2022美赛C题：交易策略 Trading Strategies 解题方案
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题目描述：
背景 市场交易员经常买卖波动性资产，其目标是使其总回报最大化。每一次买卖通常都有一笔佣金。其中两种资产是黄金和比特币。
要求 交易员要求您开发一个模型，该模型仅使用迄今为止过去的每日价格流来确定交易员每天是否应该购买、持有或出售其投资组合中的资产。
你将在2016 年11 月9 日从1000 美元开始。您将使用从2016 年11 月9 日至2021 年10 月9 日的五年交易期。在每个交易日，交易员将拥有一个包括现金、黄金和比特币C、G，B]的投资组合。美元，金衡盎司和比特币。初始状态是[1000、0、0]。每笔交易（买卖）的佣金成本为交易金额的α%。假设α黄金=1%和α比特币= 2%.持有资产没有成本。
请注意，比特币可以每天交易，但黄金只在市场开盘的日子交易，这在定价数据文件LBMA-GOLD 中所反映的那样。csv 和BCHAIN-MKPRU.csv你的模型应该考虑到这个交易时间表。
- 开发一个模型，仅基于当天的价格数据，给出最佳的每日交易策略。
- 使用你的模式和策略，在2021 年10 月9 日开始的1000 美元的初始投资值多少钱？
- 提供证据，证明您的模型是提供最佳策略的。确定该策略对交易成本的敏感程度。交易成本如何影响策略和结果？
- 在一份最多两页的备忘录中向交易员传达你的策略、模型和结果。
英文原版：
Background
Market traders buy and sell volatile assets frequently, with a goal to maximize their total return. There is usually a commission for each purchase and sale. Two such assets are gold and bitcoin.
Requirement
You have been asked by a trader to develop a model that uses only the past stream of daily prices to date to determine each day if the trader should buy, hold, or sell their assets in their portfolio.
You will start with $1000 on 9/11/2016. You will use the five-year trading period, from 9/11/2016 to 9/10/2021. On each trading day, the trader will have a portfolio consisting of cash, gold, and bitcoin [C, G, B] in U.S. dollars, troy ounces, and bitcoins, respectively. The initial state is [1000, 0, 0]. The commission for each transaction (purchase or sale) costs α% of the amount traded. Assume αgold = 1% and αbitcoin = 2%. There is no cost to hold an asset.
Note that bitcoin can be traded every day, but gold is only traded on days the market is open, as reflected in the pricing data files LBMA-GOLD.csv and BCHAIN-MKPRU.csv. Your model should account for this trading schedule.
To develop your model, you may only use the data in the two spreadsheets provided: LBMA-GOLD.csv and BCHAIN-MKPRU.csv.
• Develop a model that gives the best daily trading strategy based only on price data up to that day. How much is the initial $1000 investment worth on 9/10/2021 using your model and strategy?
• Present evidence that your model provides the best strategy.
• Determine how sensitive the strategy is to transaction costs. How do transaction costs affect the strategy and results?
• Communicate your strategy, model, and results to the trader in a memorandum of at most two pages.