Foreword
This is my reading notes on Financial Economics, in which I aim to construct an intuitive map, highlighting the key concepts and their logical relationships. The mathematics are intentionally left out as the goal is to lay a foundational understanding of the ‘why’ and ‘how’ behind the theories.
With this conceptual framework in place, we can choose to dive into the mathematical intricacies later, if and when we wish to deepen the understanding
What is Finance?
Simply put, finance is study on allocation of financial assets.
But then, what are financial assets? Financial assets can be understood as contracts on future economic benefits. Since “future” is involved, it’s always related with time and uncertainty. But humans hate uncertainty and that’s why finance was born to answer some basic questions like “should I buy asset A or asset B?” or “how do I know I’m not being taken advantage of for paying this price?”
Financial Markets
There are always people who want to sell assets for money and people who want to buy assets for satisfaction or future benefits. When all these people gather together, a market is formed, in which the price of things got determined automatically by demand and supply with no controversy, you can easily sell or buy things, and you don’t need to go all over the world to find a buyer or seller. We just described the three main functions of financial markets which are price discovery, liquidity, and lowering transaction cost.
How to Measure Future Benefits?
Now, we need to think about how to measure how much benefits an asset could bring in the future, this crystal ball is cash flow analysis. Basically we estimate how much money the asset could bring in the future, however, money today and money in the future are like apples and oranges – similar, but not the same. This difference is due to the time value of money, a fundamental concept in finance that reflects the idea that a dollar today is worth more than a dollar tomorrow. Why? Because money now can go off and make more money!
To make sure we’re comparing apples to apples, we use a trick called discounting, which adjusts the future cash flows to their present value, the rate used is called discount rate, adjusting for risk and the opportunity cost of capital – essentially, what you could earn if you invested your money elsewhere.
By calculating the present value of future cash, we get a real-deal picture of an asset’s worth. The sum of all this time-traveled cash is the net present value (NPV), the golden key to figuring out if an asset is a treasure trove or a pirate’s bluff.
Analyzing Bonds
When it comes to bonds, cash flow analysis is like a detective’s toolkit. It’s all about understanding how much cash you’ll get and when. Imagine a bond as a series of cash envelopes that you’ll receive in the future. Each envelope represents a coupon payment, and there’s a big one at the end – the bond’s face value.
First, we need to talk about each envelope’s worth today – not just its face value. This is where discounting steps in, using what’s known as the spot rate. Think of the spot rate as the current interest rate for a specific period. It’s like the going rate for borrowing money today for that particular time frame.
But how do we find the spot rate? Enter the Bootstrap method, our financial detective’s magnifying glass. It cleverly uses the prices of existing bonds to figure out the spot rates for each year. You start with the first year and work your way up, like climbing a ladder.
Once you have these rates, it’s time to bring those future cash envelopes (coupon payments and face value) back to the present using these spot rates. This is like adjusting their values from future prices to today’s prices.
The sum of these discounted cash flows gives you the bond’s price. But wait, there’s more! This process also uncovers some cool insights. By observing the pattern of spot rates, you can gauge the market’s expectations for future interest rates. For example, if longer-term spot rates are higher, it suggests that the market expects interest rates to rise.
Lastly, there’s the strategy part. If you think interest rates are going up, you might want to ‘shorten your duration’ – that’s fancy talk for preferring bonds that pay back sooner rather than later. Why? Because when rates go up, bond prices go down, and bonds with shorter durations are less affected.
Analyzing Stocks
Think of a stock like a tree that grows money in the form of dividends. The key question: How much are those future money-fruits worth today?
Gordon Growth Model is a famous formula that tells you the value of a stock tree, consisting of three key elements: the dividends a company pays out, the discount rate, and the expected growth rate of these dividends.
In our forest, stock trees are compared by their P/E (Price/Earning) ratio, which is like comparing the price of a tree to how many golden apples it produces. Some trees give lots of apples quickly (high earnings), while others take their time. The P/E ratio is a way to figure out if we’re getting a good deal on our tree.
Earnings as Dividends
The stock valuation models built on dividends suggest that higher dividends should lead to a higher stock price. However, this raises an intriguing question: why don’t companies distribute all their earnings as dividends to boost their stock prices? Moreover, what if they borrowed funds to pay dividends – would this inflate the stock price even further?
