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China Futures Investment Analysis - independent subject foundations study materials
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China Futures Investment Analysis - independent subject foundations practice questions

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Question 1Futures, options, swaps and conditional hedging models

For a DCE Soybean Meal futures contract (contract size = 10 metric tons/lot, minimum price tick = 1 RMB/metric ton), what is the minimum value fluctuation (tick value / 最小变动价值) per single contract lot?

  1. 10 RMB Correct answer.
  2. 1 RMB
  3. 5 RMB
  4. 100 RMB

Explanation

The tick value equals the minimum price fluctuation multiplied by the contract multiplier. For DCE Soybean Meal (M), the tick is 1 RMB/ton and the contract size is 10 metric tons/lot, resulting in a minimum value change of 1 RMB/ton × 10 tons = 10 RMB per contract lot.

Question 2Futures, options, swaps and conditional hedging models

A trader opens a new long position of 10 lots of DCE Corn futures (10 metric tons/lot) at an execution price of 2,400 RMB/metric ton. On the same day, the contract closes at an official daily settlement price of 2,450 RMB/metric ton. Ignoring transaction fees, what is the position profit/loss credited to the trader's account at daily settlement?

  1. +5,000 RMB Correct answer.
  2. +500 RMB
  3. -5,000 RMB
  4. +50,000 RMB

Explanation

Daily Position P&L for a new long position = (Daily Settlement Price - Execution Price) × Contract Size × Number of Lots. Here: (2,450 RMB/ton - 2,400 RMB/ton) × 10 tons/lot × 10 lots = +50 RMB/ton × 100 tons = +5,000 RMB.

Question 3Futures, options, swaps and conditional hedging models

A trader holds an existing short position of 5 lots of SHFE Aluminum futures (5 metric tons/lot) carried over from the previous day at a previous settlement price of 19,200 RMB/metric ton. Today, the contract settles at 19,050 RMB/metric ton. What is the holding profit/loss for today's mark-to-market clearing?

  1. +3,750 RMB Correct answer.
  2. -3,750 RMB
  3. +750 RMB
  4. +15,000 RMB

Explanation

Holding P&L for an existing short position = (Previous Day Settlement Price - Current Day Settlement Price) × Contract Multiplier × Number of Lots. Here: (19,200 RMB/ton - 19,050 RMB/ton) × 5 tons/lot × 5 lots = 150 RMB/ton × 25 tons = +3,750 RMB profit.

Question 4Futures, options, swaps and conditional hedging models

A client's futures account starts the day with an opening clearing reserve of 150,000 RMB and no open positions. Intraday, the client buys 20 lots of SHFE Rebar futures (RB, 10 metric tons/lot) at 3,600 RMB/metric ton. The contract's end-of-day settlement price is 3,450 RMB/metric ton. The margin requirement is 10%, and total transaction commissions are 100 RMB. What is the client's closing clearing reserve balance (可用资金 / 结算准备金余额) at the end-of-day settlement?

  1. 50,900 RMB Correct answer.
  2. 80,900 RMB
  3. 119,900 RMB
  4. -18,100 RMB

Explanation

Step 1: Daily Position P&L = (3,450 - 3,600) × 10 tons/lot × 20 lots = -150 × 200 = -30,000 RMB. Step 2: Dynamic Equity = Opening Balance (150,000) - Commission (100) + P&L (-30,000) = 119,900 RMB. Step 3: Required Trading Margin = Settlement Price × Multiplier × Lots × Margin Rate = 3,450 × 10 × 20 × 10% = 69,000 RMB. Step 4: Closing Clearing Reserves = Equity (119,900) - Margin (69,000) = 50,900 RMB.

Question 5Futures, options, swaps and conditional hedging models

A trader starts the day with 200,000 RMB in cash and no positions. Intraday, the trader buys 15 lots of DCE Palm Oil futures (10 metric tons/lot) at 8,000 RMB/metric ton. The trading margin rate is 12%. At the end of the day, the palm oil settlement price falls to 7,400 RMB/metric ton. Ignoring commissions, how much must the trader deposit to restore account equity to the required trading margin?

  1. 23,200 RMB Correct answer.
  2. 133,200 RMB
  3. 90,000 RMB
  4. 43,200 RMB

Explanation

Step 1: Daily P&L = (7,400 - 8,000) × 10 tons/lot × 15 lots = -90,000 RMB. Step 2: Account equity after settlement = 200,000 - 90,000 = 110,000 RMB. Step 3: Required trading margin = 7,400 × 10 × 15 × 12% = 133,200 RMB. Step 4: Required deposit = 133,200 - 110,000 = 23,200 RMB. The starting cash also exceeds the 144,000 RMB initial margin required to open the position.

Question 6Futures, options, swaps and conditional hedging models

A day trader sells short 8 lots of CZCE PTA futures (5 metric tons/lot) at 5,900 RMB/metric ton in the morning session, and completely buys to close (平仓) all 8 lots at 5,780 RMB/metric ton in the afternoon. The brokerage charges a round-trip transaction fee of 3 RMB/lot. What is the trader's net realized profit for the day?

  1. 4,776 RMB Correct answer.
  2. 4,800 RMB
  3. 960 RMB
  4. 2,388 RMB

Explanation

Gross Realized Profit = (Selling Price - Buying Price) × Contract Multiplier × Lots = (5,900 - 5,780) RMB/ton × 5 tons/lot × 8 lots = 120 RMB/ton × 40 tons = 4,800 RMB. Total Commission = 8 lots × 3 RMB/lot = 24 RMB (round-trip total). Net Profit = 4,800 - 24 = 4,776 RMB.

