Appreciation / IR effect. Profitability of Borrowing DAI
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How to use and understand this tool
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The Appreciation / IR effect is an analytical tool to understand the limitations of interest rate-driven stablecoins such as MakerDAO's DAI.
Since DAI can be borrowed against a cryptocurrency deposit (currently ether) and can be used for a leveraged position (buying more ether with the borrowed DAI), we can analyse under which conditions is such an operation still profitable.

When evaluating profitability of such leveraged position, there are 3 variables that come into play:
* DAI price when borrowing
* % ether appreciation
* % interest rate (dubbed "stability fee" within MakerDAO)

First, input the DAI price when borrowing (yellow cells). It can go below the $1 soft peg and as the tool shows, borrowing at sub-peg prices and repaying the loan at the peg can still be profitable.
Second, pick the assumed ETH appreciation rate - variables are in the rows and grow exponentially for better analytical picture.
Third, see the corresponding interest rates in the columns (these also gro exponentially).
The individual cells show whether leveraged positions under the given conditions (DAI borrow and repay price, loan interest rate and ETH appreciation) is profitable, and what would be the necessary interest rate to render such operation unprofitable (thus lowering the pressure on the peg).

The main point of the tool is to show that DAI can go well below the $1 peg and still offer a good use case for its users (which also spells doom for use cases other than leveraged positions, because the interest rate can reach hundreds of percent, while DAI price still remains under the peg).

The table is divided into three tables, showing different time scenarios - the first on weekly basis, the second on monthly basis, the third on yearly basis.