The true value of a stock is rooted not just in dividends, but in the ownership of the company and the shareholder’s influence over its operations. Think of a company like a chef in a kitchen. Just like a chef decides how much ingredient to put in a dish, a company decides how much profit to serve as dividends. They could give it all away, but what about tomorrow’s meals? Or, they could borrow money to make the dish even richer, but then they create a pile of dirty dishes (debts) for later.
Here’s where the balance comes in. A company should aim to harmonize its marginal rate of return on investments with the prevailing market interest rate. When a company’s returns are robust and exceed market rates, it’s generally more beneficial to reinvest the profits for future growth rather than distribute them. This strategy can potentially create greater long-term value for shareholders. In contrast, if the company’s returns lag behind the market rates, paying out dividends might be more attractive since shareholders could find more lucrative opportunities elsewhere in the market.
Fisher’s Separation Theorem
Enter Fisher’s Separation Theorem, which asserts that the process of cooking up investments is distinct from serving dividends. It advises companies to focus on preparing the best possible dish (maximizing stock value) while allowing shareholders the freedom to choose between savoring the meal now (receiving dividends) or saving the ingredients for an even grander feast in the future.
Fisher’s Separation Theorem further elucidates that a business’s investment decisions are distinct from its owners’ or investors’ preferences regarding consumption and savings. This principle encourages businesses to focus on maximizing stock value through strategic decisions (investment, dividends) while allowing shareholders to transform the dividends into their preferred consumption stream via borrowing or lending in the capital market.
A Bundle of Assets
Now let’s say we have a bundle of assets including risk free assets like government bonds and risky assets like stocks, how do we maximize return while minimizing risk?
This is the essence of portfolio theory, a concept pioneered by Markowitz in his groundbreaking 1952 work “Portfolio Selection.” This theory revolutionized the way we look at investments by considering the combination of various assets as a unified whole, rather than in isolation.
Imagine you’re a captain charting a course through the investment ocean. Your goal? To find the perfect balance between the calm seas (risk-free assets like government bonds) and the stormy waters (risky assets like stocks). This is the heart of portfolio theory - creating a harmonious blend of safety and adventure in your investment journey.
Now, let’s talk about the extra gold coins we get for sailing into riskier waters - this is our risk premium. If our stock ship promises a 25% return and our government bond boat offers a steady 11%, our risk premium is the extra 14% treasure we might find for braving the stormier seas.
In this quest, the Mean-Variance Analysis is our compass. It tells us not just where the treasure lies (the expected return or mean) but also how rough the seas might be (the risk or variance). Markowitz’s wisdom teaches us that by mixing different types of assets in our treasure chest, we can weather different storms (reduce overall volatility). This strategy is visually captured in the efficient frontier, a curve that shows us the best possible return for every level of risk we’re willing to take.
The line that starts at the risk-free rate and tangentially touches the efficient frontier is called Capital Market Line(CML). This tangent point is incredibly significant – it’s where our market portfolio, a perfectly balanced mix of all risky assets, resides. This point is like the ‘X’ on a treasure map, marking the spot where the risk-return trade-off is at its best.
Mutual Fund Theorem
The essence of the Mutual Fund Theorem is this: Every investor, whether cautious or bold, should sail with the same ship - the market portfolio. Then each investor decides how much of their treasure to place in this market portfolio and how much to keep in the safety of risk-free assets, like government bonds. The proportion depends on their appetite for risk, but essentially they’re all just gliding on Capital Market Line.
Following the Mutual Fund Theorem, investment managers can guide clients in constructing their portfolio in two crucial steps: first, by creating a market portfolio based on the returns and characteristics of the various risky assets, without considering the client’s specific preferences; second, by allocating the client’s assets between this market portfolio and a risk-free asset in a way that aligns with their risk preferences.
Capital Asset Pricing Model
Now we know how to construct an optimal portfolio, but how can we assess the individual contributions of each asset within that portfolio? This is where the Capital Asset Pricing Model (CAPM) comes into play.
It introduces the concept of systematic risk, also known as market risk, which is the risk inherent to the entire market or market segment. This includes factors like economic recessions, political instability, or global events that impact the entire market.
On the other hand, unsystematic risks, also known as diversifiable risks, are unique to individual companies or industries. These can include risks like a company’s management decisions, product failures, or sector-specific downturns. These risks can be largely mitigated through diversification—by holding a variety of assets from different sectors or industries, the impact of any one company or sector is minimized.
