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wzh4464 committed Jun 17, 2024
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9 changes: 4 additions & 5 deletions .github/workflows/release-pdf.yml
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Expand Up @@ -41,11 +41,10 @@ jobs:

- name: Convert Markdown to PDF with xelatex
run: |
mkdir pdfs
for file in $(find . -name "*.md"); do
# pandoc $file -o pdfs/$(basename $file .md).pdf --pdf-engine=xelatex --template=template/template.tex # address issue with blank in file name
pandoc "$file" -o "pdfs/$(basename "$file" .md).pdf" --pdf-engine=xelatex --template=template/template.tex
done
mkdir -p pdfs
find . -name "*.md" | while IFS= read -r file; do
pandoc "$file" -o "pdfs/$(basename "$file" .md).pdf" --pdf-engine=xelatex --template=template/my_template.latex
done
- name: Create Release
id: create_release
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75 changes: 7 additions & 68 deletions CFA/CFA Rates and Return.md
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---
toc: true
documentclass: "ctexart"
classoption: "UTF8"
---
# CFA Rates and Return

## INTEREST RATES, PRESENT VALUE, AND FUTURE VALUE

1. interpret interest rates as required rates of return, discount rates, or opportunity costs
解释利率为所需的回报率,折现率或机会成本
1. interest rate = real risk-free rate + premium
Expand All @@ -13,11 +16,8 @@
不同的复利频率
1. calculate and interpret the effective annual rate (EAR) and annual interest rate (APR)
计算和解释有效年利率(EAR)和年利率(APR)

## Note

### Interest Rates

- Real Risk-free rate: the time preferences of individuals for current versus future real consumption.
不考虑通货膨胀的情况下的无风险利率, 通常是美国国债利率。代表个人对现在和未来消费的偏好
- Inflation premium: The inflation premium compensates investors for the expected erosion of purchasing power of a bond’s future cash flows due to inflation.
Expand All @@ -34,144 +34,96 @@ governmental short-term debt (T-bills) is often used as a proxy for the nominal
美国T票的流动性溢价为零
- Maturity risk premium: The maturity premium compensates investors for the increased sensitivity of the market value of debt to a change in market interest rates as maturity is extended, in general (holding all else equal). The difference between the interest rate on longer-maturity, liquid Treasury debt and that on short-term Treasury debt reflects a positive maturity premium for the longer-term debt (and possibly different inflation premiums as well).
到期风险溢价:到期风险溢价补偿投资者对债务市场价值对市场利率变化的敏感性,因为到期日延长,一般来说(其他条件不变)。较长期限的流动性美国国债利率与短期美国国债利率之间的差异反映了较长期债务的正到期溢价(以及可能的不同通货膨胀溢价)。

### FUTURE VALUE OF A SINGLE CASH FLOW

- Future value (FV)
- Present value (PV)
- Number of periods (n)
- Stated annual interest rate 是年利率,不是实际利率

lump sum (一次性支付): 仍然是 $FV = PV(1+r)^n$
Pension fund: 养老金

$$
FV = PV(1+r)^n
$$

### NON-ANNUAL COMPOUNDING (FUTURE VALUE)

LO: calculate the solution for time value of money problems with different frequencies of compounding

### Annuity (年金)

- Ordinary annuity (普通年金): payments occur at the end of each period
- Annuity due (年金): payments occur at the beginning of each period
- Perpetuity (永续年金): an annuity with an infinite life

### Mortgage (抵押贷款)

- Down payment (首付)
- We use the equation from annuity to calculate the monthly payment

<!-- TODO: Need Review -->

<div style="border: 1px solid red; padding: 10px;">

e.g. 30-year mortgage, 8% interest rate, \$100,000 loan, monthly payment = \$733.76
$$
\begin{aligned*}
\begin{aligned}
FV &= 100,000 * (1+0.08/12)^{30*12} \\
&= 1.903 * 10^6 \\
A &= FV / \left(\frac{(1+0.08/12)^{30*12}-1}{0.08/12}\right) \\
&= 733.7646
\end{aligned*}
\end{aligned}
$$
</div>

