (3)

Smart-contract/protocol risk — code bug or exploit can drain the pool.
De-peg / stablecoin risk — the coin may lose its $1 peg, causing capital loss.
(Accept: custody/wallet-key loss, no deposit insurance, liquidity/withdrawal freeze, regulatory risk.)

(c) A de-peg means the stablecoin trades away from its intended $1 reference (e.g.$ 0.90). Part (a) assumes 1 coin $=\$ 1 $; if it de-pegs, the \$ 10,600 nominal is worth less in real USD, so the "safe pegged" assumption collapses. (2)

Question 5 (8 marks)

(a) (2 marks each: direction + mechanism)

Long crude futures — unfavourable: rate hikes strengthen USD & slow growth expectations, typically pressuring commodity/oil prices down.
Short USD/INR — unfavourable: higher US rates strengthen USD vs INR, so USD/INR rises; a short loses.
Long Bitcoin — unfavourable: risk-off, higher discount rates hurt speculative/risk assets like BTC.

(b) Bitcoin is most volatile — crypto has the highest historical volatility and is most sensitive to risk-sentiment/liquidity shifts. (2)

[
  {"claim":"Q1a fair futures = 6339.50", "code":"S=6200; carry=(0.08+0.01)*0.25; F=S*(1+carry); result=(F==6339.5)"},
  {"claim":"Q1c arbitrage profit per 100g contract = 4050", "code":"F=6339.5; mkt=6380; profit=(mkt-F)*100; result=(profit==4050.0)"},
  {"claim":"Q2a EUR/INR cross = 90.272 and cost = 45136000", "code":"cross=1.0850*83.20; cost=500000*cross; result=(cross==90.272 and cost==45136000.0)"},
  {"claim":"Q2b USD/INR P/L for long 5 lots = 2250", "code":"pips=(83.65-83.20)/0.0001; pl=5*1000*(83.65-83.20); result=(round(pips)==4500 and pl==2250.0)"},
  {"claim":"Q3b new value 50880 and return -5.78%", "code":"btc=0.5*60000*0.80; eth=8*3000*1.12; tot=btc+eth; ret=(tot-54000)/54000*100; result=(tot==50880.0 and round(ret,2)==-5.78)"},
  {"claim":"Q4a USD deposited 10000 and after 1yr 10600", "code":"usd=830000/83.00; fin=usd*1.06; result=(usd==10000.0 and fin==10600.0)"}
]