Essentially, in the framework of CAPM, the expected return on an asset is not influenced by the asset’s total risk (which includes both systematic and unsystematic risks), but only by its systematic risk, which is quantified through a metric known as beta (β) that measures an asset’s sensitivity to systematic market risks. By investing in a well-diversified portfolio, investors can reduce their exposure to unsystematic risk, but they cannot eliminate systematic risk. Hence, the market compensates investors only for the latter, the non-diversifiable, systematic risk.
The Security Market Line(SML) is a graphical representation of the CAPM and serves as a visual tool for assessing the expected return of an investment given its systematic risk (beta). In the SML graph, the y-axis represents the expected return of an investment, while the x-axis represents the beta, or the systematic risk of the investment.
Sharpe Ratio
Suppose there are multiple portfolios for us to invest, how can we measure and compare the performance of different investments or portfolios, taking into account their risk?
We can think the portfolios form multiple SMLs, and the one with the highest slope signifies that investors are being rewarded with highest returns for each unit of risk they take on, another name for the slope is Sharpe Ratio. Note that Sharpe Ratio works best when comparing two already diversified portfolios.
Jensen’s Alpha
Investors and analysts also want to know if a fund manager’s skill or a specific investment strategy was truly adding value, accounting for the risk involved as indicated by the portfolio’s beta in relation to CAPM.
Jensen’s Alpha provides a metric to answer this by quantifying the excess return of a portfolio over its expected return, as predicted by CAPM, effectively isolating the manager’s performance or the strategy’s effectiveness.
One of the simple applications is to compare one’s yearly return with S&P500 yearly return as a true measure for performance.
The Two Pricing Models
As we’ve explored, the quest to answer “how to price assets” forms the cornerstone of financial theory. In summary, there are two fundamental models at the heart of this pursuit:
To generalize, there are two fundamental pricing models:
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Equilibrium Pricing or Absolute Pricing: This model starts from the ground up, determining asset prices based on a supply and demand framework. It’s an intrinsic approach, focusing on the inherent value of assets. Within this model, the Consumption-CAPM emerges as a key theory. It extends the classic CAPM by integrating an investor’s consumption patterns into investment decisions, highlighting CAPM as a special, more limited case.