Question 7Futures, options, swaps and conditional hedging models

If the spot price of copper increases from 65,000 RMB/ton to 66,200 RMB/ton while the corresponding futures price increases from 65,500 RMB/ton to 66,000 RMB/ton, how has the basis changed?

  1. The basis strengthened (基差走强) by 700 RMB/ton Correct answer.
  2. The basis weakened (基差走弱) by 700 RMB/ton
  3. The basis remained unchanged at -500 RMB/ton
  4. The basis strengthened by 1,200 RMB/ton

Explanation

Initial Basis = Initial Spot - Initial Futures = 65,000 - 65,500 = -500 RMB/ton. Final Basis = Final Spot - Final Futures = 66,200 - 66,000 = +200 RMB/ton. Change in Basis = Final Basis - Initial Basis = (+200) - (-500) = +700 RMB/ton. Since the basis increased, it strengthened (基差走强) by 700 RMB/ton.

Question 8Futures, options, swaps and conditional hedging models

A livestock feed manufacturer needs to purchase 1,000 tons of soybean meal in 2 months and initiates a Long Hedge (买入套期保值). Under which basis scenario will the manufacturer achieve an effective purchase price LOWER than the initial spot price?

  1. When the basis weakens (基差走弱, i.e., final basis is smaller than initial basis) Correct answer.
  2. When the basis strengthens (基差走强, i.e., final basis is larger than initial basis)
  3. When the futures price decreases by more than the spot price decreases
  4. Only when futures price reaches parity with the Treasury repo rate

Explanation

For a Long Hedger (Short Spot exposure, Long Futures), the Net Effective Purchase Price = Initial Spot Price + Final Basis - Initial Basis = Initial Spot Price + (Change in Basis). When the basis weakens (Change in Basis < 0), the effective purchase price is lower than the initial spot price, generating a net hedging gain.

Question 9Futures, options, swaps and conditional hedging models

A copper smelter holds 200 metric tons of copper in inventory at a spot price of 68,000 RMB/metric ton. To hedge price risk, it sells 40 lots of SHFE Copper futures (5 metric tons/lot) at 68,500 RMB/metric ton. Two months later, spot copper drops to 64,000 RMB/metric ton and the smelter sells its spot inventory, simultaneously closing its futures position at 64,200 RMB/metric ton. What is the total net financial outcome of the hedge across both markets?

  1. Net profit of +60,000 RMB Correct answer.
  2. Net loss of -60,000 RMB
  3. Net loss of -800,000 RMB
  4. Net profit of +860,000 RMB

Explanation

Step 1: Spot market P&L = (64,000 - 68,000) RMB/ton × 200 tons = -800,000 RMB loss. Step 2: Futures market P&L = (68,500 - 64,200) RMB/ton × 5 tons/lot × 40 lots = +4,300 RMB/ton × 200 tons = +860,000 RMB gain. Step 3: Total net outcome = -800,000 + 860,000 = +60,000 RMB profit. (Alternatively: Initial Basis = 68,000 - 68,500 = -500; Final Basis = 64,000 - 64,200 = -200; Basis strengthened by +300 RMB/ton × 200 tons = +60,000 RMB).

Question 10Futures, options, swaps and conditional hedging models

A vegetable oil processing plant plans to purchase 500 metric tons of soybean oil in 3 months. The current spot price is 8,200 RMB/metric ton. The plant executes a long hedge by buying 50 lots of DCE Soybean Oil futures (10 metric tons/lot) at 8,350 RMB/metric ton. When purchasing spot oil 3 months later, spot price is 8,900 RMB/metric ton and futures price is 9,150 RMB/metric ton. What is the plant's effective purchase price per metric ton?

  1. 8,100 RMB/metric ton Correct answer.
  2. 8,900 RMB/metric ton
  3. 8,350 RMB/metric ton
  4. 7,950 RMB/metric ton

Explanation

Futures gain = 9,150 - 8,350 = +800 RMB/ton. Actual spot purchase price = 8,900 RMB/ton. Effective Purchase Price = Spot Price Paid - Futures Gain = 8,900 - 800 = 8,100 RMB/ton. (Check via basis: Initial Basis = 8,200 - 8,350 = -150; Final Basis = 8,900 - 9,150 = -250; Basis weakened by 100 RMB/ton -> Effective Price = Initial Spot - 100 = 8,200 - 100 = 8,100 RMB/ton).

Question 11Futures, options, swaps and conditional hedging models

Using the Minimum-Variance Optimal Hedge Ratio formula, if the standard deviation of spot price changes (σ_S) is 0.04, the standard deviation of futures price changes (σ_F) is 0.05, and the correlation coefficient (ρ) between spot and futures price changes is 0.85, what is the optimal hedge ratio (h*)?

  1. 0.68 Correct answer.
  2. 0.85
  3. 1.06
  4. 0.72

Explanation

The Minimum-Variance Optimal Hedge Ratio is calculated as: h* = ρ × (σ_S / σ_F). Substituting the given values: h* = 0.85 × (0.04 / 0.05) = 0.85 × 0.80 = 0.68.

Question 12Futures, options, swaps and conditional hedging models

An enterprise holds 10,000 metric tons of fuel oil inventory. The SHFE Fuel Oil futures contract size is 10 metric tons/lot. If the econometric analysis determines that the optimal hedge ratio (h*) is 0.75, how many futures contracts should the enterprise short to establish an optimal hedge?