For questions and more analysis, follow us on Twitter: @debnkio.
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created by DEBNK.io
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follow us on
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https://twitter.com/debnkio
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Table I: Weekly appreciation / Interest rate
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DAI borrow at:$5.00
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DAI repay at:$1.00
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Interest rate (per annum, recalculated to weekly basis)
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0.00%1.00%1.62%2.62%4.24%6.85%11.09%17.94%29.03%46.97%76.00%122.97%198.96%321.92%520.86%
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ETH appreciation (per week)0.00%80.00%80.00%79.99%79.99%79.98%79.97%79.96%79.93%79.89%79.82%79.71%79.53%79.23%78.76%78.00%
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1.00%81.00%81.00%80.99%80.99%80.98%80.97%80.96%80.93%80.89%80.82%80.71%80.53%80.23%79.76%79.00%
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1.62%81.62%81.61%81.61%81.61%81.60%81.59%81.58%81.55%81.51%81.44%81.33%81.15%80.85%80.38%79.61%
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2.62%82.62%82.61%82.61%82.61%82.60%82.59%82.58%82.55%82.51%82.44%82.33%82.14%81.85%81.38%80.61%
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4.24%84.24%84.23%84.23%84.23%84.22%84.21%84.19%84.17%84.12%84.06%83.94%83.76%83.47%83.00%82.23%
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6.85%86.85%86.85%86.85%86.84%86.84%86.83%86.81%86.78%86.74%86.67%86.56%86.38%86.09%85.62%84.85%
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11.09%91.09%91.09%91.08%91.08%91.07%91.06%91.05%91.02%90.98%90.91%90.80%90.62%90.32%89.85%89.09%
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17.94%97.94%97.94%97.94%97.93%97.93%97.92%97.90%97.87%97.83%97.76%97.65%97.47%97.18%96.70%95.94%
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29.03%109.03%109.03%109.02%109.02%109.01%109.00%108.99%108.96%108.92%108.85%108.74%108.56%108.26%107.79%107.03%
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46.97%126.97%126.97%126.96%126.96%126.95%126.94%126.93%126.90%126.86%126.79%126.68%126.50%126.21%125.73%124.97%
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76.00%156.00%155.99%155.99%155.99%155.98%155.97%155.96%155.93%155.89%155.82%155.71%155.53%155.23%154.76%154.00%
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122.97%202.97%202.96%202.96%202.96%202.95%202.94%202.92%202.90%202.85%202.79%202.67%202.49%202.20%201.73%200.96%
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198.96%278.96%278.96%278.95%278.95%278.94%278.93%278.92%278.89%278.85%278.78%278.67%278.49%278.19%277.72%276.96%
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321.92%401.92%401.91%401.91%401.91%401.90%401.89%401.87%401.85%401.80%401.74%401.62%401.44%401.15%400.68%399.91%
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520.86%600.86%600.86%600.85%600.85%600.84%600.83%600.82%600.79%600.75%600.68%600.57%600.39%600.09%599.62%598.86%
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^^^ Leveraged position profitability ^^^
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Table II: Monthly appreciation / Interest rate
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DAI borrow at:$0.90
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DAI repay at:$1.00
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Interest rate (per annum, recalculated to monthly basis)
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0.00%1.00%1.62%2.62%4.24%6.85%11.09%17.94%29.03%46.97%76.00%122.97%198.96%321.92%520.86%
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ETH appreciation (per month)0.00%-11.11%-11.20%-11.26%-11.35%-11.50%-11.75%-12.14%-12.77%-13.80%-15.46%-18.15%-22.50%-29.53%-40.92%-59.34%
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1.00%-10.11%-10.20%-10.26%-10.35%-10.50%-10.75%-11.14%-11.77%-12.80%-14.46%-17.15%-21.50%-28.53%-39.92%-58.34%
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1.62%-9.49%-9.59%-9.64%-9.74%-9.89%-10.13%-10.52%-11.15%-12.18%-13.84%-16.53%-20.88%-27.92%-39.30%-57.72%
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2.62%-8.49%-8.59%-8.64%-8.74%-8.89%-9.13%-9.52%-10.15%-11.18%-12.84%-15.53%-19.88%-26.92%-38.30%-56.72%
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4.24%-6.88%-6.97%-7.03%-7.12%-7.27%-7.51%-7.90%-8.54%-9.56%-11.22%-13.91%-18.26%-25.30%-36.68%-55.10%
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6.85%-4.26%-4.35%-4.41%-4.50%-4.65%-4.89%-5.28%-5.92%-6.95%-8.61%-11.29%-15.64%-22.68%-34.06%-52.49%
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11.09%-0.02%-0.11%-0.17%-0.26%-0.41%-0.66%-1.05%-1.68%-2.71%-4.37%-7.06%-11.41%-18.44%-29.83%-48.25%
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17.94%6.83%6.74%6.68%6.59%6.44%6.20%5.80%5.17%4.14%2.48%-0.21%-4.55%-11.59%-22.98%-41.40%
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29.03%17.92%17.83%17.77%17.68%17.53%17.28%16.89%16.26%15.23%13.57%10.88%6.53%-0.50%-11.89%-30.31%
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46.97%35.86%35.77%35.71%35.62%35.47%35.23%34.83%34.20%33.17%31.51%28.82%24.47%17.44%6.05%-12.37%
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76.00%64.89%64.80%64.74%64.65%64.50%64.25%63.86%63.23%62.20%60.54%57.85%53.50%46.47%35.08%16.66%
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122.97%111.85%111.76%111.71%111.61%111.46%111.22%110.83%110.19%109.17%107.51%104.82%100.47%93.43%82.05%63.63%
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198.96%187.85%187.76%187.70%187.61%187.46%187.21%186.82%186.19%185.16%183.50%180.81%176.46%169.43%158.04%139.62%
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321.92%310.80%310.71%310.65%310.56%310.41%310.17%309.78%309.14%308.12%306.46%303.77%299.42%292.38%281.00%262.58%
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520.86%509.75%509.66%509.60%509.51%509.36%509.11%508.72%508.09%507.06%505.40%502.71%498.36%491.33%479.94%461.52%
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^^^ Leveraged position profitability ^^^
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Table III: Yearly appreciation / Interest rate
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DAI borrow at:$1.00
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DAI repay at:$1.00
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Interest rate (per annum, yearly basis)
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0.00%1.00%1.62%2.62%4.24%6.85%11.09%17.94%29.03%46.97%76.00%122.97%198.96%321.92%520.86%
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ETH appreciation (per year)0.00%0.00%-1.00%-1.62%-2.62%-4.24%-6.85%-11.09%-17.94%-29.03%-46.97%-76.00%-122.97%-198.96%-321.92%-520.86%
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1.00%1.00%0.00%-0.62%-1.62%-3.24%-5.85%-10.09%-16.94%-28.03%-45.97%-75.00%-121.97%-197.96%-320.92%-519.86%
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1.62%1.62%0.62%0.00%-1.00%-2.62%-5.24%-9.47%-16.32%-27.41%-45.35%-74.38%-121.35%-197.34%-320.30%-519.24%
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2.62%2.62%1.62%1.00%0.00%-1.62%-4.24%-8.47%-15.32%-26.41%-44.35%-73.38%-120.35%-196.34%-319.30%-518.24%
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4.24%4.24%3.24%2.62%1.62%0.00%-2.62%-6.85%-13.71%-24.79%-42.74%-71.76%-118.73%-194.72%-317.68%-516.62%
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6.85%6.85%5.85%5.24%4.24%2.62%0.00%-4.24%-11.09%-22.18%-40.12%-69.15%-116.11%-192.11%-315.06%-514.01%
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11.09%11.09%10.09%9.47%8.47%6.85%4.24%0.00%-6.85%-17.94%-35.88%-64.91%-111.88%-187.87%-310.83%-509.77%
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17.94%17.94%16.94%16.32%15.32%13.71%11.09%6.85%0.00%-11.09%-29.03%-58.06%-105.02%-181.02%-303.97%-502.92%
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29.03%29.03%28.03%27.41%26.41%24.79%22.18%17.94%11.09%0.00%-17.94%-46.97%-93.94%-169.93%-292.89%-491.83%
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46.97%46.97%45.97%45.35%44.35%42.74%40.12%35.88%29.03%17.94%0.00%-29.03%-76.00%-151.99%-274.94%-473.89%
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76.00%76.00%75.00%74.38%73.38%71.76%69.15%64.91%58.06%46.97%29.03%0.00%-46.97%-122.96%-245.92%-444.86%
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122.97%122.97%121.97%121.35%120.35%118.73%116.11%111.88%105.02%93.94%76.00%46.97%0.00%-75.99%-198.95%-397.89%
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198.96%198.96%197.96%197.34%196.34%194.72%192.11%187.87%181.02%169.93%151.99%122.96%75.99%0.00%-122.96%-321.90%
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321.92%321.92%320.92%320.30%319.30%317.68%315.06%310.83%303.97%292.89%274.94%245.92%198.95%122.96%0.00%-198.94%
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520.86%520.86%519.86%519.24%518.24%516.62%514.01%509.77%502.92%491.83%473.89%444.86%397.89%321.90%198.94%0.00%
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^^^ Leveraged position profitability ^^^
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