Chapter 24 Exercises: Stablecoins: The Bridge Between Crypto and the Dollar

Conceptual Questions

Exercise 24.1 — Stablecoin Architecture Comparison

Compare the three stablecoin architectures (fiat-backed, crypto-collateralized, algorithmic) across the following dimensions. For each, identify which architecture performs best and worst, and explain why.

a) Peg stability under normal market conditions b) Peg stability under extreme market stress c) Decentralization and censorship resistance d) Capital efficiency (how much collateral is needed per dollar of stablecoin) e) Regulatory risk f) Scalability (ability to grow market cap without degrading stability)

Exercise 24.2 — The Arbitrage Loop

A fiat-backed stablecoin (USDT) is trading at $0.985 on Binance.

a) Describe the steps an authorized participant would take to profit from this deviation. b) Explain how these actions push the price back toward $1.00. c) What are the risks to the arbitrageur in this trade? (Consider: redemption time, minimum redemption amounts, counterparty risk.) d) Now suppose USDT is trading at $1.015. Describe the reverse arbitrage. e) Why can't ordinary retail traders perform this arbitrage directly with Tether?

Exercise 24.3 — DAI Vault Mechanics

Alice deposits 10 ETH into a MakerDAO Vault when ETH is priced at $2,000. The liquidation ratio for ETH is 150%.

a) What is the maximum amount of DAI Alice can mint? b) Alice mints 10,000 DAI. What is her current collateralization ratio? c) At what ETH price will Alice's Vault be liquidated? d) If ETH drops to $1,400, describe what happens during the liquidation process. e) Why does MakerDAO require over-collateralization? Why not 100% collateral? f) How does the Peg Stability Module (PSM) differ from the Vault system in maintaining DAI's peg?

Exercise 24.4 — Terra/Luna Death Spiral Mechanics

Trace the Terra/Luna death spiral step by step. Assume the following starting conditions: - UST market cap: $18 billion - LUNA price: $80 - LUNA supply: 350 million tokens

a) UST drops to $0.95. Arbitrageurs burn $1 billion of UST. How many new LUNA tokens are minted? What happens to LUNA's supply? b) The massive LUNA selling pushes LUNA's price to $50. Now another $1 billion of UST is burned. How many new LUNA tokens are minted at this price? c) Compare your answers to (a) and (b). Explain why the spiral accelerates as LUNA's price falls. d) At what point does the spiral become mathematically irreversible? (Hint: consider when the LUNA being minted exceeds the market's ability to absorb it.) e) Could rate-limiting the burn/mint mechanism have prevented the collapse? Argue both sides.

Exercise 24.5 — Anchor Protocol Analysis

The Anchor Protocol offered ~20% APY on UST deposits.

a) At UST's peak market cap of ~$18 billion, and assuming 70% was deposited in Anchor, how much annual yield would need to be paid? b) Where was this yield coming from? (Describe the revenue sources and the subsidy mechanism.) c) Why was this yield unsustainable in the long run? d) How did the high yield create fragile demand for UST? What is the difference between organic demand and yield-driven demand for a stablecoin? e) Draw an analogy to traditional finance. What historical financial product or scheme does the Anchor yield most resemble?

Exercise 24.6 — Reserve Composition Analysis

Below is a simplified representation of Tether's reserve composition at two points in time:

Q1 2021: - Cash and bank deposits: 3.87% - Treasury bills: 2.94% - Commercial paper: 49.6% - Secured loans: 12.55% - Corporate bonds: 9.96% - Other investments: 21.08%

Q4 2024 (approximate): - US Treasury bills: ~80% - Cash and bank deposits: ~5% - Money market funds: ~5% - Secured loans: ~5% - Other: ~5%

a) Compare the risk profiles of these two reserve compositions. Which is safer for stablecoin holders, and why? b) Why is commercial paper riskier than Treasury bills as a reserve asset? c) Even with the improved reserve composition, what fundamental concern remains about Tether's reserves? d) Explain the difference between an attestation and an audit. Why does this distinction matter? e) If you were designing reserve requirements for a stablecoin regulatory framework, what would you require? Justify your choices.

Applied Problems

Exercise 24.7 — Peg Deviation Analysis

Use the code/peg_stability.py simulation to explore peg stability under stress.

a) Run the fiat-backed simulation with a $500 million redemption shock. How quickly does the peg recover? What is the maximum deviation? b) Now run with a $2 billion redemption shock. How does the recovery change? c) Run the crypto-collateralized simulation with a 30% collateral price drop. How many liquidations occur? Does the peg hold? d) Run with a 50% collateral price drop (similar to Black Thursday). What happens? e) Based on your simulations, rank the three stablecoin types by resilience to a sudden $1 billion sell event. Explain your ranking.

Exercise 24.8 — Terra Death Spiral Simulation

Use the code/terra_death_spiral.py simulation to model the collapse.

a) Run the baseline simulation with default parameters. At what time step does LUNA's price cross below $1? Below $0.01? b) Modify the initial UST sell pressure from $500M to $150M (the approximate actual initial sell). Does the spiral still occur? At what threshold of initial selling does the system survive? c) Add a "rate limiter" that caps UST-to-LUNA burns at $100M per day. Does this prevent the collapse or merely slow it? d) Add a "reserve defender" with $3B in Bitcoin reserves (modeling the LFG). At what point do the reserves run out? Does the defense succeed? e) Write a one-paragraph analysis of what your simulation reveals about the fundamental stability (or instability) of the burn/mint mechanism.