  1. 750 lots Correct answer.
  2. 1,000 lots
  3. 1,333 lots
  4. 7,500 lots

Explanation

Number of Contracts N = (Quantity_spot × h*) / Contract Multiplier = (10,000 tons × 0.75) / (10 tons/lot) = 7,500 / 10 = 750 lots.

Question 13Futures, options, swaps and conditional hedging models

In Chinese commodity commercial practice, how is the spot delivery settlement price formulated in Basis Trading (基差交易 / 基差定价)?

  1. Spot Price = Futures Benchmark Price + Agreed Basis (现货价格 = 期货价格 + 升贴水) Correct answer.
  2. Spot Price = Producer Cost + Statutory VAT Rate
  3. Spot Price = Exchange Daily Limit Price - Storage Cost
  4. Spot Price = Previous Year Average Spot Price × CPI Inflation Multiplier

Explanation

Basis Trading (基差交易) is the dominant institutional pricing model in bulk commodities (soybeans, metals, plastics). Under this model, the physical transaction price is agreed as: Spot Transaction Price = Price of a designated futures contract on the exchange at pricing time + Agreed Basis premium/discount (现货结算价 = 期货升贴水 + 选定期货合约价格).

Question 14Futures, options, swaps and conditional hedging models

What is the standard trade execution structure of a Bull Calendar Spread (牛市跨期套利 / 正向套利组合)?

  1. Buying the near-month futures contract while simultaneously selling the distant-month futures contract (买入近期合约，卖出远期合约) Correct answer.
  2. Selling the near-month futures contract while simultaneously buying the distant-month futures contract (卖出近期合约，买入远期合约)
  3. Buying spot physical inventory and buying distant-month put options
  4. Selling call options on two different exchanges simultaneously

Explanation

A Bull Calendar Spread (牛市跨期套利) involves buying the near-delivery contract and selling the distant-delivery contract in the same underlying commodity. The trader anticipates that the near-month price will rise faster than (or fall less than) the distant-month price.

Question 15Futures, options, swaps and conditional hedging models

In a Normal Market (Contango / 正向市场, where Distant-Month Price > Near-Month Price), under what spread condition will a Bull Spread trader (Buy Near Month, Sell Distant Month) realize a net profit upon closing both legs?

  1. When the price spread narrows (价差缩小, i.e., Distant Month - Near Month becomes smaller) Correct answer.
  2. When the price spread widens (价差扩大, i.e., Distant Month - Near Month becomes larger)
  3. When both contracts rise by exactly the same amount, leaving the spread unchanged
  4. Whenever the near-month price falls, regardless of the distant-month move

Explanation

In a contango market, Spread = Distant Price - Near Price > 0. A Bull Spread buys Near and sells Distant (Net Short Spread). Therefore, the position profits when the spread narrows (价差缩小). For example, if initial spread is 200 RMB and closes at 100 RMB, the trader captures a 100 RMB/ton profit.

Question 16Futures, options, swaps and conditional hedging models

In an Inverted Market (Backwardation / 反向市场, where Near-Month Price > Distant-Month Price), when does a Bull Spread (Buy Near Month, Sell Distant Month) generate a trading profit?

  1. When the price spread widens (价差扩大, i.e., Near Month premium over Distant Month increases) Correct answer.
  2. When the price spread narrows (价差缩小, i.e., Near Month premium over Distant Month decreases)
  3. Only when both contracts hit their lower price limit
  4. When the spot inventory is entirely destroyed by natural disaster

Explanation

In a backwardation market, Near Price > Distant Price, so Spread = Near Price - Distant Price > 0. The Bull Spread buys the more expensive near contract and sells the cheaper distant contract (Net Long Spread). It profits when the near-month premium widens (价差扩大).

Question 17Futures, options, swaps and conditional hedging models

A spread trader executes a Bull Calendar Spread on DCE Soybean Meal (10 metric tons/lot): - Buys 10 lots of May contract (M2405) at 3,200 RMB/metric ton - Sells 10 lots of September contract (M2409) at 3,320 RMB/metric ton One month later, the trader closes both legs when M2405 reaches 3,380 RMB/metric ton and M2409 reaches 3,440 RMB/metric ton. What is the total net trading profit?

  1. +6,000 RMB Correct answer.
  2. +18,000 RMB
  3. -12,000 RMB
  4. +12,000 RMB

Explanation

Step 1: May contract P&L = (3,380 - 3,200) × 10 tons/lot × 10 lots = +180 RMB/ton × 100 tons = +18,000 RMB gain. Step 2: September contract P&L = (3,320 - 3,440) × 10 tons/lot × 10 lots = -120 RMB/ton × 100 tons = -12,000 RMB loss. Step 3: Total net profit = +18,000 - 12,000 = +6,000 RMB. (Alternatively: Initial Spread M09 - M05 = 3,320 - 3,200 = 120; Final Spread = 3,440 - 3,380 = 60; Spread narrowed by 60 RMB/ton × 100 tons = +6,000 RMB profit).

Question 18Futures, options, swaps and conditional hedging models

A trader establishes a Bear Calendar Spread on SHFE Copper (5 metric tons/lot) in a contango market: - Sells 5 lots of March contract at 65,000 RMB/metric ton - Buys 5 lots of July contract at 65,600 RMB/metric ton At exit, March copper trades at 64,200 RMB/metric ton and July copper trades at 65,100 RMB/metric ton. What is the net profit or loss on this spread trade?