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Non-Arbitrage Pricing or Relative Pricing: Contrasting with the equilibrium model, this approach prices assets based on existing market prices. It’s the theory that supports financial derivatives market.
It’s time to take a break in our journey through the world of finance. From cash flow analysis to the nuances of CAPM, We’ve navigated the foundational principles of and theoretical models that drive financial valuations.
Stay tuned for the next series of posts where we’ll delve deeper into these fascinating areas, unraveling more complexities and exploring how these theories play out in real-world scenarios.
中文版
前言
这是我在学习《金融经济学》的读书笔记。这里突出展示关键理念及其之间的逻辑联系而特意略去了数学内容，目的是为了让读者能更加直观地理解这些理论的核心思想和运作方式。
通过这个基础框架，我们可以在未来根据需要来深入探索其背后的数学原理和细节。
什么是金融？
简单来说，金融是关于金融资产分配的研究。
那么，什么是金融资产呢？金融资产可以理解为对未来经济利益的合约。由于涉及到“未来”，这自然与时间和不确定性相关。但人类生性厌恶不确定性，这就是为什么我们需要金融理论来帮忙回答一些基本问题，比如“我应该买资产A还是资产B？”或者“我怎么知道我这个价格是不是冤大头？”
金融市场
总有些人想卖掉资产换取现金，也有些人想买入资产作为未来的收益。当这些人聚集在一起时，就形成了一个市场。在这个市场里，商品的价格会自然地根据供求关系来确定，你可以轻松地买卖东西，而且不需要跑遍全世界去找买家或卖家。这其实就是金融市场的三大主要功能：价格发现、提供流动性，以及降低交易成本。
如何衡量未来的收益？
我们需要考虑如何衡量一个资产将来可能带来的收益，这个“预测未来”的工具就是现金流分析。基本上，我们估计资产将来能带来多少钱，但是，今天的钱和将来的钱就像苹果和橘子——看似相似，却并不相同。这种差异是由于货币的时间价值造成的，它反映了一个道理：今天的一块钱比明天的一块钱更有价值。为什么呢？因为现在的钱可以去赚更多的钱！
为了确保比较的是同样的东西，需要使用一个叫做折现的技巧，它将未来的现金流调整为现值，使用的比率叫做贴现率，这个比率需要考虑风险和资本的机会成本。
通过计算未来现金的现值，我们可以得到一个资产真正价值的实际画面。所有这些经过时间旅行的现金之和就是净现值（NPV），这是判断一个资产是宝藏还是海盗的虚张声势的关键。
债券分析
想象一下，债券就像是一系列你未来将会收到的现金信封。每个信封代表一次息票支付，而在最后还有一个大的——那就是债券的面值。
首先，我们需要讨论的是每个信封今天的价值——而不仅仅是它的面值。这就是折现的作用所在，使用的是所谓的即期利率。把即期利率想象成特定时期的当前利率。它就像是你今天为那个特定时间段借款的行情利率。
但我们如何找到即期利率呢？这就需要引入Bootstrap方法，它巧妙地利用现有债券的价格来计算每一年的即期利率。从第一年开始，就像爬梯子一样可以计算出每年的即期利率。
一旦有了这些利率，就可以使用这些即期利率将那些未来的现金信封（息票支付和面值）从未来价格调整为今天的价格。
这些折现现金流的总和就给出了债券的价格。这个过程还能揭示一些有趣的见解。通过观察即期利率的模式，可以判断市场对未来利率的预期。例如，如果长期即期利率更高，这表明市场预计利率将会上升。
最后是策略部分。如果认为利率会上升，债券投资经理们可能会想要“缩短久期”——这是一种专业说法，意味着配置更多短期的债券。为什么？因为当利率上升时，债券价格下降，而短期债券受的影响较小。
股票分析
想象股票就像一棵能长出分红金苹果的树。关键问题是：这个树值多少钱？
戈登增长模型（Gordon Growth Model）是一个著名的公式，它可以告诉你一棵股票树的价值，包括三个关键元素：公司支付的股息、折现率和这些股息的预期增长率。
在我们的森林中，股票树可以通过其市盈率（P/E，价格与收益的比率）来比较，这就像是比较一棵树的价格与它能产生多少金苹果。有些树很快就能结出许多果实（高收益），而另一些则需要更长的时间。
收益作为股息分红
当我们讨论股票估值时，基于股息的模型表明较高的股息应该会导致股价上升。然而，这有一个问题：为什么公司不将所有的盈利都作为股息分发出去，以提高它们的股价呢？更进一步，如果公司借款来支付股息，会不会进一步推高股价呢？