### Compound Continuous

连续复利

$$
FV = PV e^{r n}
$$

## Return

### Holding Period Return (HPR)

$$
R = \frac{P_1 - P_0 + I_1}{P_0}
$$

- $P_0$ is the initial price
- $P_1$ is the final price
- $I_1$ is the income received during the period

### Arithmetic or Mean Return

$$
\bar{R_i} = \frac{1}{n} \sum_{t=1}^n R_{it}
$$

### Geometric Mean Return

$$
\bar{R_i} = \sqrt[n]{\prod_{t=1}^n (1 + R_{it})} - 1
$$

A geometric mean return provides a more accurate representation of the growth in portfolio value over a given time period than the arithmetic mean return.

### The Harmomic Mean

Used in cost averaging (The periodic investment of a fixed amount of money.)

### Trimmed Mean

A trimmed mean is the mean calculated after removing a certain percentage of the highest and lowest values.

### Winsorized Mean

A winsorized mean is the mean calculated after replacing a certain percentage of the highest and lowest values with the highest and lowest values.

## Money-Weighted and Time-Weighted Rate of Return

### Money-Weighted Rate of Return

$$
\sum_{t=1}^n \frac{CF_t}{(1 + r)^t} = 0
$$

> Steps:
>
> 1. Suppose the return $r$ (see it as interest rate) is unknown.
> 2. Calculate the present value of all cash flows using the unknown return $r$.
> 3. Solve for $r$.
#### Time-Weighted Rate of Return

$$
\prod_{t=1}^n (1 + r_t) = \frac{P_n}{P_0}
$$

> Steps:
>
> 1. Everytime there is a cash flow, normalize the portfolio value to the previous period.
> 2. Calculate the geometric mean return. (Compound return)
#### Money-Weighted vs. Time-Weighted

<span style="color:red;">Money-weighted rate reveals the ability of the investor. Time-weighted rate reveals the market performance.</span>

## CFA OTHER MAJOR RETURN MEASURES AND THEIR APPLICATIONS

<!-- tag cfa -->

### Learning Outcome

计算并解释其他主要回报率的含义和应用。

- Fee (gross / net return)
- taxes (pre-tax / after-tax return)
- inflation (nominal / real return)
- leverage (杠杆)
- management fee (管理费)

### Gross and Net Return

#### Gross Return

- 不扣除:
- management fees (管理费)
- custodian fees (托管费)
Expand All @@ -182,42 +134,29 @@ $$
- trading expenses (交易费用)
- Commissions (佣金)
- 交易费用直接贡献于管理者所赚取的收益

因此, **毛收益是评估和比较资产管理者投资技能的适当指标,因为它不包括任何与投资的管理和行政相关的费用.**

#### Net Return

- Deduct everything

### Pre-tax and After-tax Return

- 除非明确说明, 否则回报率都是税前的
- selecting appropriate securities (选择合适的证券)
- reducing trading turnover (降低交易频率)
-

### Real and Nominal Return

$$
(1 + r_{\text{nominal risk-free}}) = (1 + r_{\text{real risk-free}}) \times (1 + \text{inflation premium})
$$

$$
(1 + \text{return}_{\text{real}}) = \frac{1 + r_{\text{nominal risk-free}}(1 + \text{risk premium})}{1 + \text{inflation premium}}
$$

From example:

$$
\frac{1 + \text{after taxed net return}}{1 + \text{inflation}} - 1 = \text{after taxed real return}
$$

### Leverage return

$$
R_L = \frac{\text{Portfolio Return}}{\text{Investor's Equity}} = \frac{R_P(V_E + V_B)-V_B r_D}{V_E} = R_P + \frac{V_B}{V_E}(R_P - r_D)
$$

- $R_L$: leverage return
- $R_P$: portfolio return 投资组合回报率
- $V_E$: investor's equity 投资者的股权
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12 changes: 5 additions & 7 deletions CFA/CFA Time Value of Money in Fixed Income and Equity.md
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---
toc: true
documentclass: "ctexart"
classoption: "UTF8"
---
# CFA The Time Value of Money in Finance