  1. Net profit of +7,500 RMB Correct answer.
  2. Net loss of -7,500 RMB
  3. Net profit of +20,000 RMB
  4. Net loss of -12,500 RMB

Explanation

Step 1: March short leg P&L = (65,000 - 64,200) × 5 tons/lot × 5 lots = +800 RMB/ton × 25 tons = +20,000 RMB gain. Step 2: July long leg P&L = (65,100 - 65,600) × 5 tons/lot × 5 lots = -500 RMB/ton × 25 tons = -12,500 RMB loss. Step 3: Net P&L = +20,000 - 12,500 = +7,500 RMB profit. (Alternatively: Initial Spread July - March = 600 RMB; Final Spread = 65,100 - 64,200 = 900 RMB; Spread widened by 300 RMB/ton × 25 tons = +7,500 RMB profit).

Question 19Futures, options, swaps and conditional hedging models

What is an Inter-Commodity Raw Material vs. Product Spread (相关商品/原料与成品跨品种套利), such as the Soybean Crush Spread (大豆提油套利 / 压榨套利)?

  1. Buying raw materials (Soybeans) on futures while selling finished products (Soybean Meal and Soybean Oil) when processing margins are abnormally high Correct answer.
  2. Buying gold futures while shorting crude oil futures across different continents
  3. Simultaneously buying Treasury bond futures and shorting stock index futures
  4. Selling pork futures while buying live cattle futures

Explanation

A Soybean Crush Spread (大豆提油套利) is an inter-commodity processing spread where the trader buys the raw material (Soybeans) and sells the processed outputs (Soybean Meal and Soybean Oil) to lock in a profitable gross processing margin (压榨利润) when product prices are high relative to bean costs.

Question 20Futures, options, swaps and conditional hedging models

In Chinese soybean crushing industry practice, 1 metric ton of soybeans yields approximately 0.80 metric tons of soybean meal and 0.18 metric tons of soybean oil (with 0.02 processing loss). If soybean purchase cost is 4,200 RMB/ton, processing costs are 150 RMB/ton, soybean meal sells for 3,400 RMB/ton, and soybean oil sells for 8,000 RMB/ton, what is the theoretical Crush Margin (压榨利润) per metric ton of soybeans?

  1. -190 RMB/metric ton Correct answer.
  2. +190 RMB/metric ton
  3. +350 RMB/metric ton
  4. -40 RMB/metric ton

Explanation

Step 1: Total Revenue per ton of soybeans = (0.80 tons × 3,400 RMB/ton) + (0.18 tons × 8,000 RMB/ton) = 2,720 RMB + 1,440 RMB = 4,160 RMB. Step 2: Total Cost per ton = Soybean Cost (4,200) + Processing Cost (150) = 4,350 RMB. Step 3: Crush Margin = Revenue (4,160) - Cost (4,350) = -190 RMB/metric ton.

Question 21Futures, options, swaps and conditional hedging models

What is the operational structure of a Cash-and-Carry Arbitrage (期现正向套利) in commodity futures markets?

  1. When futures price significantly exceeds spot price plus all carrying costs, the arbitrageur buys spot physical inventory, borrows funds, and shorts futures contracts to deliver at expiration Correct answer.
  2. When spot price significantly exceeds futures price, the arbitrageur buys futures and sells physical spot to immediate retail consumers
  3. The arbitrageur buys call options and sells put options with identical strikes on foreign exchanges
  4. The arbitrageur borrows physical goods from the exchange to sell into foreign black markets

Explanation

Cash-and-Carry Arbitrage (期现正向套利) is initiated when Futures Price > Spot Price + Total Carrying Costs (financing interest + storage + insurance + delivery/trading fees). The arbitrageur locks in a riskless profit by buying spot, financing the purchase, shorting futures, and delivering the physical goods into the exchange warehouse at maturity.

Question 22Futures, options, swaps and conditional hedging models

What structural market limitation often makes Reverse Cash-and-Carry Arbitrage (反向期现套利) more difficult to execute in commodity markets compared to standard Cash-and-Carry Arbitrage?

  1. Short-selling physical commodity spot inventory is often restricted or impossible due to the lack of an efficient physical lending/borrowing market Correct answer.
  2. Futures exchanges legally prohibit buying futures contracts when prices are low
  3. Commercial banks refuse to accept cash deposits from commodity corporations
  4. Storage costs become negative during market downturns

Explanation

Reverse Cash-and-Carry Arbitrage requires selling spot and buying futures when futures are underpriced. Unless the arbitrageur already owns existing physical inventory that can be sold and replaced later, short-selling physical commodities is difficult or impossible due to the absence of a liquid securities-lending-like physical borrow market.

Question 23Futures, options, swaps and conditional hedging models

The spot price of rebar is 3,800 RMB/metric ton. The annual financing interest rate is 6%. Storage and insurance costs are 20 RMB/metric ton per month. Round-trip trading, delivery, and inspection fees total 30 RMB/metric ton. For a 3-month (0.25 year) futures contract, what is the Theoretical No-Arbitrage Upper Bound (无套利区间上限)?

