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APR、通胀、费用与借贷成本 | Stratmill

文章 Quant Q&A · 作者: Eduardo J. Sanchez
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总结

本文探讨年化百分率如何与名义利率、实际利率、通胀、费用和贷款总成本相关。文中提出一个简单计算：从名义年利率中减去通胀率，再按本金加费用与本金的比值对所得实际利率进行调整。作者询问该公式是否适用于一年期贷款，以及较短借款期限是否需要按天数折算成年化利率。

本文的主要价值在于指出，解读APR时应区分报价利率、经通胀调整后的收益、费用、贷款期限和还款金额。该脚本是学习辅助工具，并非经过验证的APR计算方法。具体而言，它没有说明实际贷款机构如何计算APR、费用如何计时，或复利和还款安排如何影响利率。所提出的公式还以一种有待评估的方式将实际利率与费用结合起来，因此不应将其视为通用贷款定价方法。

核心观点

  • 讨论APR时，应区分名义利率、经通胀调整的利率、费用和还款成本。
  • 作者提出通过以本金为基准进行调整，将全部费用纳入经通胀调整的利率。
  • 示例假设借款期限为一年，并提出较短期限是否需要调整的问题。
  • 该脚本仅供探索，并未确立贷款机构通用的APR计算方法。
  • 本文没有讨论复利、费用计时和还款安排。

标签

固定收益统计学
全文
# Understanding APR via programming


# Understanding APR via programming












I am trying to better understand different types of interest rates. However, I am having difficulties complete, consistent and pedagogically-efficient explanations online. Thus, I have decided to design and program a couple of scripts. I find that programming can be a powerful bridge to truly understand tricky concepts.

The first concept I am trying to understand is the so-called annualized percentage rate (APR). Common explanations basically mention this one as an interest rate that somehow accounts for the costs of the loan...

- The name is very misguiding... right?

- Does it have to be annualized if and only if the given rate is not quoted per annum?

- Also, is it computing using the real interest rate, rather than a nominal interest rate?

- How is the APR used in practice by loan providers? Do they establish a nominal rate that makes sense to them, add the fees and then compute the "APR" to then use it to compute interest payments?

Does the following piece of code make sense? In this piece of code, I use the term "cost-of-borrowing interest rate" to refer to the "APR":

```
  inflation_rate_per_year            // Annual inflation rate.
  nominal_interest_rate_per_year     // Nominal interest rate per year.
  real_interest_rate_per_year        // Inf-adj inf. rate per year.
  cost_borrow_interest_rate_per_year // Cost-of-borrowing int. rate.
  principal_money                    // Amount being loaned.
  total_fees_money                   // Total to be payed in fees.
  total_cost_loan_money_per_year     // Total cost of loan per year.
  total_owned_money                  // Total to pay back.

  // Given: inflation_rate_per_year, nominal_interest_rate_per_year
  // Given: principal_money, total_fees_money

  // Compute real interest rate and percentage.
  real_interest_rate_per_year = nominal_interest_rate_per_year - inflation_rate_per_year

  // Compute cost-of-borrowing interest rate and percentage.
  cost_borrow_interest_rate_per_year =
    (total_fees_money + principal_money)/principal_money*
    real_interest_rate_per_year

  // Compute appreciation on principal.
  total_cost_loan_money_per_year =
    principal_money*((1 + cost_borrow_interest_rate_per_year) - 1)

  total_owned_money = principal_money*(1 + cost_borrow_interest_rate_per_year)
```

Why do I mean by "making sense"? Well, is it OK, considering the given interest rates assume the borrowing period to be 1 year? If it were not a year... Should I have to add the annualization factor of `365/n`, with `n` equaling the number of days in the borrowing period.

I understand the question is posed a little vaguely. I basically want to better understand the APR via this script :)

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此摘要由 Stratmill 研究智能体根据原文撰写，并非原文副本。