Exercise 24.9 — Stablecoin Comparison Dashboard

Use code/stablecoin_comparison.py to analyze stablecoin performance.

a) Compare the peg deviation histories of USDT, USDC, and DAI over a simulated one-year period. Which has the tightest peg? b) Identify the largest peg deviation for each stablecoin. What event caused each deviation? c) Create a risk scorecard for each stablecoin across the dimensions of: reserve quality, decentralization, regulatory risk, and peg stability. d) Based on your analysis, which stablecoin would you recommend for: (i) a crypto trader, (ii) a DeFi protocol, (iii) a person in Argentina saving in dollars? Justify each choice.

Exercise 24.10 — Regulatory Analysis

You are an advisor to a government considering stablecoin regulation. Evaluate the following policy options:

a) Option A: Ban all stablecoins. What are the consequences? Who is harmed? Is this enforceable? b) Option B: Require all stablecoins to be fully backed by cash or Treasury bills, audited quarterly, with the issuer holding a banking license. What are the effects on USDT, USDC, DAI, and algorithmic stablecoins? c) Option C: Require 1:1 reserves but allow crypto-collateralized stablecoins with minimum overcollateralization ratios. How would you set the ratio? What collateral types would you allow? d) Option D: Allow algorithmic stablecoins but require prominent risk warnings and cap individual holdings. Is this sufficient consumer protection? e) Draft a one-page memo recommending one of these options (or a combination), with justification.

Critical Thinking

Exercise 24.11 — The Decentralization Trade-off

"The most stable stablecoins are the most centralized, and the most decentralized stablecoins are the least stable."

a) Evaluate this claim using evidence from the chapter. b) Is there a theoretical path to a stablecoin that is both highly stable and highly decentralized? What would it require? c) Does the DAI Peg Stability Module (which relies on USDC) represent a fundamental compromise of DAI's decentralization? Or is it a pragmatic engineering choice? d) LUSD (Liquity) has no governance and is fully immutable. What are the advantages and disadvantages of this approach compared to DAI's governance-heavy model?

Exercise 24.12 — The USDT Thought Experiment

Imagine that tomorrow, a credible whistleblower reveals that Tether's reserves are only 70% of outstanding USDT (a $27 billion shortfall).

a) Trace the immediate market effects, hour by hour, for the first 48 hours. b) How would this affect Bitcoin's price? (Consider: USDT is the base pair for most BTC trading.) c) How would DeFi protocols respond? Which protocols are most exposed? d) Would this event trigger a broader financial crisis beyond crypto? Why or why not? e) What parallels exist between this scenario and the 2008 money market fund "breaking the buck" event (Reserve Primary Fund)?

Exercise 24.13 — Mechanism Design Challenge

You are tasked with designing a new stablecoin that avoids the flaws of each existing architecture. Your design must: - Maintain a peg within 1% of $1.00 under normal conditions - Not rely on a centralized issuer - Not require more than 120% collateralization - Not use a reflexive burn/mint mechanism (no death spiral risk)

a) Propose a mechanism. Describe its components, incentive structures, and peg maintenance logic. b) Identify the three most likely failure modes of your design. c) How does your design handle a 40% crash in collateral value over 24 hours? d) Explain why achieving all four requirements simultaneously is extremely difficult. What trade-off does your design make?

Exercise 24.14 — The Ethics of Yield

Anchor Protocol offered 20% APY on UST, attracting billions of dollars from retail investors — many of whom did not understand the risks.

a) Was the Anchor yield predatory? Compare it to traditional financial products with high advertised yields (e.g., junk bonds, high-yield savings accounts). b) Do DeFi protocol designers have an ethical obligation to ensure users understand the risks? How does this obligation differ from TradFi duties of suitability? c) After the collapse, Do Kwon (Terra's co-founder) was arrested and charged with fraud. Evaluate: at what point does an overpromising protocol designer cross the line from optimism to fraud? d) Should there be a legal distinction between a stablecoin that depegs due to a design flaw and one that depegs due to fraud? How would you draw that line?

Exercise 24.15 — Emerging Market Impact

Stablecoins are widely used in Argentina, Nigeria, Turkey, and other countries with currency instability.

a) Explain why USDT and USDC are attractive to citizens of these countries. What problem do they solve? b) What are the risks to users in these countries if USDT fails? How does this differ from risks to US-based crypto traders? c) How does stablecoin adoption affect these countries' monetary sovereignty? If citizens hold dollars (via stablecoins) instead of local currency, what happens to the central bank's ability to manage monetary policy? d) Should stablecoin issuers have a responsibility to users in emerging markets who use their product as a savings vehicle? Why or why not? e) Compare stablecoin adoption to historical "dollarization" episodes (e.g., Ecuador, Zimbabwe). What are the parallels and differences?