  1. 3,947 RMB/metric ton Correct answer.
  2. 3,857 RMB/metric ton
  3. 4,088 RMB/metric ton
  4. 3,800 RMB/metric ton

Explanation

Step 1: Financing Cost for 3 months = 3,800 × 6% × 0.25 = 57 RMB/ton. Step 2: Storage & Insurance for 3 months = 20 × 3 = 60 RMB/ton. Step 3: Transaction & Delivery fees = 30 RMB/ton. Step 4: Total Carrying Cost = 57 + 60 + 30 = 147 RMB/ton. Step 5: No-Arbitrage Upper Bound = Spot Price (3,800) + Total Carrying Cost (147) = 3,947 RMB/metric ton. If futures trades above 3,947 RMB/ton, a cash-and-carry arbitrage profit exists.

Question 24Futures, options, swaps and conditional hedging models

In commodity cost-of-carry theory, what does the Convenience Yield (便利收益) represent?

  1. The non-monetary operational benefit and supply security value derived from physically holding physical inventory during periods of spot scarcity Correct answer.
  2. The statutory tax rebate granted by customs to high-volume exporters
  3. The interest discount offered by futures exchanges on overnight margin deposits
  4. The monetary dividend paid out quarterly by mining companies to contract holders

Explanation

Convenience Yield (便利收益) represents the economic benefit and operational flexibility associated with holding physical inventory (e.g. keeping production lines running, avoiding plant shutdowns, capturing unexpected spot premiums during shortages). When convenience yield is very high, spot prices rise above futures prices, creating an inverted/backwardation market structure.

Question 25Futures, options, swaps and conditional hedging models

In a fictional sizing calculation, risk allowance is2%of RMB500,000. Assume no fees or slippage and exact stop execution50points away on a contract worth RMB200per point. What maximum whole-contract count fits that allowance?

  1. 1 lot Correct answer.
  2. 5 lots
  3. 10 lots
  4. 25 lots

Explanation

The supplied allowance is500000×0.02=10000. The assumed per-contract stop loss is50×200=10000, giving one whole contract. This model assumes exact execution and ignores fees and gaps; an actual stop does not guarantee that the realized loss is limited to the planned amount.

Question 26Investment instruments, portfolios and measured performance

Why can a dealer's index-futures hedge for a Snowball structured product change sharply as the underlying approaches a Knock-In or Knock-Out barrier?

  1. Barrier proximity can change the product's model delta and gamma nonlinearly, so the dealer must recompute and rebalance; the direction depends on the exact payoff, dealer side, barrier observations, portfolio netting, and model inputs rather than one universal buy-or-sell rule. Correct answer.
  2. The issuer holds a 100% short futures position throughout the product life and never adjusts hedges.
  3. The issuer buys put options on the exchange with zero futures hedging.
  4. Near the Knock-In barrier, the issuer is forced to buy massive volumes of index futures, creating an upward price squeeze.

Explanation

Snowball payoffs are path dependent. As an observation or barrier becomes likely, small underlying moves can materially change estimated activation, autocall, and terminal-payoff probabilities, producing nonlinear delta and gamma changes. The desk then rebalances its net hedge. A fixed claim that every issuer is short the same option or must sell futures near every Knock-In barrier ignores contract terms, whether the desk is issuer or offsetting counterparty, and portfolio-level netting.

Question 27Investment instruments, portfolios and measured performance

In the Risk Parity (风险平价模型 - Qian 2005) asset allocation framework, how are portfolio asset weights determined, and how does this overcome the primary structural defect of traditional 60/40 Equity/Bond portfolios?

  1. Weights are allocated so each asset class contributes an equal share of modeled portfolio risk; this addresses the tendency of a capital-weighted 60/40 portfolio to have risk dominated by its more volatile equity allocation. Correct answer.
  2. Weights are strictly set to 50% equities and 50% gold regardless of volatility or correlation.
  3. Weights are determined by selecting only the asset class with the highest historical return over the past 10 years.
  4. Weights are assigned in inverse proportion to asset market capitalization with zero leverage permitted.

Explanation

Risk parity sets weights so each included asset or sleeve contributes an equal share of modeled portfolio volatility: TRC_i = w_i × (∂σ_p / ∂w_i). This can reduce equity-risk concentration relative to a capital-weighted 60/40 portfolio. The actual risk shares depend on estimated volatilities and correlations, and leverage is a design choice rather than a defining requirement.

Question 28Investment instruments, portfolios and measured performance

How does the Black-Litterman (BL) asset allocation model mitigate the input-sensitivity and 'error maximization' problems of classical Markowitz mean-variance optimization?

  1. It begins with the neutral market equilibrium implied returns derived from Reverse Optimization (Π = λ × Σ × w_mkt) as the baseline prior, and combines them with subjective investor views and view-confidence matrices via Bayesian updating to generate robust posterior expected returns. Correct answer.
  2. It completely eliminates covariance matrices and assumes all asset correlations are exactly zero.
  3. It relies exclusively on technical candlestick charting patterns to set portfolio weights.
  4. It forces all portfolio asset weights to be strictly equal to 1/N under all economic conditions.

Explanation

Markowitz optimization can be highly sensitive to expected-return inputs. Black-Litterman mitigates that problem by reverse-engineering equilibrium implied returns from market weights, expressing investor views with uncertainty, and combining the prior and views through Bayesian updating. The result is often more stable, but it still depends on the covariance estimate, risk aversion, view specification, and confidence assumptions.

Question 29Investment instruments, portfolios and measured performance

In classical Markowitz Mean-Variance Portfolio Theory, what represents the 'Efficient Frontier' (有效前沿), and what portfolio is formed at the tangency point between the Efficient Frontier and the Capital Allocation Line (CAL)?

