Daily article 66: Understand the interest rate
Let’s just follow the topics in the textbook to start our journey to CFA. I always believe that to learn something is not merely to memorize the equations, solve the questions and get high scores. Rather, we should understand the logic behind and physical meanings to really master the knowledge, which will also be the principle in my future articles.
Leaving the first part, ethical and professional standards for the future, let’s jump into the second part: the time value of money. I’ve discussed this topic in my daily article 11, so let’s just agree that time value of money can be measured using the interest rate. Given a positive interest rate, the same amount of money today is actually worth more than that in the future because you can simply save money in the bank and earn the interest. But as we discuss more financial instruments or just look at financial products in the real world, we can tell that interest rates of different investments are different. We need to understand the reasons behind.
Interest rate consists of 5 components. The first is real risk-free interest rate, which is an ideal rate of return that one can get from a 100% safe investment without inflation. The second is inflation premium. There is always inflation in the real world so we usually sum the first two and call the result nominal risk-free interest rate. In CFA exam, we use a country’s governmental short-term debt to represent nominal risk-free interest rate in that country over that time horizon. The third is default risk premium, which compensates the possibilities that financial instruments fail to pay the money back. We can intuitively agree that a more risky one pays more interest rate given other conditions the same. The fourth is liquidity premium, which compensates for the liquidities. In other words, how soon I can cash the financial instruments. Intuitively, the sooner I can transfer the financial instruments into cash the better. So the one with higher liquidity (easier to cash) pays less on liquidity premium. The last one is maturity premium, which compensates for the market changes as maturity is extended. In general, we agree that a long-term bond should pay more interest than a short-term one holding all else equal.
So now we can draw a conclusion that Interest rate = Real risk-free interest rate Inflation premium Default risk premium Liquidity premium Maturity premium. We not only memorize the equation but also understand the physical meaning of each component. The ideas - returns, risks and time are the vital concepts in financial world and CFA exams which we will talk again and again. Since now, we can start using the interest rate to solve many problems in the exam as well as the real world. I’ll meet you in next article.
让我们沿着CFA教材的思路开始CFA之旅。我一直认为，学习并不仅仅是记忆公式、解决题目、获得高分。更重要的是，我们需要掌握知识背后的逻辑和物理含义。这一原则也会体现在我以后的文章中。
让我们把第一部分，《道德和职业标准》放一放，先来看教材第二个部分：《货币的时间价值》。因为我在每日文章11中有过介绍，这里就不再赘述，而是默认货币的时间价值可以用利率来进行衡量。在利率为正的情况下，同样数量的钱在今天总比在未来值钱，因为你可以简单地把本金放在银行并赚取利息。但随着我们深入讨论各种金融产品，或者我们在现实生活中看到各种金融产品时，我们会发现这些产品的利率（回报率）是不同的。我们需要了解这背后的原因。
利率由五部分组成。第一部分是真实无风险利率，这是在不考虑通货膨胀的情况下，一个绝对安全的金融产品可以带来的理想收益率。第二部分是通货膨胀溢价。因为在现实生活中通货膨胀一直存在，我们通常把前两部分加在一起，称其为名义无风险利率。在CFA考试中，我们会把一个国家政府债券的收益率认为是那一个国家当时的名义无风险利率。第三部分是违约风险溢价，它用以补偿一项金融产品违约，从而无法支付本息的风险。自然而然地，我们可以认为同等情况下，风险越大的产品，应该支付越多的利息。第四部分是流动性溢价，它用以补偿流动性。流动性说白了，就是多长时间我可以把金融产品变现。越容易变现，投资人越喜欢。所以流动性大的金融产品支付更少的流动性溢价。最后一个部分是期限溢价，它用以弥补金融产品期限长时，市场变化引起的风险。通常我们认为，其他条件相同时，一个期限更长的债券应该比期限更短的债券支付更多的利息。
通过上面的介绍，我们可以总结出一个公式： 利率 = 真实无风险利率 通货膨胀溢价 违约风险溢价 流动性溢价 期限溢价。我们并不是单纯地记忆这个公式，而是理解了公式背后每一项的物理意义。这其中涉及的利率（回报率），风险和时间等概念，会贯穿金融世界和CFA考试的始终。之后，我们就可以开始应用利率来解答很多CFA和现实世界的问题。我们下篇文章见。
