Commodities, Forex & Crypto

Question 1

(a) $T = 0.25$, exponent $= (0.068 + 0.012 - 0)(0.25) = 0.08 \times 0.25 = 0.02$. $F = 72000 \, e^{0.02} = 72000 \times 1.020201 = \text{₹}73{,}454.5$. (5)

• Correct $T$ and rate sum (2), exponentiation (2), final value (1).

(b) Market future ₹73,500 > fair ₹73,454.5 → future is overpriced → cash-and-carry arbitrage: buy spot gold, sell the future. (3) Profit = market future − fair future = $73500 - 73454.5 = \text{₹}45.5$ per 10g. (3)

• Direction identified (3), magnitude (3).

(c) Backwardation means $F < S_0 \Rightarrow e^{(r+u-y)T} < 1 \Rightarrow (r+u-y) < 0 \Rightarrow y > r + u$. (2) Economic meaning: a high convenience yield reflects the benefit of holding the physical commodity (avoiding stockouts, meeting production needs); when this exceeds financing + storage costs, holders prefer the physical over the future, pushing futures below spot. (2)

(d) Annualised basis $= \dfrac{F - S}{S} \times \dfrac{365}{\text{days}} \times 100\%$. (2)

def annualised_basis(spot, fut, days):
    return (fut - spot) / spot * (365 / days) * 100

(3) — formula (2), correct code (3).

Question 2

(a) In USD/INR, USD = base (the priced currency, quantity 1), INR = quote (units of INR per 1 USD). (2) Move 83.20 → 83.26 = 0.06 = 6 pips (1 pip = 0.01 for INR pairs). (1.5) P&L (long USD): $100{,}000 \times 0.06 = \text{₹}6{,}000$ profit. (1.5)

(b) Implied EUR/INR = EUR/USD × USD/INR = $1.0850 \times 83.20 = 90.272$. (3) Market EUR/INR = 90.60 > implied 90.272 → EUR is overvalued in INR terms in the direct market → arbitrage exists. (2) Direction (start ₹1,000,000):

1. Buy EUR directly? No — sell the overpriced side. Convert ₹ → USD → EUR (cheap synthetic), then sell EUR → INR at high market rate.
   • ₹1,000,000 / 83.20 = $12,019.23
   • $12,019.23 / 1.0850 = €11,077.63
   • €11,077.63 × 90.60 = ₹1,003,633.4 Profit ≈ ₹3,633. (4)

(c) (3)

• USD/INR — minor (INR is an emerging-market currency paired with a major; not a G10 cross). Some texts call it exotic-ish, but conventionally minor/emerging.
• EUR/USD — major (two most-traded reserve currencies, deepest liquidity).
• EUR/TRY — exotic (Turkish lira is an illiquid emerging-market currency, wide spreads).

(d) Loop direction: ₹ → USD → EUR → ₹ (the profitable direction found in (b)). (2)

def triangular_profit(eurusd, usdinr, eurinr, capital_inr):
    usd = capital_inr / usdinr        # INR -> USD
    eur = usd / eurusd                # USD -> EUR
    back = eur * eurinr               # EUR -> INR (sell high)
    return back - capital_inr

(3)

Question 3

(a) $\sigma_{annual} = \sigma_d \sqrt{365} = 0.035 \times 19.105 = 0.6687 = \mathbf{66.9\%}$. (3) This is ~4× the equity index's 16% — crypto is far more volatile. (1)

(b) VaR_{99\%} = \text{Position} \times z \times \sigma_d = 50000 \times 2.326 \times 0.042 = \mathbf{\4{,}884.6}$. (5)

• Formula (2), z & σ substitution (2), value (1).

(c) Fiat-collateralised stablecoin: each token is backed 1:1 by reserves (cash / short-term treasuries) held by the issuer; redemption at $1 + reserve audits + arbitrage keep the peg (if price < $1, arbitrageurs buy and redeem for $1). (2) Algorithmic stablecoin systemic risk: no hard collateral — the peg relies on a mint/burn mechanism with a paired token; under a confidence loss it can enter a death spiral (e.g., UST/LUNA), where falling price triggers reflexive supply expansion and total collapse. (2)

(d) Each block stores a hash of its data concatenated with the previous block's hash. Altering $\text{data}_k$ changes $H_k$; since block $k{+}1$ committed to the old $H_k$, its stored pointer no longer matches, and this mismatch cascades to every $j > k$. Because hashes are collision-resistant, an attacker cannot cheaply recompute a consistent chain. (2)

def verify_chain(blocks):
    for n in range(1, len(blocks)):
        if blocks[n].prev_hash != H(blocks[n-1].data + blocks[n-1].prev_hash):
            return False
    return True

(3)

[
  {"claim":"Gold fair future = 72000*e^0.02 ≈ 73454.5","code":"import sympy as sp\nF = 72000*sp.exp(sp.Rational(2,100))\nresult = abs(float(F)-73454.5) < 1.0"},
  {"claim":"Cash-and-carry profit ≈ 45.5 per 10g","code":"F = 72000*sp.exp(0.02)\nprofit = 73500 - F\nresult = abs(float(profit)-45.5) < 1.5"},
  {"claim":"Implied EUR/INR = 1.0850*83.20 = 90.272","code":"result = abs(1.0850*83.20 - 90.272) < 1e-6"},
  {"claim":"Triangular profit from 1,000,000 INR ≈ 3633","code":"cap=1000000\nusd=cap/83.20\neur=usd/1.0850\nback=eur*90.60\nresult = abs((back-cap)-3633) < 5"},
  {"claim":"BTC annualised vol = 0.035*sqrt(365) ≈ 0.669","code":"v=0.035*sp.sqrt(365)\nresult = abs(float(v)-0.6687) < 0.01"},
  {"claim":"ETH 1-day 99% VaR = 50000*2.326*0.042 ≈ 4884.6","code":"var=50000*2.326*0.042\nresult = abs(var-4884.6) < 1.0"}
]