  1. The set of optimal portfolios that offer the maximum expected return for a given level of risk (variance); the tangency point represents the Optimal Risky Portfolio (Max Sharpe Ratio Portfolio). Correct answer.
  2. The set of portfolios with the lowest possible trading commissions; the tangency point is the 100% cash portfolio.
  3. A straight line connecting the lowest-priced asset to the highest-priced asset.
  4. The portfolio with the maximum possible standard deviation and lowest return.

Explanation

The Markowitz Efficient Frontier represents the locus of non-dominated portfolios in mean-variance space that maximize expected return for a given level of variance (or minimize variance for a target return). When a risk-free asset is introduced, the Capital Allocation Line (CAL) is drawn from the risk-free rate tangent to the efficient frontier. The tangency portfolio achieves the maximum possible Sharpe Ratio (market optimal risky portfolio).

Question 30Investment instruments, portfolios and measured performance

In quantitative portfolio management, a Constant Proportion Portfolio Insurance (CPPI / 恒定比例投资组合保险) rule sets risky-asset exposure as E_t = m × (V_t - F_t), where m is the multiplier, V_t is portfolio value, and F_t is the target floor. Under the rule, what allocation follows if V_t is observed exactly at F_t?

  1. The measured cushion is zero, so the rule sets risky-asset exposure E_t to zero and allocates to the defensive asset, subject to execution and market constraints. Correct answer.
  2. The rule sets risky exposure to m times the full portfolio value because the floor no longer matters
  3. The rule keeps the prior risky exposure unchanged until the next scheduled annual rebalance
  4. The rule sets risky exposure to the floor value and allocates only the excess to the defensive asset

Explanation

In the CPPI rule, Cushion C_t = V_t - F_t and risky exposure E_t = m × C_t. If the observed value equals the floor, the calculated risky exposure is zero and the strategy seeks to move into the defensive asset. CPPI does not guarantee the floor: gaps, discrete rebalancing, transaction costs, liquidity limits, or defensive-asset credit risk can produce a breach before the strategy can rebalance.

Question 31Investment instruments, portfolios and measured performance

A structured income note offers a participation rate (参与率) of 85.0% on the price appreciation of the CSI 300 index over a 1-year term, with 100% principal protection at maturity: Payoff = Principal × [1 + max(0, 0.85 × (S_T - S_0) / S_0)]. If an investor allocates 1,000,000 RMB and the CSI 300 index rises by 30.0% over the year, what is the total payout received at maturity?

  1. 1,255,000 RMB (25.5% total return) Correct answer.
  2. 1,300,000 RMB (30.0% total return)
  3. 1,085,000 RMB (8.5% total return)
  4. 1,000,000 RMB (0.0% return)

Explanation

Index appreciation = +30.0%. Participation return = Participation Rate × Index Return = 85.0% × 30.0% = 25.50%. Total Payout = 1,000,000 RMB × (1 + 0.2550) = 1,255,000 RMB.

Question 32Investment instruments, portfolios and measured performance

Why do institutional asset allocators incorporate commodity-linked structured products (大宗商品联动型收益凭证, such as gold- or crude oil-linked notes) into multi-asset portfolios?

  1. Commodity exposure can diversify equity and bond risk and can be sensitive to inflation surprises, but the benefit depends on the commodity, product structure, and market regime. Correct answer.
  2. Commodity-linked returns are always negatively correlated with both equities and bonds in every market regime
  3. The note removes issuer credit, liquidity, and structural payoff risk while retaining only commodity upside
  4. All commodity exposures respond identically to inflation, so the underlying and note structure are immaterial

Explanation

Commodity returns can respond to supply shocks and inflation surprises differently from equities and bonds, so a carefully sized exposure may diversify a portfolio. Correlations and inflation sensitivity vary by commodity, horizon, derivative roll yield, note terms, and market regime; diversification and an improved Sharpe ratio are possibilities, not guarantees.

Question 33Investment instruments, portfolios and measured performance

In quantitative asset allocation, how does the Maximum Diversification Portfolio (最大分散化组合 - Choueifaty & Coignard) define the Diversification Ratio (DR), and what does its optimization maximize?

  1. DR = [∑ w_i × σ_i] / σ_p; it maximizes the ratio of the weighted sum of individual asset volatilities to the total diversified portfolio volatility. Correct answer.
  2. DR = Portfolio Return / Portfolio Max Drawdown.
  3. DR = ∑ w_i²; it minimizes the number of assets in the portfolio.
  4. DR = [∑ w_i] / [∑ σ_i]; it maximizes total capital leverage.

Explanation

The Diversification Ratio is defined as the ratio of weighted asset volatilities to total portfolio volatility: DR(w) = (w^T σ) / √(w^T Σ w) = (∑ w_i σ_i) / σ_p. Due to diversification (sub-additivity of risk when correlations ρ_{ij} < 1), portfolio volatility σ_p is less than the weighted sum of individual volatilities. Maximizing DR constructs a portfolio that extracts the highest possible diversification benefit from pairwise cross-asset correlation offsets.

Question 34Financial appraisal, financing and conditional valuation models

What is the cost of equity capital for a firm listed on the Ghana Stock Exchange if its beta is 1.2, the risk-free rate (yield on 91-day Treasury bill) is 15%, and the expected market return is 22%?

  1. 15.00%
  2. 22.00%
  3. 23.40% Correct answer.
  4. 31.40%

Explanation

Using CAPM: Cost of Equity = Rf + Beta * (Rm - Rf) = 15% + 1.2 * (22% - 15%) = 15% + 1.2 * (7%) = 15% + 8.4% = 23.4%.