## Outcome

- Bond Pricing 债券定价
- Value of a Stock 股票定价
- Stock Valuation Models 股票估值模型
Expand All @@ -14,15 +17,10 @@
- Cash Flow Additivity 现金流可加性
- Application of Cash Flow Additivity 现金流可加性的应用
- Real-World Applications of Cash Flow Additivity 现金流可加性的现实应用 (no-arbitrage) 无套利

## TIME VALUE OF MONEY IN FIXED INCOME AND EQUITY 固定收益和股权的时间价值

### Fixed-Income Instruments and the Time Value of Money 固定收益工具和时间价值

Cash flows from fixed-income instruments:

- Discount(折现): 一次性支付, zero-coupon bond (零息债券), coupon bond (票息债券)
- Perioidic payments(定期支付): 一段时间内的多次支付
- Level payments(定额支付): 每期支付相同金额

固定收益工具是一种债务工具,例如债券或贷款,它们代表着发行人向投资者借款并承诺未来偿还的合同。固定收益工具的贴现率是一种利率,而债券或贷款的回报率通常被称为其到期收益率(YTM)。
6 changes: 5 additions & 1 deletion CFA/CFA_vocabulary.md
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---
toc: true
documentclass: "ctexart"
classoption: "UTF8"
---
# Vocabulary

- forgone: [adj.] given up, renounced, 放弃的
- protfolio: [n.] a range of investments held by a person or organization, 投资组合
- dividend: [n.] a sum of money paid regularly (typically quarterly) by a company to its shareholders out of its profits (or reserves), 股息
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25 changes: 5 additions & 20 deletions CFA/CFA错题本.md
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---
toc: true
documentclass: "ctexart"
classoption: "UTF8"
---
# CFA 错题本

## 1: Rates and Returns

The minimum rate of return an investor must receive in order to accept an investment is best described as the

A. internal rate of return.

B. required rate of return.

C. expected return.

<details><summary>答案</summary>
Solution B
A. Incorrect. The required rate of return is the minimum rate of return an investor must receive in order to accept an investment. The internal rate of return is the discount rate that makes net present value equal to zero.
Expand All @@ -18,38 +17,24 @@ C. Incorrect. The required rate of return is the minimum rate of return an inves
> Rates and Returns
interpret interest rates as required rates of return, discount rates, or opportunity costs and explain an interest rate as the sum of a real risk-free rate and premiums that compensate investors for bearing distinct types of risk
</details>

## 2: Annuities

An investor purchases one share of stock for \$85. Exactly one year later, the company pays a dividend of \$2.00 per share. This is followed by two more annual dividends of \$2.25 and \$2.75 in successive years. Upon receiving the third dividend, the investor sells the share for \$100. The money-weighted rate of return on this investment is closest to

A. 7.97%.

B. 8.15%.

C. 8.63%.

<details><summary>答案</summary>
Solution B
</details>

## 3

Grupo Ignacia issued 10-year corporate bonds two years ago. The bonds pay an annualized coupon of 10.7 percent on a semiannual basis, and the current annualized YTM is 11.6 percent. The current price of Grupo Ignacia’s bonds (per MXN100 of par value) is closest to:

A. MXN 95.47.
B. MXN 97.18.
C. MXN 95.39.

<details><summary>答案</summary>
Solution C
coupon = 5.35

discount rate = 5.8

number of periods = 16

FV_2 = 1/(1 + r) + 1/(1 + r)^2 + ... + 1/(1 + r)^16 + 100/(1 + r)^16

用付息时间来线性导出年化收益率
</details>
11 changes: 5 additions & 6 deletions CFA/Corporate Issuers/Breakeven_Point.md
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@@ -1,20 +1,19 @@
---
toc: true
documentclass: "ctexart"
classoption: "UTF8"
---
# Breakeven point

## $Q_{\text{BE}}$ (Breakeven point)

NI 等于 0 时的销量。

$$
Q_{\text{BE}} = \frac{F + C}{P - V}
$$

- $F$ = 固定运营成本
- $C$ = 固定财务成本
- $P$ = 单位价格
- $V$ = 单位变动成本

Operating breakeven point

$$
Q_{\text{OBE}} = \frac{F}{P - V}
$$
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