股票的真正价值不仅在于股息，更在于公司的所有权以及股东对公司运营的影响。我们可以把公司比作厨房里的厨师。就像厨师决定在菜肴中放多少配料一样，公司决定将多少利润作为股息分发。他们可以把所有利润都分发出去，但这样做对未来的影响如何呢？或者，他们可以借钱使股息更加丰厚，但这样做就像是制造了一堆待清理的脏碗碟（债务）。
这里的平衡是公司应该努力使其投资的边际回报率与市场利率保持一致。当公司的回报率超过市场利率时，通常将利润再投资以促进未来增长更有利，而不是分发股息。这种策略可能会为股东创造更大的长期价值。相比之下，如果公司的回报率低于市场利率，那么支付股息可能更有吸引力，因为股东可能在市场上找到更有利可图的投资机会。
费雪分离定律
费雪分离定律定理指出，制定投资计划和支付股息是两个不同的过程。它建议公司专注于制作最佳的“菜肴”（最大化股票价值），同时允许股东自由选择是现在享用这“菜肴”（接收股息）还是为将来更宏伟的盛宴保存“食材”。
费舍尔分离定理进一步阐明，企业的投资决策与其所有者或投资者关于消费和储蓄的偏好是不同的。这一原则鼓励企业通过战略决策（投资、股息）专注于最大化股票价值，同时允许股东通过在资本市场上借贷，将股息转换为他们偏好的消费流。
一揽子资产
现在假设我们拥有一揽子资产，包括像政府债券这样的无风险资产和像股票这样的风险资产，我们如何在最大化回报的同时最小化风险呢？这就是组合理论的开端，马科维茨在其1952年的开创性作品《投资组合选择》中首次提出了这个概念。这一理论彻底改变了我们看待投资的方式，它将各种资产的组合视为一个统一的整体，而不是孤立地看待。
想象你是一名在投资海洋中航行的船长。你的目标是什么？找到平静海域（像政府债券这样的无风险资产）和风暴海域（像股票这样的风险资产）之间的完美平衡。
现在，让我们谈谈航向更危险水域所得到的额外金币——这就是我们的风险溢价。如果我们的股票船承诺带来25%的回报，而我们的政府债券船提供稳定的11%，那么我们的风险溢价就是额外的14%，这是我们勇敢地驶向更风暴的海域而可能找到的宝藏。
在这次探索中，均值-方差分析是我们的指南针。它不仅告诉我们宝藏在哪里（预期回报或均值），还告诉我们海洋有多颠簸（风险或方差）。马科维茨的智慧告诉我们，通过在宝藏箱中混合不同类型的资产，我们可以降低整体波动性。这一策略在有效前沿曲线上得到了直观的展现，其展示了每一级风险所能获得的最佳可能回报。
从无风险利率开始并与有效前沿曲线相切的线被称为资本市场线（CML）。这个切点极为重要——它是我们的市场组合所在的地方，这是所有风险资产的完美平衡组合。这个点就像宝藏地图上的“X”，标志着风险-回报权衡最佳的地方。
共同基金定理
共同基金定理的核心思想是：每位投资者，无论是谨慎还是大胆，都应该选择市场投资组合。然后，每位投资者决定将他们的财富中有多少投入到这个市场投资组合中，以及有多少保留在像国债这样的无风险资产中。这个比例取决于他们对风险的偏好，但本质上它们只是资本市场线上不同的点。
按照共同基金定理，投资经理可以通过两个关键步骤来帮助客户构建他们的投资组合：首先，根据各种风险资产的回报和特性创建一个市场投资组合，而不需考虑客户的具体偏好；其次，根据客户的风险偏好，在这个市场投资组合和无风险资产之间分配客户的资产。
资本资产定价模型
现在我们知道了如何构建一个市场组合，但我们如何评估组合内每个资产的贡献呢？这就是资本资产定价模型（CAPM）发挥作用的地方。
它引入了系统性风险的概念，也被称为市场风险，这是整个市场或市场细分领域固有的风险。包括经济衰退、政治不稳定或影响整个市场的全球事件等因素。
另一方面，非系统性风险，也称为可分散风险，是特定于个别公司或行业的。这些可能包括公司的管理决策、产品失败或特定行业的衰退等风险。通过多样化投资——持有来自不同行业或行业的各种资产，可以在很大程度上减轻任何一个公司或行业的影响。
在CAPM框架中，资产的预期回报不受资产总风险（包括系统性和非系统性风险）的影响，而只受其系统性风险的影响。这种风险通过称为贝塔（β）的指标量化，该指标衡量资产对系统性市场风险的敏感性。通过投资于一个多样化的投资组合，投资者可以减少对非系统性风险的暴露，但他们无法消除系统性风险。因此，市场只对后者，即不可分散的系统性风险，对投资者进行补偿。
证券市场线（SML）是CAPM的图形表示，是评估投资的预期回报与其系统性风险（贝塔）的视觉工具。在SML图表中，y轴代表投资的预期回报，而x轴代表贝塔，即投资的系统性风险。
夏普比
假设我们有多个投资组合可供投资，我们如何衡量和比较不同投资或投资组合的表现，同时考虑到它们的风险呢？
我们可以认为这些投资组合形成了多个证券市场线（SML），其中斜率最高的线表示投资者每承担一单位风险所获得的回报最高，这个斜率又被称为夏普比率。需要注意的是，夏普比主要用在比较已经多样化的投资组合。
阿尔法
投资者和分析师还想知道，在考虑了投资组合在CAPM中的贝塔所指示的风险之后，基金经理的技能或特定的投资策略是否真正增加了价值。
阿尔法通过量化投资组合的实际回报超过CAPM预测的预期回报，为此提供了一个衡量指标，有效地区分了经理人的表现或策略的有效性。
一个简单的应用是将某人的年度回报与标准普尔500指数的年度回报进行比较，作为衡量绩效的真实指标。
两种定价模型
“如何定价资产”是金融的基本问题。总的来说，有两种基本的定价模型：
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均衡定价或绝对定价：这个模型基于供需框架来确定资产价格。其中，消费资本资产定价模型（Consumption-CAPM）作为一个关键理论浮现出来。它通过将投资者的消费模式整合到投资决策中，扩展了经典的CAPM，凸显CAPM是一个特殊、更有限的情况。
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无套利定价或相对定价：与均衡模型形成对比，这种方法是基于现有市场价格来定价资产。这是支撑金融衍生品市场的理论。
下一个帖子中，我们将会聊到均衡定价的一般模型和无套利定价的模型以及他们的应用，敬请期待。