Question 35Financial appraisal, financing and conditional valuation models

Which of the following capital budgeting evaluation methods is structurally superior when evaluating mutually exclusive projects with differing scales of investment and conflicting IRR and NPV results?

  1. Net Present Value (NPV) because it measures absolute wealth creation. Correct answer.
  2. Internal Rate of Return (IRR) because it measures percentage efficiency.
  3. Payback Period because it measures liquidity and cash recovery time.
  4. Accounting Rate of Return (ARR) because it uses book profit metrics.

Explanation

NPV is the preferred metric for mutually exclusive projects because it maximizes absolute shareholder wealth and assumes reinvestment at the cost of capital, whereas IRR assumes reinvestment at the project's IRR (which can be unrealistic).

Question 36Financial appraisal, financing and conditional valuation models

A corporate manager calculates a firm's Degree of Financial Leverage (DFL) as 2.5. If the firm's Operating Income (EBIT) increases by 10%, what will be the percentage change in Earnings Per Share (EPS)?

  1. 4.00%
  2. 10.00%
  3. 25.00% Correct answer.
  4. 250.00%

Explanation

DFL measures the sensitivity of EPS to changes in EBIT: % Change in EPS = DFL * % Change in EBIT = 2.5 * 10% = 25%.

Question 37Financial appraisal, financing and conditional valuation models

A company's capital structure consists of 60% equity and 40% debt. The cost of equity is 20%, and the before-tax cost of debt is 12%. If the marginal corporate tax rate in Ghana is 25%, what is the firm's Weighted Average Cost of Capital (WACC)?

  1. 14.80%
  2. 15.60% Correct answer.
  3. 16.80%
  4. 18.00%

Explanation

WACC = (Weight of Equity * Cost of Equity) + (Weight of Debt * Cost of Debt * [1 - Tax Rate]) = (0.60 * 20%) + (0.40 * 12% * [1 - 0.25]) = 12% + (4.8% * 0.75) = 12% + 3.6% = 15.6%.

Question 38Financial appraisal, financing and conditional valuation models

Which working capital policy is characterized by a firm financing all its permanent current assets and a portion of its seasonal temporary current assets with long-term debt and equity?

  1. Conservative approach Correct answer.
  2. Aggressive approach
  3. Matching (maturity matching) approach
  4. Restrictive approach

Explanation

The conservative approach uses long-term capital (low risk, high cost) to finance permanent assets and some temporary assets, keeping short-term debt financing to a minimum.

Question 39Financial appraisal, financing and conditional valuation models

According to the "bird-in-the-hand" theory of dividend policy proposed by Myron Gordon and John Lintner:

  1. Shareholders are indifferent between dividends and capital gains.
  2. Dividends are taxed at a lower rate than capital gains, so investors prefer high payouts.
  3. Investors prefer high current dividends over future capital gains because current dividends are less risky. Correct answer.
  4. Dividends serve as a negative signal about a firm's future investment opportunities.

Explanation

The bird-in-the-hand theory argues that investors value current dividend payments more highly than uncertain future capital gains, so a higher dividend payout reduces the required return and increases stock price.

Question 40Financial appraisal, financing and conditional valuation models

An Accra-based distributor has a Cash Conversion Cycle (CCC) of 45 days. If its Days Inventory Outstanding (DIO) is 30 days and Days Sales Outstanding (DSO) is 40 days, what is the firm's Days Payable Outstanding (DPO)?

  1. 15 days
  2. 25 days Correct answer.
  3. 35 days
  4. 115 days

Explanation

Cash Conversion Cycle = DIO + DSO - DPO. Substituting values: 45 = 30 + 40 - DPO → 45 = 70 - DPO → DPO = 70 - 45 = 25 days.

Question 41Financial appraisal, financing and conditional valuation models

A company listed on the Ghana Stock Exchange paid a dividend of GHS 2.00 yesterday. If the dividends are expected to grow at a constant rate of 6% per year indefinitely, and the required rate of return is 14%, what is the estimated intrinsic value of the stock using the Gordon Growth Model?

  1. GHS 14.28
  2. GHS 25.00
  3. GHS 26.50 Correct answer.
  4. GHS 33.33

Explanation

Gordon Growth Model: V0 = D1 / (k - g). Here, D0 = GHS 2.00. Expected dividend next year (D1) = D0 * (1 + g) = 2.00 * (1.06) = GHS 2.12. V0 = 2.12 / (0.14 - 0.06) = 2.12 / 0.08 = GHS 26.50.

Question 42Financial appraisal, financing and conditional valuation models

A bond has a face value of GHS 1,000, a coupon rate of 10% paid annually, and a maturity of 3 years. If the market required yield (YTM) is 12%, what is the price of the bond?

  1. GHS 951.96 Correct answer.
  2. GHS 1,000.00
  3. GHS 1,050.00
  4. GHS 1,120.00

Explanation

Bond Price = PV of coupons + PV of principal. Coupon = 10% * 1000 = GHS 100. Price = [100 / (1.12)^1] + [100 / (1.12)^2] + [100 / (1.12)^3] + [1,000 / (1.12)^3] = 89.29 + 79.72 + 71.18 + 711.78 = GHS 951.97 (closest option: 951.96).

Question 43Financial appraisal, financing and conditional valuation models

If a GHS 1,000 face value bond with a coupon rate of 12% is currently trading in the secondary market at GHS 960, what is the Current Yield of the bond?

  1. 11.50%
  2. 12.00%
  3. 12.50% Correct answer.
  4. 13.20%

Explanation

Current Yield = Annual Coupon Payment / Bond Market Price = (12% * 1,000) / 960 = 120 / 960 = 0.125 = 12.50%.

Question 44Financial appraisal, financing and conditional valuation models

Under equity valuation, the Price-to-Earnings (P/E) multiple of a firm is directly related to its dividend payout ratio (payout) and inversely related to its:

  1. Expected earnings growth rate (g).
  2. Required rate of return (k). Correct answer.
  3. Book value of assets.
  4. Debt-to-equity ratio.

Explanation

P/E = (Payout Ratio) / (k - g). As k (required rate of return) increases, the denominator (k - g) increases, causing the P/E ratio to fall. Thus, P/E is inversely related to the required return.

Question 45Financial appraisal, financing and conditional valuation models

What is the value of a share of preferred stock that pays a constant annual dividend of GHS 8.00 if the required rate of return is 10%?

  1. GHS 8.00
  2. GHS 80.00 Correct answer.
  3. GHS 100.00
  4. GHS 180.00

Explanation

Preferred stock value is valued as a perpetuity: V0 = D / k = 8.00 / 0.10 = GHS 80.00.

Question 46Financial appraisal, financing and conditional valuation models

If a bond's Macaulay duration is 6 years, and its yield to maturity is 8%, what is the modified duration of the bond?

  1. 4.82 years
  2. 5.56 years Correct answer.
  3. 6.00 years
  4. 6.48 years

Explanation

Modified Duration = Macaulay Duration / (1 + y/m). For annual payments (m=1): Modified Duration = 6 / (1 + 0.08) = 6 / 1.08 = 5.56 years.

Question 47Financial appraisal, financing and conditional valuation models

Which of the following describes the relationship between bond price sensitivity and coupon rate, holding maturity and yield constant?

  1. Bonds with lower coupon rates have higher interest rate sensitivity (duration) than bonds with higher coupon rates. Correct answer.
  2. Bonds with higher coupon rates have higher interest rate sensitivity than bonds with lower coupon rates.
  3. Coupon rates have no effect on bond price sensitivity.
  4. Bond price sensitivity is only affected by maturity, not coupon.

Explanation

Bonds with lower coupon rates pay less of their cash flows early. Thus, more of the bond's total value is concentrated at maturity, resulting in a higher duration and greater price sensitivity to interest rate changes.

Question 48Financial appraisal, financing and conditional valuation models

Enterprise Value (EV) of a firm is calculated as:

  1. Market Capitalization + Total Debt - Cash and Cash Equivalents. Correct answer.
  2. Market Capitalization + Total Assets - Total Liabilities.
  3. Net Income * P/E Multiple.
  4. Total Equity + Long-term Debt.

Explanation

EV measures the total value of a company as a functioning business. It is computed as the market value of equity (market cap) plus debt (which an acquirer must assume) minus cash (which reducing the acquisition cost).

Question 49Market, credit, liquidity and model-risk reasoning

Value at Risk (VaR / 风险价值) is a foundational metric for corporate and financial risk management. How is VaR formally defined, and what does a statement that a company's '1-day 99% VaR is 5.0 million RMB' mean?

  1. Under the stated VaR model and assumptions, 1% of one-day loss outcomes lie beyond RMB 5.0 million and 99% lie at or below that threshold. Correct answer.
  2. The company is guaranteed to lose exactly 5.0 million RMB every trading day with 99% certainty.
  3. The company's maximum possible loss under any imaginable catastrophic scenario is strictly 5.0 million RMB.
  4. The company has a 99% probability of earning at least 5.0 million RMB in profit tomorrow.

Explanation

VaR is a loss quantile for a specified horizon, confidence level, model, and data set: under a continuous-distribution convention, Pr(Loss > VaR) = α. A one-day 99% VaR of RMB 5.0 million therefore places 1% of modeled one-day loss outcomes beyond that threshold. It is not a maximum possible loss, and model error or changing markets can alter the realized exception rate.

Question 50Market, credit, liquidity and model-risk reasoning

A commodity trading enterprise holds a physical copper inventory valued at V = 200 million RMB. Daily price volatility is estimated at σ_daily = 1.80%. Assuming daily returns are normally distributed with zero drift, what is the enterprise's 1-day 99% Parametric VaR (given Z_{0.99} = 2.33), and what is its 10-day 99% VaR using the square-root-of-time rule (√10 ≈ 3.1623)?

  1. 1-day 99% VaR = 8.388 million RMB; 10-day 99% VaR = 26.526 million RMB Correct answer.
  2. 1-day 99% VaR = 3.600 million RMB; 10-day 99% VaR = 36.000 million RMB
  3. 1-day 99% VaR = 5.940 million RMB; 10-day 99% VaR = 18.784 million RMB
  4. 1-day 99% VaR = 12.500 million RMB; 10-day 99% VaR = 125.000 million RMB

Explanation

Parametric VaR formula under normality is: VaR = Z_α × σ_daily × V. 1-day 99% VaR = 2.33 × 0.0180 × 200,000,000 = 2.33 × 3,600,000 = 8,388,000 RMB (8.388 million RMB). Under the square-root-of-time scaling rule: 10-day VaR = 1-day VaR × √10 = 8,388,000 × 3.1623 = 26,526,000 RMB (26.526 million RMB).